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COAL^  METAL  MINERS' 
POCKETBOOK 


OF 

PRINCIPLES,  RUL'ES,  FORMULAS, 
AND  TABLES. 


SPECIALLY  COMPILED  AND  PREPARED  FOR  THE  CONVENIENT  USE  OF 
MINE  OFFICIALS,  MINING  ENGINEERS,  AND  STUDENTS  PREPAR- 
ING THEMSELVES  FOR  CERTIFICATES  OF  COMPETENCY 
AS  MINE  INSPECTORS  OR  MINE  FOREMEN. 


EIGHTH  EDITION:  REVISED  AND  ENLARGED, 

WITH 

ORIGINAL  MATTER. 


•‘Though  index  learning  turns  no  student  pale, 
It  grasps  the  Eel  of  Science  by  the  tail.” 

Pope. 


SCRANTON.  PA.: 

INTERNATIONAL  TEXTBOOK  COMPANY, 


Copyright,  1890,  1893,  1900, 

BY 

The  Colliery  Engineer  CoMPi 
Copyright,  1902, 

BY 

International  Textbook  Comp 
Entered  at  Stationers’  Hall,  L( 


All  Rights  Reserved. 


PRINTED  BY 

International  Textbook  Company, 
Scranton,  Pa.,  U.  S.  A. 


6ZZ.06 

C&'icd 


Preface  to  Seventh  Edition. 

The  speedy  exhaustion  of  the  sixth  edition  of  The  Coal  and 
Metal  Miners^  Pocketbook,  coupled  with  a steady  and  increas- 
ing demand  for  it,  has  made  necessary  this  seventh  edition. 
In  it  a few  typographical  errors  which  unavoidably  occurred 
(as  is  the  case  in  every  book  of  this  nature  and  size),  have 
been  corrected,  all  departments  have  been  carefully  revised, 
improved,  and  brought  up  to  date,  and  considerable  new 
matter  has  been  added.  Thus,  the  value  of  the  work  has  been 
materially  increased.  The  value  of  suggestions  as  to  improve- 
ments in  this  edition  made  by  users  of  the  sixth  edition  is 
acknowledged  with  thanks,  and  we  request  that  users  of  this 
new,  or  seventh,  edition,  will  kindly  call  our  attention  to  any 
errors  or  omissions  they  may  discover,  so  that  future  editions 
may  be  kept  fully  abreast  with  the  requirements  of  mining 
practice  as  such  practice  continues  to  advance. 


iii 


Preface  to  Sixth  Edition. 


The  fifth  edition  of  The  Coal  and  Metal  Miners’  Pocketbook 
was  very  kindly  received,  and  the  criticisms  of  it  were  most 
friendly  and  flattering. 

The  sixth  edition  has  been  compiled  under  particularly 
favorable  circumstances  and  is  much  more  complete  than  any 
previous  edition. 

Prominent  engineers  and  manufacturers  of  mining  machinery 
throughout  the  world  have  kindly  criticized  the  previous 
edition,  have  suggested  wherein  it  could  be  improved,  and 
have  sent  to  us  information  from  their  private  note  books 
that  has  never  before  been  published. 

The  staff  of  Mines  and  Minerals,  the  large  force  of  Mining, 
Mechanical,  and  Electrical  Engineers  connected  with  The 
International  Correspondence  Schools,  and  many  other  engi- 
neers and  mine  managers  have  contributed  to  it. 

All  this  material  has  been  carefully  sifted,  verified  wherever 
possible,  and  combined  with  the  data  in  the  former  edition. 
By  careful  selection  and  rewriting,  or  by  different  methods  of 
presentation,  it  has  been  possible  to  include  essentially  all  that 
was  in  the  fifth  edition,  and  at  the  same  time  to  add  from  one- 
third  to  one-half  again  as  much  entirely  new  matter,  without 
materially  increasing  the  size  of  the  book. 

Every  portion  of  the  fifth  edition  has  been  either  entirely 
rewritten,  or  revised,  enlarged,  and  brought  up  to  date.  New 
illustrations  have  been  drawn,  and  the  entire  book  has  been 
printed  from  new  plates. 

The  sections  on  Mathematics  and  Surveying  have  been 
amplified  by  the  addition  of  new  tables  and  by  text  treating 
of  the  Solar  Transit  and  Rocky  Mountain  methods  of  sur- 
veying. 

The  sections  on  Hydraulics;  the  Application  of  Electricity  to 
Mining;  Timbering,  Haulage,  Blasting,  Ore  Dressing,  and  Coal 
Washing  are  entirely  new. 

v 


VI 


PREFACE. 


The  sections  on  Prospecting,  Ventilation,  and  Methods  of 
Working  have  been  entirely  rewritten,  enlarged,  and  greatly 
improved. 

The  tables  of  Logarithms,  Trigonometric  Functions,  etc.  have 
been  reset  from  the  latest  corrected  editions  of  standard  tables. 
The  Traverse  Table  has  been  greatly  reduced  in  length,  but 
without  affecting  its  efficiency,  while  the  table  of  Squares, 
Cubes,  etc.  has  been  added  to  by  the  addition  of  Circumfer- 
ences and  Areas  of  Circles. 

The  Glossary,  which  contains  about  2,500  words,  is  believed 
to  be  the  most  complete  mining  glossary  ever  published,  as  it 
is  a combination  of  all  the  mining  glossaries  extant  of  which 
the  compilers  could  hear. 

Wherever  possible,  credit  has  been  given  the  authorities 
from  whom  data  have  been  taken,  but  in  such  a work  it  is  mani- 
festly impossible  to  give  full  credit  for  everything  that  has 
been  extracted,  quoted,  and  compiled,  and  we  can  only  in  this 
very  general  way  acknowledge  our  indebtedness  to  the  large 
number  of  authors  and  engineers  whom  we  have  failed  to 
mention  by  name  in  the  text. 

No  one  appreciates  as  fully  as  does  the  editor  of  such  a pub- 
lication the  value  of  the  suggestions  and  data  that  have  been 
so  generously  furnished  to  assist  us  in  the  compilation.  We 
shall  be  greatly  obliged  to  all  readers  of  this  volume  who  may 
call  our  attention  to  any  errors  that  they  may  discover,  or  to 
the  omission  of  any  data  that  they  may  feel  the  lack  of,  so 
that  attention  may  be  given  to  these  matters  in  future  editions. 


TABLE  OF  CONTENTS, 


{For  detailed  Index,  see  hack  of  volume.  See  also  Glossary  of  Mining  Terms, 
page  565.)  


WEIGHTS  AND  MEASURES. 

The  Metric  System.— 1. 

We  IGHTS.— Troy,  1;  Apothecaries’,  1;  Avoirdupois,  2;  Metric,  2. 

M EASU  RES  OF  Le NOTH.— American  and  British,  2;  Reduction  of  Inches 
to  Decimals  of  a Foot,  2;  Decimals  of  a Foot  for  Each  ^ of  an  Inch,  3; 
Metric,  3;  Russian,  3;  Prussian,  Danish,  and  Norwegian,  3;  Austrian,  3; 
Swedish,  4;  Chinese,  4. 

Measures  of  Area.— American  and  British,  4;  Table  for  Reducing 
Square  Feet  to  Acres,  4;  Metric,  4. 

Measures  of  Volume. — American  and  British,  5;  Metric,  5;  Liquid 
(U.  S.),  5;  Dry  (U.  S.),  5;  British  Imperial  (Liquid  and  Dry),  5; 
Contents  of  Cylinders  or  Pipes  for  1 Foot  in  Length,  6;  Mexican, 
Central  American,  and  South  American  Weights  and  Measures,  7. 

Conversion  Tables.— Customary  to  Metric,  7;  Metric  to  Customary,  9. 

Money.— United  States,  10;  British,  10;  Standard  U.  S.  Coins,  Weights  and 
Fineness,  Space  Required  to  Store,  10;  Conversion  of  English  and 
American  Money  Values,  11;  Value  of  Foreign  Coins,  U.  S.  Treasury 
Department,  11;  Carat  Measures,  12. 

Timber  and  Board  Measure.— Rule  for  Measuring,  12;  Timber 
Measure,  12;  Round  Timber,  Table  of  \ Girths,  13;  Board  Measure,  13. 

Mathematios.— Ceneral  Principles,  14;  Signs  and  Abbreviations,  14. 

Arithmetic.— To  Cast  the  Nines  Out  of  a Number,  15;  To  Prove  Addition, 
Subtraction,  Multiplication,  and  Division,  15;  Common  Fractions,  15; 
Decimals,  16;  Simple  and  Compound  Proportion,  18;  Involution,  19; 
Evolution,  19;  Percentage,  20;  Arithmetical  Progression,  20;  Geomet- 
rical Progression,  21;  Logarithms,  22. 

Geometry.— Principles,  24;  Practical  Problems  in  Geometrical  Construc- 
tion, 25. 

M ENSU ration.  Surfaces,  28;  Solids,  33;  Prismoidal  Formula,  34. 

Plane  Trigonometry.— Principles  of  Trigonometry,  34;  Practical 
Examples  in  the  Solution  of  Triangles,  35. 

Surveying.— The  Compass,  38;  Adjustments,  38;  Use  of  Compass,  39; 
Magnetic  Variation,  39;  Isogonic  Chart,  39;  The  Vernier,  39;  The 
Transit,  40;  Adjustments,  41;  The  Chain,  or  Steel  Tape  and  Pins,  42; 
Plumb-Bob,  44;  The  Clinometer  or  Slope  Level,  44;  Field  Notes  for  an 
Outside  Compass  Survey,  44;  Transit  Surveying,  45;  Determination  of 
Meridian  by  Polaris,  46;  Determination  of  Meridian  With  Solar  Attach- 
ment, 47;  Use  of  Solar  Attachment,  47;  General  Remarks,  49;  Plotting, 
49;  Coordinates,  51;  Contents  of  Coal  Seam,  52;  Leveling,  53;  Adjust- 
ments, 53;  Use  of  Level,  54;  Field  Work  54;  Notes,  55;  Trigonometric 
Leveling,  56;  Underground  Surveying,  56;  Establishment  and  Marking 
of  Stations,  57;  Centers,  59;  Notes,  60;  Stope  Books,  62;  Mine  Corps,  66; 
Surveying  Methods,  67;  Outside  Surveys,  67;  Inside  Surveys,  67;  Closing 
Surveys,  68;  Connecting  Outside  and  Inside  Works  Through  Shafts 
and  Slopes,  68;  Notes  on  Mapping,  74;  Locating  Errors,  76;  Locating 
Special  Work,  77;  Calculation  of  Areas,  77;  Railroad  Curves,  78;  Hints 
to  Beginners,  80;  Theory  of  Stadia  Measurements,  81;  Tables,  88. 

vii 


Vlll 


TABLE  OF  CONTENTS. 


Elements  of  Mechanics.— Levers,  91;  Wheel  and  Axle,  92;  Inclined 
Plane,  93;  Screw,  93;  Wedge,  93;  Pulleys,  94;  Composition  of  Forces,  95. 


Fr  I CTi ON. —Coefficients,  95;  Shafting,  96;  Friction  of  Mine  Cars,  96. 
Lubrication.— Best  Lubricants  for  Different  Purposes,  102. 


APPLIED  MECHANICS. 

Strength  and  Weight  of  Materials. — Wooden  Beams,  102;  Iron 
and  Steel  Beams,  103;  Structural-Steel  I Beams,  104;  Pillars  or  Props 
105;  Cast-Iron  Columns,  106;  Specific  Gravity,  Weight,  and  Properties 
of  Materials,  107;  Line  Shafting,  110;  Weight  of  Castings,  Sheets,  and 
Plates,  111;  Weight  of  Cast-Iron  Pipe  per  Foot  in  Pounds,  113;  Wood 
Screws,  113;  Weight  of  Wrought  Iron,  114;  Iron'Required  for  1 Mile  of 
Track,  117;  Rails,  Splices,  and  Bolts  for  1 Mile  of  Track,  117;  Wire  and 
Sheet-Metal  Gauges,  122d. 


Wire  Ropes.— General  Remarks,  118;  Flat  Ropes,  119;  Standard  Hoisting 
Ropes,  120;  Transmission  or  Haulage  Rope,  122;  Stress  in  Hoisting 
Ropes,  123;  Relative  Effects  of  Various  Sheaves  on  Wire  Rope,  123; 
Working  Load  for  Hoisting  Ropes,  125;  Starting  Strain,  126;  Horse- 
power of  Manila  Ropes,  126;  Rapid  Method  of  Splicing  a Wire  Rope, 
127;  Ordinary  Long  Splice,  129;  Chains,  129. 

Hydrostatics.— General  Principles,  130;  Equilibrium  of  Liquids,  130; 
Pressures  of  Liquids  on  Surfaces,  130;  Pressure  Exerted  by  Quiet  Water 
Against  the  Side  of  a Gangway  or  Heading,  130;  Total  Pressure  of  Quiet 
Water  Against  and  Perpendicular  to  Any  Surface  Whatever,  131;  Trans- 
mission of  Pressure  Through  Water,  132;  Pressure  at  Any  Given  Depth, 
132;  Pressure  of  Water  in  Pipes,  132;  Construction  of  Mine  Dams,  133. 

Hydraulics.— General  Principles,  135;  Theoretical  Velocity  of  a Jet  of 
Water,  135;  Theoretical  Quantity  of  Water  Discharged  in  a Given 
Time,  135;  Flow  of  Water  Through  Orifices,  135;  Coefficients  of  Con- 
traction, Velocity,  Discharge,  135;  Suppression  of  the  Contraction,  136; 
Gauging  Water,  136;  Miners’  Inch,  136;  Duty  of  a Miners’  Inch  of 
Water,  137;  Right-Angled  V Notch,  137;  Discharge  of  Water  Through 
a Right-Angled  V Notch,  138;  Gauging  by  Weirs,  138;  Coefficient  of 
Discharge  for  Weirs  With  and  Without  End  Contractions,  140;  Weir 
Table  Giving  Cubic  Feet  Discharged  per  Minute,  141;  Conversion 
Factors,  141;  Flow  of  Water  in  Open  Channels,  142;  Ditches,  142;  Safe 
Bottom  Velocity,  142;  Resistance  of  Soils  to  Erosion  by  Water,  143; 
Carrying  Capacity  of  Ditches,  143;  Grade,  143;  Ditch  Banks,  143; 
Infiuence  of  Depths  on  Ditch,  144;  Measuring  the  Flow  of  Water 
in  Channels,  144;  Flow  in  Brooks  and  Rivers,  145;  Flumes,  145;  Grade 
and  Form,  145;  Timber  Flumes,  145;  Connection  With  Ditches,  146; 
Trestles,  146;  Curves,  146;  Waste  Gates,  146;  Flow  of  Water  Through 
Flumes,  146;  Tunnels,  147;  Flow  Through  Tunnels,  147;  Hydraulic 
Gradient,  147;  Flow  in  Pipes,  147;  Siphons,  149;  Table  Showing  Actual 
Flow  in  Pipes  From  f"  to  30"  Diameter.  150;  Loss  of  Head  in  Pipe  by 
Friction,  151;  Friction  of  Knees  and  Bends,  153;  Reservoir  Site,  15-4; 
Dams,  154;  Foundations,  154;  Wooden  Dams,  154;  Abutments  and  Dis- 
charge Gates,  154;  Spillways  or  Wasteways,  155;  Stone  Dams,  155;  Earth 
Dams,  156;  Wing  Dams,  156;  Masonry  Dams,  156;  Theoretical  Efficiency 
of  a Water-Power,  156;  Horsepower  of  a Running  Stream,  157;  Current 
Motors,  157;  Breast  and  Undershot  Wheels,  157;  Overshot  Wheels,  158; 
Impulse  Wheels,  158;  Turbines,  158. 

Pump  Machinery.— Cornish  Pumps,  158;  Simple  and  Duplex  Pumps, 
158;  Packing,  159;  Speed  of  Water  Through  Valves,  Pipes,  and 
Pump  Passages,  160;  Ratio  of  Steam  and  Water  Cylinders  in  the 
Direct- Acting  Pump,  160;  Piston  Speed  of  Pumps,  161;  Boiler  Feed- 
Pumps,  161;  Theoretical  Capacity  of  Pumps  and  the  Horsepower 
Required  to  Raise  Water,  161;  Depth  of  Suction,  162;  Amount  of 
Water  Raised  by  a Single-Acting  Lift  Pump,  162;  Pump  Valves,  162; 
Power  Pumps,  162;  Electrically  Driven  Pumps,  162;  Table  Giving  Water 
Delivered  per  Minute  for  Various  Sized  Pumps,  163;  Miscellaneous 
Forms  of  Water  Elevators,  164;  Air-Lift  Pumps,  164:  Vacuum  Pumps, 
164;  Water  Buckets,  164;  Sinking  Pumps,  165;  Pumps  for  Acid  Water,  165. 


TABLE  OF  CONTENTS. 


IX 


FORMS  OF  POWER. 

Fuels. — Table  of  Combustibles,  166;  Analyses  and  Heating  Values  of 
American  Coals,  168;  Thermal  Unit,  168;  Composition  of  Fuels,  169; 
Classification,  Composition,  and  Properties  of  Coals,  169;  Weights  and 
Measurements  of  Coal,  170;  Coke,  172;  Analysis  of  Coal,  173. 

Steam.— High-Pressure  Steam,  175;  Expansion  of  Steam,  176:  Condens- 
ers, 176. 

Boilers.— Lancashire  Boiler,  177;  Horsepower  of  Boilers,  177;  Heating 
Surface,  177;  Choice  of  a Boiler,  179;  Explosions,  179;  Questions  to  Be 
Asked  Concerning  New  Boilers,  180;  Incrustation  and  Scale,  182; 
Covering  for  Boilers,  Steam  Pipes,  Etc.,  183;  Data  for  Proportioning  an 
Economizer,  185;  Care  of  Boilers,  185;  Thickness  of  Boiler  Iron,  187; 
Pressure  of  Steam  at  Different  Temperatures,  188;  Maximum  Economy 
of  Plain  Cylinder  Boilers,  188;  Scheme  for  Boiler  Test,  188;  Chim- 
neys, 189. 

Steam  Engines.— What  Is  a Good  Engine?  190;  Determination  of 
M.  E.  P.,  190;  Rules  for  Engine  Drivers,  191;  Belting  and  Velocity  of 
Pulleys,  193. 

Compressed  Air.— Classification  of  Compressors,  194;  Construction  of 
Compressors,  194;  Theory  of  Air  Compression,  194;  Rating  of  Com- 
pressors, 195;  Cooling,  195;  Dry  Versus  Wet  Compressors,  196;  Trans- 
mission of  Air  in  Pipes,  196;  Losses  in  the  Transmission  of  Compressed 
Air,  198;  Friction  of  Air  in  Pipes,  201;  Loss  of  Pressure  in  Pounds  per 
Square  Inch,  by  Flow  of  Air  in  Pipes,  202;  Loss  by  Friction  in  Elbows, 
203. 

Electricity.— Practical  Units,  203;  Strength  of  Current,  203;  Electric 
Pressure  or  Electromotive  Force,  203;  Resistance,  203;  Power,  204;  Cir- 
cuits, 205;  Series  Circuits,  205;  Parallel  Circuits,  206;  Resistance  in 
Series  and  Multiple,  206;  Shunt,  207;  Electric  Wiring,  207;  Materials, 
207;  Forms  of  Conductors,  207;  Wire  Gauge,  207;  Estimation  of  Cross- 
Section  of  Wires,  207;  Properties  of  Copper  Wire,  208;  Properties  of 
Aluminum  and  Copper,  209;  Estimation  of  Resistance,  209;  Calculation 
of  Wires  for  Electric  Transmission,  210;  Current  Estimates,  212;  Incan- 
descent Lamps,  213;  Arc  Lamps,  214;  Motors,  214;  Conductors  for  Electric- 
Haulage  Plants,  214;  Dynamos  and  Motors,  215;  Direct-Current  Dynamos, 
215;  Factors  Determining  E.  M.  F.  Generated,  218;  Field  Excitation  of 
Dynamos,  218;  Series-Wound  Dynamos,  219,  Shunt-Wound  Dynamos, 
219;  Compound-Wound  Dynamos,  219;  Direct-Current  Motors,  220; 
Principles  of  Operation,  220;  Speed  Regulation  of  Motors,  222;  Connec- 
tions for  Continuous-Current  Motors,  223;  Alternating-Current  Dyna- 
mos, 224;  Single-Phase  Alternators,  225;  Multiphase  Alternators,  225; 
Uses  of  Multiphase  Alternators,  226;  Alternating-Current  Motors,  226; 
Synchronous  Motors,  226;  Induction  Motors,  227,  Transformers,  228; 
Electric  Signaling,  229;  Batteries,  229;  Bell  Wiring,  230;  Special  Mine 
Applications,  233;  Telephones,  233. 


MINING. 

Prospecting.- Outfit  Necessary,  235;  Plan  of  Operations,  236;  Geological 
Table,  237;  Coal  or  Bedded  Materials,  238;  Formations  Likely  to  Con- 
tain Coal,  238;  Ore  Deposits,  238;  Position  of  Veins  and  Ore  Deposits,  239; 
Underground  Prospecting,  239;  Prospecting  for  Placer  Deposits,  240; 
Value  of  Free  Gold  per  Ton  of  Quartz,  241;  Gems  and  Precious  Stones, 
241;  Exploration  by  Drilling  or  Bore  Holes,  242;  Earth  Augers,  242; 
Percussion  or  Churn  Drills,  242;  The  Diamond  Drill,  243;  Selecting  the 
Machine,  243;  Size  of  Tools,  243;  Drift  of  Diamond-Drill  Holes,  243; 
The  Surveying  of  Diamond-Drill  Holes,  243;  The  Value  of  the  Record 
Furnished  by  the  Diamond  Drill,  244;  The  Arrangement  of  Holes,  244; 
The  Cost  and  Speed  of  Drilling,  244;  Records  of  Cost  per  Foot  in 
Diamond  Drilling,  246;  Cost  of  Operation  per  Month  of  Bed-Rock 
Exploration,  247;  Magnetic  Prospecting,  248;  Prospecting  for  Petro- 
leum, Natural  Gas,  and  Bitumen,  249;  Construction  of  Geological  Maps 
and  Cross-Sections,  249;  To  Obtain  Dip  and  Strike  From  Bore-Hole 
Records,  250;  Sampling  and  Estimating  the  Amount  of  Mineral  Avail- 
able, 251;  Diagram  for  Reporting  on  Mineral  Lands,  252. 


X 


TABLE  OF  CONTENTS. 


Opening  a Min  e.— Opening  a Gold  Mine,  258;  Form  of  Shafts,  259;  Com- 
partments, 259;  Shaft  Sinking,  259;  Size  of  Shaft,  259;  Forepoling,  260; 
Metal  Linings  Forced  Down,  260;  Pneumatic  Method  of  Shaft  Sinking, 
260;  Freezing  Process,  260;  Table  of  Well-Known  Shafts,  261;  Kind- 
Chaudron  Method,  262;  Long-Hole  Process,  262;  Comparison  of  Methods 
of  Shaft  Sinking,  262;  Sinking  Head-Frames,  262;  Sinking  Engines,  263; 
Tools,  263;  Speed  and  Cost  of  Sinking,  263;  Slope  Sinking,  263;  The 
Sump,  264;  Driving  the  Gangway,  264;  Levels  in  Metal  Mines,  264; 
Mining  Tunnels,  265. 

Mine  Timber  and  Timbering.— Choice  of  Timber,  265;  Preserva- 
tion of  Timber,  265;  Placing  of  Timber,  266;  Size  of  Timber,  267;  Joints 
in  Mine  Timbering,  267;  Undersetting  of  Props,  267;  Forms  of  Mine 
Timbering  and  Underground  Supports,  267;  Gangway  or  Level  Tim- 
bers, 268;  Shaft  Timbering,  270;  Square  Sets,  270;  Landing,  Plats,  or 
Stations,  272;  Special  Forms  of  Supports,  272;  Iron  and  Steel  Supports, 
272;  Trestles,  274;  Timber  Head-Frames  or  Head-Gears,  275;  Steel  Shaft 
Bottoms,  276. 

Methods  of  Working. — Open  Work,  277;  Steam-Shovel  Mines,  278; 
Milling,  278;  Cableways,  278;  Placers,  278;  Hydraulicking,  278;  Dredg- 
ing, 279;  Closed  Work,  279;  Bedded  Deposits,  279;  Coal  Mining,  279; 
Roof  Pressure,  280;  Character  of  Floor,  280;  Systems  of  Working  Coal, 
280;  Room-and-Pillar  System,  280;  Longwall  Method,  281;  Panel  System, 
283;  Control  of  Roof  Pressure,  284;  Number  of  Entries,  284;  Direction 
of  Face,  284;  Size  of  Pillars,  285;  Room  Pillars,  286;  Barrier  Pillars,  287; 
Weight  on  Pillars  in  Pounds  per  Square  Inch,  287;  Drawing  Pillars,  289; 
Compressive  Strength  of  Anthracite,  290;  Gob  Fires,  291;  Spontaneous 
Combustion,  291;  Coal  Storage,  291;  Modifications  of  Room-and-Pillar 
Methods,  291;  Buggy  Breasts,  291;  Chute  Breasts,  292;  Pillar-and-Stall, 
292;  Connellsville  Region,  293;  Pittsburg  Region,  295;  Clearfield  Region, 
295;  Reynoldsville  Region,  295;  West  Virginia,  296;  Alabama  Methods, 
297;  George’s  Creek,  297;  Blossburg  Region,  Pa.,  298;  Indiana  Mining,  298; 
Iowa  Mining,  299;  Tesla,  California,  Method,  300;  New  Castle,  Colorado, 
Method,  302;  Modifications  of  Longwall  Methods,  302;  Overhand 
Stoping,  304;  Methods  of  Mining  Anthracite,  305;  Brown’s  Method, 
306;  Battery  Working,  307;  Single-Chute  Battery,  309;  Double-Chute 
Battery,  309;  Rock-Chute  Mining,  310;  Williams’  Method,  312;  Running 
of  Coal,  312;  Hints  for  Working  Thin  Seams,  313;  Flushing  of  Culm,  314; 
Methods  of  Mining  Mineral  Deposits,  316;  Winzes,  316;  Raises,  316; 
Stoping,  316;  I'lat  Deposits,  318;  Large  Deposits,  Over  8 Feet  Thick,  318; 
Square  Work,  318;  Filling,  319;  Slicing,  319;  Transverse  Rooming  With 
Filling,  319;  Caving,  320;  Square-Set  System,  321;  Irregular  Deposits, 
321;  Coyoting,  321;  Special  Methods,  322;  Frozen  Ground,  322;  Leaching, 
322;  Costs  of  Mining  Anthracite,  323;  Lehigh  Region  (Pa.),  323; 
Wyoming  Region  (Pa.),  325;  Prices  of  Coal,  326;  Cost  of  Coking  Coal,  328. 

Explosives.— Low  Explosives,  329;  High  Explosives,  329;  Thawing 
Dynamite,  329;  Common  Blasting  Explosives,  330;  Drilling,  330;  Diam- 
eter of  Hole,  330;  Amount  of  Charge,  331;  Tamping,  331;  Firing,  331; 
Detonators;  332;  Electric  Firing,  332;  Power  of  an  Explosive,  334; 
Arrangement  of  Drill  Holes,  335. 

Machine  Mining.— Pick  Machines,  336;  Chain-Cutter  Machines,  337; 
Shearing,  337;  Capacity,  337. 

Ventilation  of  Mines. — Atmosphere,  337;  Atmospheric  Pressure,  339; 
Barometric  Variations,  339;  Barometers,  339;  Water  Column  Corre- 
sponding to  Any  Mercury  Column,  340;  Barometric  Elevations,  340; 
Chemistry  of  Gases,  341;  Absolute  Temperature,  344;  Absolute  Pressure, 
345;  Diffusion  and  Transpiration,  346;  Gases  Found  in  Mines,  348;  Con- 
stants for  Mine  Gases,  349;  Gas  Feeders,  352;  Pressure  of  Occluded 
Gases,  352;  Amount  of  Gas,  352;  Outbursts  of  Gas,  352;  Testing  for  Gas 
by  Lamp  Flame,  354;  Safety  I^amps,  355;  Lamps  for  Testing,  355;  Detec- 
tion of  Small  Percentages  of  Gas,  356;  Oils  for  Safety  Lamps,  356;  Types 
of  Safety  Lamps,  356;  Locking  Lamps,  358;  Cleaning  Safety  Lamps,  358; 
Relighting  Stations,  359;  Illuminating  Power  of  Safety  Lamps,  359; 
Explosive  Conditions  in  Mines,  359;  Derangement  of  Ventilating  Cur- 
rent, 359;  Sudden  Increase  of  Gas,  360;  Effect^  of  Coal  Dust  in  Mine 


TABLE  OF  CONTENTS. 


xl 


Workings,  360;  Pressure  as  Affecting  Explosive  Conditions,  361;  Rapid 
Succession  of  Shots  in  Close  Workings,  361;  Mine  Explosions,  361; 
Recoil  of  an  Explosion,  361;  Exploring  Workings  After  a Serious  Explo- 
sion,361;  Quantity  of  Air  Required  for  Ventilation,  362;  Elements  in  Ven- 
tilation, 363;  Power  of  the  Current,  363;  Mine  Resistance,  364;  Velocity 
of  the  Air-Current,  364;  Measurement  of  Ventilating  Currents,  364; 
Water  Gauge,  365;  Thermometers,  366;  Calculation  of  Mine  Resistance, 
366;  Calculation  of  Power  or  Units  of  Work  per  Minute,  367;  Equivalent 
Orifice,  367;  Potential  Factor  of  a Mine,  367;  Formulas,  370;  Variation 
of  the  Elements,  372;  Practical  Splitting  of  the  Air-Current,  373; 
Primary  Splits,  374;  Secondary  Splits,  374;  Tertiary  Splits,  374;  Equal 
Splits  of  Air,  374;  Unequal  Splits  of  Air,  374;  Natural  Division  of  the 
Air-Current,  374;  Calculation  of  Natural  Splitting,  374;  Proportional 
Division  of  the  Air-Current,  375;  Box  Regulator,  375;  Door  Regulator, 
375;  Splitting  Formulas,  378;  Methods  and  Appliances  in  the  Ventila- 
tion of  Mines,  381;  Ascensional  Ventilation,  381;  General  Arrangement 
of  Mine  Plan,  381;  Natural  Ventilation,  381;  Ventilation  of  Rise  and 
Dip  Workings,  382;  Influence  of  Seasons,  382;  Construction  of  a Mine 
Furnace,  383;  Air  Columns  in  Furnace  Ventilation,  384;  Inclined  Air 
Columns,  384;  Calculation  of  Ventilating  Pressure  in  Furnace  Ventila- 
tion, 384;  Calculation  of  Motive  Column  or  Air  Column,  384;  Influence 
of  Furnace  Stack,  385;  Mechanical  Ventilators,  385;  Vacuum  System  of 
Ventilation,  386;  Plenum  System  of  Ventilation,  386;  Comparison  of 
Vacuum  and  Plenum  Systems,  386;  Types  of  Centrifugal  Fans,  387; 
Manometrical  Efficiency,  390;  Mechanical  Efficiency,  390;  Fan  Con- 
struction, 391;  High-Speed  and  Low-Speed  Motors,  392;  Fan  Tests,  392; 
Conducting  Air-Currents,  393;  Doors,  393;  Stoppings,  393;  Bridges,  393; 
Air  Brattice,  394;  Curtains,  394. 


Hoisting.— I^ouhle  Cylindrical  Drums,  394;  Single  Cylindrical  Drums,  394; 
Koepe  System,  395;  Whiting  System,  395;  Problems  in  Hoisting,  396; 
Balancing  a Conical  Drum,  396;  Horsepower  of  an  Engine  for  Hoisting, 
396;  Load  That  a Given  Pair  of  Engines  Will  Start,  396;  Approximate 
Period  of  Winding  on  a Cylindrical  Drum,  397;  Head-Frames,  397; 
Head-Sheaves,  397;  Guides  and  Conductors,  398;  Safety  Catches,  398; 
Detaching  Hooks,  398. 


H AU  LAG  E.— Gravity  Planes,  398;  Number  of  Cars  in  a Trip  on  a Self-Acting 
Incline,  399;  Engine  Planes,  399;  Size  of  Engines  Required  for  Engine- 
Plane  Haulage,  399;  Horsepower  of  an  Engine  to  Hoist  a Given  Load 
Up  an  Incline,  400;  Rope  Haulage,  400;  Tail-Rope  System,  400;  Tension 
of  Hauling  Rope,  401;  Endless-Rope  System,  401;  Friction  Pull  on  an 
Endless-Rope  Haulage,  402;  Inclined  Roads,  402;  Motor  Haulage,  402; 
Locomotive  Haulage,  402;  Compressed-Air  Haulage,  403;  Tractive 
Efforts  of  Compressed-Air  Locomotives,  404;  Electric  Haulage,  406; 
Speed  of  Haulage,  408;  Cost  of  Haulage,  409;  Mine  Roads  and  Tracks, 
410;  Grade,  410;  Rails,  411;  Gauge,  411;  Curves,  411;  To  Bend  Rails  to 
Proper  Arc  for  Any  Radius,  412;  Rail  Elevation,  412;  Rollers,  412; 
Switches,  413;  Turnouts,  413;  Slope  Bottoms,  413;  Tracks  for  Bottom  of 
Shafts,  416;  Surface  Tracks  for  Slopes  and  Shafts,  417. 


Ore  Dressing  and  the  Preparation  of  Coal.  — Crushing 
Machinery,  418;  Object  of  Crushing,  418;  Selection  of  a Crusher,  418; 
Jaw  Crushers,  419;  Blake  Crusher,  419;  Dodge  Crusher,  419;  Roll-Jaw 
Crushers,  420;  Gyratory  Crushers,  420;  Rolls,  421;  Cracking  Rolls,  421; 
Corrugated  Rolls,  422;  Disintegrating  Rolls  and  Pulverizers,  423;  Ham- 
mers, 423;  Crushing  Rolls,  423;  Amount  Crushed,  424;  Speeds,  424;  Speed 
of  Rolls,  425;  Crushing  Mills,  426;  Roller  Mills,  426;  Ball  Mills,  427;  Gravity 
Stamps,  427;  Order  of  Drop,  428;  Speed  of  Stamps,  429;  Shoes  and  Dies, 
429;  Life  of  the  Shoes  and  Dies,  429;  Cams,  Stamp  Heads,  and  Stems, 
429;  Tappets,  429;  Battery  Water,  430;  Duty  of  Stamps,  430;  Horsepower 
of  Stamps,  430;  Cost  of  Stamping,  430;  Pneumatic  Stamps,  430;  Power 
Stamps,  431;  Steam  Stamp,  431;  Miscellaneous  Forms  of  Crushers,  431. 


Sizing  and  Classifying  Apparatus.— Stationary,  Screens,  Griz- 
zlies, Head-Bars,  or  Platform  Bars,  431;  Adjustable  Bars,  432;  Shaking 
Screens,  432;  Revolving  Screens,  or  Trommels,  433;  Speed,  434;  Duty  of 
Anthracite  Screens,  434;  Revolving  Screen  Mesh  for  Anthracite,  434; 
Hydraulic  Classifiers,  434;  Spitzkasten,  435;  Spitzlutten,  435;  Calum^'" 


TABLE  OF  CONTENTS. 


xii 


Classifier,  435;  Settling  Boxes,  435;  Jeffrey-Robinson  Coal  Washer,  436; 
Log  Washer,  436;  Scaife  Trough  Washer,  437;  Jigs,  437;  Stationary 
Screen  Jigs,  437;  Theory  of  Jigging,  439;  Equal  Settling  Particles,  439; 
Interstitial  Currents,  439;  Acceleration,  440;  Suction,  440;  Removal  of 
Sulphur  From  Coal,  441;  Preparation  of  Anthracite,  442. 

Handling  of  Material.— Anthracite  Coal,  443;  Bituminous  Coal,  443; 
Ore,  Rock,  Etc.,  443;  Flumes  and  Launders,  443;  Horizontal  Pressure 
Exerted  Against  Vertical  Retaining  Walls,  444;  Horsepowers  for  Coal 
Conveyers,  445;  Weights  and  Capacities  of  Standard  Steel  Buckets,  446; 
Elevating  Capacities  of  Malleable  Iron  Buckets,  446;  Conveying  Capaci- 
ties of  Flight  at  100  Feet  per  Minute,  446;  Cost  of  Unloading  Coal,  447; 
Briqueting,  448;  Volume  of  a Ton  of  Different  Sizes  of  Coal,  449. 

Treatment  of  Injured  Persons.— Loss  of  Blood,  449;  To  Trans- 
port a Wounded  Person  Comfortably,  450;  Bleeding  From  Scalp 
Wounds,  451;  Treatment  of  Persons  Overcome  by  Gas,  451. 

Tables.— Coal  Dealers’  Table,  Giving  Cost  of  Any  Number  of  Pounds  at 
Given  Price  Per  Ton,  452;  Natural  Sines  and  Cosines,  453;  Natural  Tan- 
gents and  Cotangents,  464;  Logarithms  of  Numbers,  473;  Logarithms  of 
Trigonometric  Functions,  Sines,  Cosines,  Tangents,  Cotangents,  492; 
Latitudes  and  Departures  (Traverse  Table),  537;  Squares,  Cubes, 
Square  and  Cube  Roots,  Circumferences,  Areas,  and  Reciprocals, 
From  1 to  1,000,  545;  Diameters,  Circumferences,  and  Areas,  ^ to 
100,  561. 

Glossary  of  Mining  Terms.— 565. 


COAL  AND  METAL  MINERS’ 


POCKETBOOK. 


WEIGHTS  AND  MEASURES. 


THE  METRIC  SYSTEM. 

Since  the  metric  system  is  the  adopted  system  in  many  countries,  and  as 
it  is  almost  universally  used  in  connection  with  scientific  work,  a brief 
description  of  it  is  here  given  as  preliminary  to  the  following  tables  of  weights 
and  measures. 

The  metric  system  has  three  principal  units: 

1.  The  meter,  or  unit  of  length,  supposed  to  be  the  one  ten-millionth  part 
of  the  distance  from  the  equator  to  the  pole  on  the  meridian  of  longitude 
passing  through  the  city  of  Paris.  Its  actual  value  is  39.370432  in.,  the  stand- 
ard authorized  by  the  United  States  Government  being  39.37  in.  According 

to  this  standard,  1 yd.  = meter. 

2.  The  gram,  or  unit  of  weight,  is  the  weight  of  a cubic  centimeter  of  dis- 
tilled water  at  4°  centigrade  and  776  millimeters  of  atmospheric  measure. 
The  kilogram  (Kg.)  = 1,000  grams  = 2.2046  lb.,  is  the  ordinary  unit  of  weight 
corresponding  to  the  English  pound.  According  to  the  United  States  Gov- 
ernment regulations,  1 lb.  avoirdupois  = - kilogram. 

3.  The  liter,  or  unit  of  liquid  volume,  is  the  volume  of  1,000  cubic  centi- 
meters of  distilled  water  at  4°  centigrade  and  776  millimeters  pressure. 

Multiples  of  these  units  are  obtained  by  prefixing  to  the  names  of  the 
printed  units  the  Greek  words  deka  (10),  hekto  (100),  kilo  (1,000).  The  sub- 
multiples or  divisions  are  obtained  by  prefixing  the  Latin  words  deci  {^f), 
centi  The  abbreviations  of  these  several  units  as  mven 

in  the  following  tables  are  those  commonly  used.  The  kilogram-meter  is  the 
work  done  in  raising  1 kg.  through  a height  of  1 m.,  and  equals  7.233  ft.-lb. 
One  metric  horsepower  (force  de  cheval  or  cheval  vapeur)  equals  .98633  English 
horsepower. 


TROY  WEIGHT. 

24  grains  = 1 pennyweight. 

20  pennyweights  = 1 ounce  = 480  grains. 

12  ounces  = 1 pound  = 5,760  grains  = 240  pennyweights. 

In  troy,  apothecaries’,  and  avoirdupois  weights,  the  grains  are  the  same. 


APOTHECARIES’  WEIGHT. 

20  grains  = 1 scruple. 

3 scruples  = 1 dram  — 60  grains. 

8 drams  = 1 ounce  = 480  grains  = 24  scruples. 

12  ounces  = 1 pound  = 5,760  grains  = 288  scruples  = 96  drams. 


2 


WEIGHTS  AND  MEASURES. 


AVOIRDUPOIS  WEIGHT. 


27.34375  grains  = 1 dram. 

16  drams  = 1 ounce 

16  ounces  = 1 pound 

28  pounds  = 1 quarter 

4 quarters  = 1 hundredweight 

20  hundredweight  = 1 ton 

1 stone 
1 quintal 
1 “ short  ton  ” 

1 “long  ton” 

1 ounce  troy  or  apothecaries’  = 1.09714 
1 pound  troy  or  apothecaries’  = .82286 
1 ounce  avoirdupois  = .911458 

1 pound  avoirdupois  = 1.21528 


= 437i  grains. 

= 7,000  grains  = 256  drams. 
= 448  ounces. 

= 112  pounds. 

= 2,240  pounds. 

= 14  pounds. 

= 100  pounds. 

= 2,000  pounds. 

= 2,240  pounds, 
avoirdupois  ounces, 
avoirdupois  pound, 
troy  or  apothecaries’  ounce, 
troy  or  apothecaries’  pounds. 


METRIC  WEIGHT. 


10  milligrams  (mg.) 
10  centigrams 
10  decigrams 
10  grams 
10  decagrams 
10  hectograms 
10  kilograms 
10  myriagrams 
10  quintals 


= 1 centigram  (eg.) 

= 1 decigram  (dg.) 

= 1 gram  (g.) 

= 1 decagram  (Dg.) 

= 1 hectogram  (Hg.) 

= 1 kilogram  (Kg.) 

= 1 myriagram  (Mg.) 

= 1 quintal  (Q.) 

= 1 tonneau,  millier,  or  tonne 


.15432  grain. 
1.5432  grains. 
15.432  grains. 
.0220461b.  avoir. 
.22046  lb.  avoir. 
, 2.2046  lb.  avoir. 

22.046  lb.  avoir. 
220.46  lb.  avoir. 
2,204  lb.  avoir. 


MEASURES  OF  LENGTH. 


AMERICAN  AND  BRITISH. 

12  inches  = 1 foot. 

3 feet  = 1 yard  = 36  in. 

6 feet  = 1 fathom  = 2 yd.  = 72  in. 

66  feet  = 1 chain  * = ll  fath.  = 22  yd.  = 792  in. 

10  chains  = 1 furlong  = 110  fath.  = 220  yd.  = 660  ft.  = 7,620  in. 

8 furlongs  = 1 mile  = 80  chains  = 880  fath.  = 1,760  yd.  = 5,280  ft.  = 

A nautical  mile,  or  knot  = 1.15136  statute  miles.  [63,360  in. 
A league  = 3 nautical  miles. 

*The  chain  of  66  ft.  is  practically  obsolete.  Chains  of  50  or  100  ft.  are  now  used  exclusively  by 
American  surveyors. 


To  Reduce  Inches  to  Decimals  of  a Foot.— Divide  the  number  of  inches  by 
12.  Thus,  7 in.  = 7 ^ 12,  or  .58333  ft.  To  reduce  fraxitions  of  inches  to  deci- 
mals of  a foot,  divide  the  fraction  by  12,  and  then  divide  the  numerator  of 
the  quotient  by  the  denominator.  Thus,  f in.  = f -f- 12  = ^.  ^ = .0313  ft. 

The  annexed  scale  shows  on  one  side,  proportionately  reduced,  a scale  of 
tenths.  On  the  other,  a scale  of  twelfths,  corresponding  to  inches.  To 
reduce  inches  to  decimal  parts  of  a foot,  find  the  number  of  inches  and 


TENTUS  OF  FOOT 


1 2 ^ 4 i 

} f.  , 7 , f. 

t 7 8 8 10  n 12 

INCHES 


fractional  parts  thereof  on  the  side  marked  “inches.”  Opposite,  on  the 
scale  of  tenths,  will  be  found  the  decimal  part  of  a foot.  Thus,  if  we  want 
to  find  the  decimal  part  of  a foot  represented  by  7i  inches,  we  find  the  mark 
corresponding  to  7i  inches  on  the  side  marked  “inches.”  Opposite  this 
mark  we  read  6 tenths,  2 hundredths,  and  5 thousandths;  or,  expressed 
decimally,  .625. 


MEASURES  OF  LENGTH. 


3 


DECIMALS  OF  A FOOT  FOR  EACH  1-32  OF  AN  INCH. 


Inch. 

0" 

1" 

2" 

3" 

4" 

5" 

6" 

7" 

8" 

9" 

10" 

11" 

0 

0 

.0833 

.1667 

.2500 

.3333 

.4167 

.5000 

.5833 

.6667 

.7500 

.8333 

.9167 

.0026 

.0859 

.1693 

.2526 

.3359 

.4193 

.5026 

.5859 

.6693 

.7526 

.8359 

.9193 

.0052 

.0885 

.1719 

.2552 

.3386 

.4219 

.5052 

.5885 

.6719 

.7552 

.8385 

.9219 

.0078 

.0911 

.1745 

.2578 

.3411 

.4245 

.5078 

.5911 

.6745 

.7578 

.8411 

.9245 

h 

.0104 

.0937 

.1771 

.2604 

.3437 

.4271 

.5104 

.5937 

.6771 

.7604 

.8437 

.9271 

.0130 

.0964 

.1797 

.2630 

.3464 

.4297 

.5130 

.5964 

.6797 

.7630 

.8464 

.9297 

'h 

.0156 

.0990 

.1823 

.2656 

.3490 

.4323 

.5156 

.5990 

.6823 

.7656 

.8490 

.9323 

X 

.0182 

.1016 

.1849 

.2682 

.3516 

.4349 

.5182 

.6016 

.6849 

.7682 

.8516 

.9349 

i 

.0208 

.1042 

.1875 

.2708 

.3542 

.4375 

.5208 

.6042 

.6875 

.7708 

.8542 

.9375 

.0234 

.1068 

.1901 

.2734 

.3568 

.4401 

.5234 

.6068 

.6901 

.7734 

.8568 

.9401 

S 

.0260 

.1094 

.1927 

.2760 

.3594 

.4427 

.5260 

.6094 

.6927 

.7760 

.8594 

.9427 

.0286 

.1120 

.1953 

.2786 

.3620 

.4453 

.5286 

.6120 

.6953 

.7786 

.8620 

.9453 

1 

.0312 

.1146 

.1979 

.2812 

.3646 

.4479 

.5312 

.6146 

.6979 

.7812 

.8646 

.9479 

.0339 

.1172 

.2005 

.2839 

.3672 

.4505 

.5339 

.6172 

.7005 

.7839 

.8672 

.9505 

X 

.0365 

.1198 

.2031 

.2865 

.3698 

.4531 

.5365 

.6198 

.7031 

.7865 

.8698 

.9531 

.0391 

.1224 

.2057 

.2891 

.3724 

.4557 

.5391 

.6224 

.7057 

.7891 

.8724 

.9557 

i 

.0417 

.1250 

.2083 

.2917 

.3750 

.4583 

.5417 

.6250 

.7083 

.7917 

.8750 

.9583 

.0443 

.1276 

.2109 

.2943 

.3776 

.4609 

.5443 

.6276 

.7109 

.7943 

.8776 

.9609 

.0469 

.1302 

.2135 

.2969 

.3802 

.4635 

.5469 

.6302 

.7135 

.7969 

.8802 

.9635 

i§ 

.0495 

.1328 

.2161 

.2995 

.3828 

.4661 

.5495 

.6328 

.7161 

.7995 

.8828 

.9661 

.0521 

.1354 

.2188 

.3021 

.3854 

.4688 

.5521 

.6354 

.7188 

.8021 

.8854 

.9688 

.0547 

.1380 

.2214 

.3047 

.3880 

.4714 

.5547 

.6380 

.7214 

.8047 

.8880 

.9714 

a 

.0573 

.1406 

.2240 

.3073 

.3906 

.4740 

.5573 

.6406 

.7240 

.8073 

.8906 

.9740 

U 

.0599 

.1432 

.2266 

.3099 

.3932 

.4766 

.5599 

.6432 

.7266 

.8099 

.8932 

.9766 

i 

.0625 

.1458 

.2292 

.3125 

.3958 

.4792 

.5625 

.6458 

.7292 

.8125 

.8958 

.9792 

§1 

.0651 

.1484 

.2318 

.3151 

.3984 

.4818 

.5651 

.6484 

.7318 

.8151 

.8984 

.9818 

H 

.0677 

.1510 

.2344 

.3177 

.4010 

.4844 

.5677 

.6510 

.7344 

.8177 

.9010 

.9844 

1? 

.0703 

.1536 

.2370 

.3203 

.4036 

.4870 

.5703 

.6536 

.7370 

.8203 

.9036 

.9870 

1 

.0729 

.1562 

.2396 

.3229 

.4062 

.4896 

.5729 

.6562 

.7396 

.8229 

.9062 

.9896 

If 

.0755 

.1589 

.2422 

.3255 

.4089 

.4922 

.5755 

.6589 

.7422 

.8255 

.9089 

.9922 

H 

.0781 

.1615 

.2448 

.3281 

.4115 

.4948 

.5781 

.6615 

.7448 

.8281 

.9115 

.9948 

.0807 

.1641 

.2474 

.3307 

.4141 

.4974 

.5807 

.6641 

.7474 

.8307 

.9141 

.9974 

10  millimeters  (mm.) 
10  centimeters 
10  decimeters 
10  meters 
10  decameters 
10  hectometers 
10  kilometers 


METRIC  SYSTEM. 

= 1 centimeter  (cm.) 
= 1 decimeter  (dm.) 

= 1 meter  (m.) 

= 1 decameter  (Dm.) 
= 1 hectometer  (Hm.) 
= 1 kilometer  (Km.) 
= 1 myriameter(Mm.) 


= .3937079  inch. 

= 3.937079  inches. 

= 3.2808992  feet. 

= 10.9363  yards. 
= 109.363  yards. 

= .6213824  mile. 

= 6.213824  miles. 


RUSSIAN. 

12  inches  = 1 foot  = 1 American  foot. 
7 feet  = 1 sachine,  or  sagene. 

500  sachine  = 1 verst  = 3,500  feet. 


PRUSSIAN,  DANISH,  AND  NORWEGIAN. 

12  inches  = 1 foot  = 1.02972  American  feet. 
12  feet  = 1 ruth  = 12.35664  American  feet. 
2,000  ruths  = 1 mile  = 4.68+  American  miles. 


AUSTRIAN. 

12  inches  = 1 foot  = 1.03713  American  feet. 

6 feet  = 1 klafter. 

4,000  klafters  = 1 mile  = 4.71+  American  miles. 


4 


WEIGHTS  AND  MEASURES. 


SWEDISH. 

12  inches  = 1 foot  = .97410  American  foot. 

6 feet  = 1 fathom. 

6,000  fathoms  = 1 mile  = 6.64+  American  miles. 


CHINESE. 

1 chih  = 1.054  American  feet. 

10  chih  =:  1 Chang  = 10.54  American  feet. 
180  chang  = 1 li  = 1,897  American  feet. 


MEASURES  OF  AREA. 


AMERICAN  AND  BRITISH. 


144  sq.  inches  = 

9 sq.  feet  = 

30i  sq.  yards  = 
40  perches  = 

4 roods  = 

640  acres  = 


1 square  foot. 

1 square  yard  = 1,296  sq.  in. 

1 perch  = 272i  sq.  ft. 

1 rood  = 1,210  sq.  yd.  = 10,890  sq.  ft. 

1 acre  = 160  perches  = 4,840  sq.  yd.  = 43,560  sq.  ft. 

1 square  mile. 


TABLE  FOR  REDUCING  SQUARE  FEET  TO  ACRES. 


Square 

Feet. 

Acres. 

Square 

Feet. 

Acres. 

Squarfe 

Feet. 

Acres. 

Square 

Feet. 

Acres. 

100,000,000 

90,000,000 

2,295.684 

2,066.116 

900,000 

20.661 

9,000 

.207 

90 

.0021 

80,000,000 

1,836.547 

800,000 

18.365 

8,000 

.184 

80 

.0018 

70,000,000 

1,606.979 

700,000 

16.070 

7,000 

.161 

70 

.0016 

60,000,000 

1,377.410 

600,000 

13.774 

6,000 

.138 

60 

.0014 

50,000,000 

1,147.842 

500,000 

11.478 

5,000 

.115 

50 

.0011 

40,000,000 

918.274 

400,000 

9.183 

4,000 

.092 

40 

.0009 

30,000,000 

688.705 

300,000 

6.887 

3,000 

.069 

30 

.0007 

20,000,000 

459.137 

200,000 

4.591 

2,000 

.046 

20 

.0005 

10,000,000 

229.568 

100,000 

2.296 

1,000 

.023 

10 

.0002 

9,000,000 

206.612 

90,000 

2.066 

900 

.021 

9 

.00021 

8,000,000 

183.655 

80,000 

1.836 

800 

.018 

8 

.00018 

7,000,000 

160.698 

70,000 

1.607 

700 

.016 

7 

.00016 

6,000,000 

137.741 

60,000 

1.377 

600 

.014 

6 

.00014 

5,000,000 

114.784 

50,000 

1.148 

500 

.011 

5 

.00011 

4,000,000 

91.827 

40,000 

.918 

400 

.009 

4 

.00009 

3,000,000 

68.870 

30,000 

.689 

300 

.007 

3 

.00007 

2,000,000 

45.914 

20,000 

.459 

200 

.005 

2 

.00005 

1,000,000 

22.957 

10,000 

.230 

100 

.0023 

1 

.00002 

METRIC  SYSTEM. 


1 square  millimeter  ^sq.  mm.) 

1 square  centimeter  (sq.  cm.) 

1 square  decimeter  (sq.  dm.) 

1 square  meter,  or  centare  (m.2  or  sq.  m.) 
1 square  decameter,  or  are  (sq.  Dm.) 

1 hectare  (ha.) 

1 square  kilometer  (sq.  Km.) 

1 square  rayriameter  (sq.  Mm.) 


= .001550  sq.  in. 

= .155003  sq.  in. 

= 15.5003  sq.  in. 
= 10.764101  sq.  ft. 
= .024711  acre. 

= 2.47110  acres. 

= 247.110  acres. 
= 38.61090  sq.  mi. 


MEASURES  OF  VOLUME. 


5 


MEASURES  OF  VOLUME. 


AMERICAN  AND  BRITISH. 

1,728  cubic  inches  = 1 cubic  foot. 

27  cubic  feet  = 1 cubic  yard. 

A cord  of  wood  = 128  cu.  ft.,  or  a pile  of  wood  8 ft.  long,  4 ft.  wide,  and 
4 ft.  high  = 1 cord.  A perch  of  masonry  contains  24^  cu.  ft.;  but  in  practice 
it  is  taken  as  25  cu.  ft. 

A ton  (2,240  lb.)  of  Pennsylvania  anthracite,  when  broken  for  domestic 
use,  occupies  about  42  cu.  ft.  of  space;  bituminous  coal,  about  46  cu.  ft.;  and 
coke,  about  88  cu.  ft.  A bushel  of  coal  is  80  lb.  in  Kentucky,  Illinois,  and 
Missouri,  76  lb.  in  Pennsylvania,  and  70  lb.  in  Indiana. 


METRIC  SYSTEM. 

.0610254  cu.  in. 
.610254  cu.  in. 
6.10254  cu.  in. 
61.0254  cu.  in. 
.353156  cu.  ft. 
3.53156  cu.  ft. 
35.3156  cu.  ft. 
353.156  cu.  ft. 


= 28.876  cu.  in. 
= 57.75  cu.  in. 

4 quarts  = 1 gallon  = 32  gills  = 8 pints  = 231  cu.  in. 

3U  gallons  ==  1 barrel  = 7,276i  cu.  in.  = 4.21  cu.  ft. 

63  gallons  = 1 hogshead. 

2 hogsheads  = 1 pipe. 

2 pipes  = 1 tun. 

A box  19f  in.  on  each  side  contains  1 barrel. 


DRY  MEASURE  (U.  S.). 

2 pints  = 1 quart  = 67.2006  cu.  in.  = 1.16365  liquid  qt. 

4 quarts  = 1 gallon  = 268.8025  cu.in.  = 1.16365  liquid  gal. 

2 gallons  = 1 peck  ==  8 quarts  537.^50  cu.  in. 

4 pecks  = 1 bushel  = 64  pints  = 32  quarts  = 8 gal.  = 2,150.42  cu.  in. 


1 milliliter,  or  cu.  centimeter  (cc.  or  cm.^)  = 

1 centiliter  (cl.)  = 

1 deciliter  (dl.  or  dl.^)  = 

1 liter,  or  cu.  decimeter  (1. ) = 

1 decaliter,  or  centistere  (Dl.  or  dal.)  = 

1 hectoliter,  or  decistere  (HI.)  = 

1 kiloliter,  or  cu.  meter,  or  stere  (Kl.  or  cm.^)  = 

1 myrialiter,  or  decastere  (Ml.)  = 


LIQUID  MEASURE  (u.  S.). 

4 gills  = 1 pint  = 16  liquid  oz. 

2 pints  = 1 quart  = 8 gills 


BRITISH  IMPERIAL  MEASURE,  BOTH  LIQUID  AND  DRY. 

4 gills  = 1 pint  = 34.6592  cu.  in. 

2 pints  = 1 quart  = 69.3185  cu.  in. 

4 quarts  = 1 gallon  = 277.274  cu.  in. 

8 quarts  = 1 peck  = 554.548  cu.  in. 

4 pecks  = 1 bushel  = 2,218.192  cu.  in. 


The  standard  U.  S.  bushel  is  the  Winchester  bushel,  which  is  in  cylinder 
form,  18i  inches  diameter  and  8 inches  deep,  and  contains  2,150.42  cubic 
inches. 

The  British  Imperial  bushel  is  based  on  the  Imperial  gallon  and  con- 
tains 8 such  gallons,  or  2,218.192  cubic  inches  = 1.2837  cubic  feet. 

Capacity  of  a cylinder  in  U.  S.  gallons  = square  of  diameter  in  inches 
X height  in  inches  X .0034  (accurate  within  1 part  in  100,000). 

Capacity  of  a cylinder  in  U.  S.  bushels  = square  of  diameter  in  inches 
X height  in  inches  X .0003652. 


6 


WEIGHTS  AND  MEMmES. 


CONTENTS  OF  CYLINDERS  OR  PIPES  FOR  1 FOOT  IN  LENGTH. 

The  contents  of  pipes  or  cylinders  in  gallons  or  pounds  are  to  each  other 
as  the  squares  of  their  diameters.  Thus,  a pipe  9 ft.  in  diameter  will  contain 
9 times  as  much  as  a 3'  pipe,  or  4 times  as  much  as  a 4i'  pipe. 


Diameters  in  Inches. 


Diam. 

in 

Inches. 

Diameter 
in  Decimals 
of  a Foot. 

Gallons  of 
231  Cu.  In. 
(U.  S.  Stand- 
ard.) 

Weight  of 
Water  in  Lb. 
in  1 Ft.  of 
Length. 

Diam. 

in 

Inches. 

Diameter 
in  Decimals 
of  a Foot. 

Gallons  of 
231  Cu.  In. 
(U.  S.  Stand- 
ard.) 

Weight  of 
Water  in  Lb. 
in  I Ft.  of 
Length. 

JL 

4 

.0208 

.0025 

.02122 

5 

.4167 

1.020 

8.488 

.0417 

.0102 

.08488 

5i 

.4583 

1.234 

10.270 

1 

.0625 

.0230 

.19098 

6 

.5000 

1.469 

12.223 

1 

.0833 

.0408 

.33952 

6i 

.5417 

1.724 

14.345 

li 

.1042 

.0638 

.53050 

7 

.5833 

1.999 

16.636 

U 

.1250 

.0918 

.76392 

7i 

.6250 

2.295 

19.098 

.1458 

.1249 

1.0398 

8 

.6667 

2.611 

21.729 

2 

.1667 

.1632 

1.3581 

8i. 

.7083 

2.948 

24.530 

2i 

.1875 

.2066 

1.7188 

9 

.7500 

3.305 

27.501 

.2083 

.2550 

2.1220 

9i 

.7917 

3.682 

30.641 

21 

.2292 

.3085 

2.5676 

10 

.8333 

4.080 

33.952 

3 

.2500 

.3672 

3.0557 

m 

.8750 

4.498 

37.432 

.2917 

.4998 

4.1591 

11 

.9167 

4.937 

41.082 

4 

.3333 

.6528 

5.4323 

Hi 

.9583 

5.396 

44.901 

4i 

.3750 

.8263 

6.8750 

12 

1.0000 

5.875 

48.891 

Diameters  in  Feet. 


li 

1.25 

9.18 

76.392 

10 

10.00 

587.6 

4,889.12 

li 

1.50 

13.22 

110.00 

lOi 

10.50 

647.7 

5,404.24 

U 

1.75 

17.99 

149.73 

11 

11.00 

710.9 

5,915.84 

2 

2.00 

23.50 

195.56 

Hi 

11.50 

777.0 

6,485.72 

2i 

2.25 

29.74 

247.51 

12 

846.1 

7,040.00 

2i 

2.50 

36.72 

305.57 

13 

992.8 

8,710.00 

2f 

2.75 

44.43 

369.74 

14 

1,152.0 

10,096.00 

3 

3.00 

52.88 

440.00 

15 

1,322.0 

11,000.50 

3i 

3.25 

65.28 

• 544.37 

16 

1,504.0 

12,516.00 

3i 

3.50 

71.97 

631.00 

17 

1,698.0 

14,166.00 

31 

3.75 

82.62 

687.53 

18 

1,904.0 

15,841.00 

4 

4.00 

94.0 

782.24 

19 

2,121.0 

17,691.00 

4i 

4.25 

106.1 

885.40 

20 

2,350.0 

19,556.50 

4i 

4.50 

119.0 

990.04 

21 

2,591.0 

21,617.00 

4^ 

4.75 

132.5 

1,105.71 

22 

2,844.0 

23,663.00 

5 

5.00 

146.9 

1,222.28 

23 

3,108.0 

25,943.00 

5i 

5.25 

161.9 

1,351.06 

24 

3,384.0 

28,160.00 

5i 

5.50 

177.7 

1,478.96 

25 

3,672.0 

30,557.00 

5f 

5.75 

194.3 

1,621.43 

26 

3,971.0 

34,840.00 

6 

6.00 

211.5 

1,760.00 

27 

4,283.0 

35,641.00 

6i 

6.25 

229.5 

1,915.18 

28 

4,606.0 

40,384.00 

6i 

6.50 

248.2 

2,177.48 

29 

4,941.0 

41,117.00 

6i 

6.75 

267.7 

2,233.96 

30 

5,288.0 

44,002.00 

7 

7.00 

287.9 

2,524.00 

31 

5,646.0 

46,9M.OO 

7i 

7.50 

330.5 

2,750.12 

32 

6,017.0 

50,064.00 

8 

8.00 

376.0 

3,128.96 

33 

6,398.0 

53,242.00 

8i 

8.50 

424.5 

3,541.60 

34 

6,792.0 

56.664.00 

9 

9.00 

475.9 

3,960.16 

35 

7,197.0 

59,891.50 

9i 

9.50 

530.2 

4,422.84 

36 

7,614.0 

63,364.00 

WEIGHTS  AND  MEASURES. 


7 


MEXICAN,  CENTRAL  AMERICAN,  AND  SOUTH  AMERICAN 
WEIGHTS  AND  MEASURES. 


The  following  table  gives  weights  and  measures  in  commercial  use  in  Mex- 
ico and  the  republics  of  Central  and  South  America,  and  their  equivalents 
in  the  United  States.  Published  by  the  Bureau  of  the  American  Republics. 


Denomination. 

Where  Used. 

U.  S.  Equivalents. 

Arobe 

Paraguay 

25  pounds. 

Arroba  (dry)  

Argentine  Republic  

25.3175  pounds. 

Arroba  (dry)  

Brazil 

32.38  pounds. 

Arroba  (dry)  

Cuba 1 

25.3664  pounds. 

Arroba  (dry)  

Venezuela  

25.4024  pounds. 

Arroba  (liquid)  — 

Cuba  and  Venezuela 

4.263  gallons. 

Barril 

Argentine  Republic  and  Mexico 

20.0787  gallons. 

Carga 

Mexico  and  Salvador  

300  pounds. 

Centavo 

Central  America 

4.2631  gallons. 

Cuadra  

Argentine  Republic 

4.2  acres. 

Cuadra  

Paraguay 

78.9  yards. 

Cuadra  (square)... 

Paraguay 

8.077  square  feet. 

Cuadra  

Uruguay  

2 acres  (nearly). 

Fanega  (dry)  

Central  America 

1.5745  bushels. 

Fanega  (dry)  

Chile 

2.575  bushels. 

Fanega  (dry)  

Cuba 

1.599  bushels. 

Fanega  (dry)  

Mexico 

1.54728  bushels. 

Fanega  (dry)  

Uruguay  (double)  

7.776  bushels. 

Fanega  (dry)  

Uruguay  (single) 

3.888  bushels. 

Fanega  (dry)  

Venezuela  

1.599  bushels. 

Frasco 

Argentine  Republic  

2.5096  quarts. 

Frasco 

Mexico 

2.5  quarts. 

League  (land) 

Paraguay 

^,633  acres. 

Libra  

Argentine  Republic  

1.0127  pounds. 

Libra  

Central  America 

1.043  pounds. 

Libra  

Chile 

1.014  pounds. 

Libra  

Cuba 

1.0161  pounds. 

Libra  

Mexico 

1.01465  pounds. 

Libra  

Peru  

1.0143  pounds. 

Libra  

Uruguay  

1.0143  pounds. 

Libra  : 

Venezuela  

1.0161  pounds. 

Livre  

Guiana 

1.0791  pounds. 

Manzana  

Costa  Rica 

If  acres. 

Marc 

Bolivia 

.507  pound. 

Pie  

Argentine  Republic  

.9478  foot. 

Quintal 

Argentine  Republic  

101.42  pounds. 

Quintal  

Brazil  

130.06  pounds. 

Quintal  

Chile,  Mexico,  and  Peru 

101.61  pounds. 

Quintal  

Paraguay 

100  pounds. 

Vara 

Argentine  Republic  

34.1208  inches. 

Vara 

Central  America 

38.874  inches. 

Vara 

Chile  and  Peru 

33.367  inches. 

Vara 

Cuba 

33.384  inches. 

Vara 

Mexico 

33  inches. 

Vara 

Paraguay 

34  inches. 

Vara 

Venezuela  

33.384  inches. 

CONVERSION  TABLES. 

( United  States  Coast  and  Geodetic  Survey. ) 

The  method  of  using  the  following  tables  for  converting  United  States 
weights  and  measures  into  metric  weights  and  measures  will  be  understood 
by  the  following  example: 

Find  the  number  of  kilometers  in  125  miles. 

From  column  “ Miles  to  Kilometers,”  1 mile  = 1.60935  kilometers,  or  100 
miles  = 160.935  kilometers;  2 miles  = 3.21869  kilometers,  or  20  miles  = 32.1869 
kilometers;  and  5 miles  = 8.04674  kilometers.  Hence,  125  miles  = 160.935  -f- 
32.1869  + 8.04674  = 201.16864  kilometers. 


8 


WEIGHTS  AND  MEASURES, 


CUSTOMARY  TO  METRIC. 


Linear. 

Capacity. 

Inches  to 
Millimeters. 

eet  to  Meters. 

Yards 
to  Meters. 

Miles  to 

Kilometers. 

luid  Drams  to 

Milliliters, 

or  Cubic 

Centimeters. 

Fluid 

Ounces  to 

Milliliters. 

Quarts  to 

Liters. 

Gallons  to 

Liters. 

1 

25.4 

0.304801 

0.914402 

1.60935 

1 

3.70 

29.57 

0.94636 

3.78543 

2 

50.8 

0.609601 

1.828804 

3.21869 

2 

7.39 

59.15 

1.89272 

7.57087 

3 

76.2 

0.914402 

2.743205 

4.82804 

3 

11.09 

88.72 

2.83908 

11.35630 

4 

101.6 

1.219202 

3.657607 

6.43739 

4 

14.79 

118.29 

3.78543 

15.14174 

5 

127.0 

1.524003 

4.572009 

8.04674 

5 

18.48 

147.87 

4.73179 

18.92717 

6 

152.4 

1.828804 

5.486411 

9.65608 

6 

22.18 

177.44 

5.67815 

22.71261 

7 

177.8 

2.133604 

6.400813 

11.26543 

7 

25.88 

207.02 

6.62451 

26.49804 

8 

203.2 

2.438405 

7.315215 

12.87478 

8 

29.57 

236.59 

7.57087 

30.28348 

9 

228.6 

2.743205 

8.229616 

14.48412 

9 

33.27 

266.16 

8.51723 

34.06891 

Square. 

Weight. 

Square  Inches 
to  Square 
Centimeters. 

Square  Feet 
to  Square 
Decimeters. 

Square  Yards 
to  Square 
Meters. 

I 

Acres  to 
Hectares. 

Grains  to 
Milligrams. 

Avoirdupois 
Ounces 
to  Grams. 

Avoirdupois 
Pounds  to 
Kilograms. 

Troy  Ounces 
to  Grams. 

1 

6.452 

9.290 

0.836 

0.4047 

1 

64.7989 

28.3495 

0.45359 

31.10348 

2 

12.903 

18.581 

1.672 

0.8094 

2 

129.5978 

56.6991 

0.90719 

62.20696 

3 

19.355 

27.871 

2.508 

1.2141 

3 

194.3968 

85.0486 

1.36078 

93.31044 

4 

25.807 

37.161 

3.344 

1.6187 

4 

259.1957 

113.3981 

1.81437 

124.41392 

5 

32.258 

46.452 

4.181 

2.0234 

5 

323.9946 

141.7476 

2.26796 

155.51740 

6 

38.710 

55.742 

5.017 

2.4281 

6 

388.7935 

170.0972 

2.72156 

186.62088 

7 

45.161 

65.032 

5.853 

2.8328 

7 

453.5924 

198.4467 

3.17515 

217.72437 

8 

51.613 

74.323 

6.689 

3.2375 

8 

518.3914 

226.7962 

3.62874 

248.82785 

9 

58.065 

83.613 

7.525 

3.6422 

9 

583.1903 

255.1457 

4.08233 

279.93133 

Cubic. 

1 

09 

OJ 

ot 

d 

“.Th 

Miscellaneous. 

OJ  W 

'g.sS 

i-H  p d 

o0.9 

.4-3 

<1^  0 . 
a>.9  09 

'Sd  . 

.00  d 

rP  h-3 

d 0^ 

‘rO  oS 

M d 

d ® 

o o 

d 

0 

1 Gunter’s  chain  = 

1 sq.  statute  mile  ^ 

20.1168  meters. 

259.000  hectares. 

1 

16.387 

.02832 

0.765 

0.35239 

1 fathom 

_ 

1.829  meters. 

2 

32.774 

.05663 

1.529 

0.70479 

3 

49.161 

.08495 

2.294 

1.05718 

1 nautical  mile  = 

1,853.25 

meters. 

4 

5 

65.549 

81.936 

.11327 

.14158 

3.058 

3.823 

1.40957 

1.76196 

1 ft.  ---  .304801  meter 

9.4,S40ir>8  log. 

6 

7 

98.323 

114.710 

.16990 

.19822 

4.587 

5.352 

2.11436 

2.46675 

1 

avoir,  pound 

453.5924277  gram. 

8 

131.097 

.22654 

6.116 

2.81914 

15, 432..3.5039  grains  - 

1 kilogram. 

9 

147.484 

.25485 

6.881 

3.17154 

CONVERSION  TABLES. 


9 


The  method  of  using  the  following  tables  for  converting  metric  weights 
and  measures  into  United  States  weights  and  measures  may  be  understood 
by  the  following  example: 

Find  the  number  of  yards  in  86  meters. 

From  column  “ Meters  to  Yards,”  8 meters  = 8.748889  yards,  or  80  meters 
= 87.48889  yards;  and  6 meters  = 6.561667  yards.  Hence,  86  meters  = 
87.48889  + 6.561667  = 94.050557  yards. 

METRIC  TO  CUSTOMARY. 


Linear. 


Capacity. 


Meters  to 
Inches. 

Meters  to 
Feet. 

Meters  to 
Yards. 

Kilometers 
to  Miles. 

Milliliters,  or 
Cubic  Centi- 

liters to 
Fluid  Drams. 

Centiliters  to 

Fluid  Ounces. 

Liters  to 

Quarts. 

Decaliters 

to 

Gallons. 

Hectoliters 

to 

Bushels. 

1 

39.37 

3.28083 

1.093611 

0.62137 

1 

0.27 

0.338 

1.0567 

2.6417 

2.8377 

2 

78.74 

6.56167 

2.187222 

1.24274 

2 

0.54 

0.676 

2.1134 

5.2834 

5.6755 

3 

118.11 

9.84250 

3.280833 

1.86411 

3 

0.81 

1.014 

3.1700 

7.9251 

8.5132 

4 

157.48 

13.12333 

4.374444 

2.48548 

4 

1.08 

1.353 

4.2267 

10.5668 

11.3510 

5 

196.85 

16.40417 

5.468056 

3.10685 

5 

1.35 

1.691 

5.2834 

13.2085 

14.1887 

6 

236.22 

19.68500 

6.561667 

3.72822 

6 

1.62 

2.029 

6.3401 

15.8502 

17.0265 

7 

275.59 

22.96583 

7.655278 

4.34959 

7 

1.89 

2.367 

7.3968 

18.4919 

19.8642 

8 

314.96 

26.24667 

8.748889 

4.97096 

8 

2.16 

2.705 

8.4535 

21.1336 

22.7019 

9 

354.33 

29.52750 

9.842500 

5.59233 

9 

2.43 

3.043 

9.5101 

23.7753 

25.5397 

Square. 


Weight. 


Square  Centi- 
meters to 
Square  Inches. 

Square 

1 Meters  to 

Square  Feet. 

Square 
Meters  to 
Square  Yards. 

Hectares  to 
Acres. 

Milligrams  to 
Grains. 

Kilograms  to 
Grains. 

Hectograms 
to  Ounces 
Avoir.  1 

Kilograms 
to  Pounds 
Avoir. 

1 

0.155 

10.764 

1.196 

2.471 

1 

.01543 

15,432.36 

3.5274 

2.20462 

2 

0.310 

21.528 

2.392 

4.942 

2 

.03086 

30,864.71 

7.0548 

4.40924 

3 

0.465 

32.292 

3.588 

7.413 

3 

.04630 

46,297.07 

10.5822 

6.61387 

4 

0.620 

43.055 

4.784 

9.884 

4 

.06173 

61,729.43 

14.1096 

8.81849 

5 

0.775 

53.819 

5.980 

12.355 

5 

.07716 

77,161.78 

17.6370 

11.02311 

6 

0.930 

64.583 

7.176 

14.826 

6 

.09259 

92,594.14 

21.1644 

13.22773 

7 

1.085 

75.347 

8.372 

17.297 

7 

.10803 

108,026.49 

24.6918 

15.43236 

8 

1.240 

86.111 

9.568 

19.768 

8 

.12346 

123,458.85 

28.2192 

17.63698 

9 

1.395 

96.875 

10.764 

22.239 

9 

.13889 

138,891.21 

31.7466 

19.84160 

Cubic. 


Cubic  Centi- 
meters to 
Cubic  Inches. 

Cubic  Deci- 
meters to 
Cubic  Inches. 

Cubic 
Meters  to 
Cubic  Feet. 

Cubic  Meters 
to 

Cubic  Yards. 

1 

.0610 

61.023 

35.314 

1.308 

1 

2 

.1220 

122.047 

70.629 

2.616 

2 

3 

.1831 

183.070 

105.943 

3.924 

3 

4 

.2441 

244.094 

141.258 

5.232 

4 

5 

.3051 

305.117 

176.572 

6.540 

5 

6 

.3661 

366.140 

211.887 

7.848 

6 

7 

.4272 

427.164 

247.201 

9.156 

7 

8 

.4882 

488.187 

282.516 

10.464 

8 

9 

.5492 

549.210 

317.830 

11.771 

9 

{Continued). 


Quintals 

to 

Pounds 

Avoir. 

Milliers, 
or  Tonnes 
to  Pounds 
Avoir. 

Kilograms 

to 

Ounces 

Troy. 

220.46 

2,204.6 

32.1507 

440.92 

4,409.2 

64.3015 

661.39 

6,613.9 

96.4522 

881.85 

8,818.5 

128.6030 

1,102.31 

11,023.1 

160.7537 

1,322.77 

13,227.7 

192.9044 

1,543.24 

15,432.4 

225.0552 

1,763.70 

17,637.0 

257.2059 

1,984.16 

19.841.6 

289.3567 

10 


WEIGHTS  AND  MEASURES, 


METRIC  CONVERSION  TABLE. 

{Arranged  by  C.  W.  Hunt,  New  York.) 


Millimeters  X .03937  = in. 

Millimeters  25.4  = in. 

Centimeters  X .3937  = in. 
Centimeters  ^ 2.54  = in. 

Meters  X 39.37  = in.  (Act  Congress). 
Meters  X 3.281  = ft. 

Meters  X 1.094  = yd. 

Kilometers  X .621  = miles. 
Kilometers  1.6093  = miles. 
Kilometers  X 3,280.7  = ft. 

Square  millimeters  X .0155  = sq.  in. 
Square  millimeters  645.1  = sq.  in. 
Square  centimeters  X .155  = sq.  in. 
Square  centimeters  6.451  = sq.  in. 
Square  meters  X 10.764  = sq.  ft. 
Square  kilometers  X 247.1  = acres. 
Hectare  X 2.471  = acres. 

Cubic  centimeters  ^ 16.383  = cu.  in. 
Cubic  centimeters  ^ 3.69  = fluid 
drams  (U.  S.  P.). 

Cubic  centimeters  ^ 29.57  = fluid  oz. 
(U.  S.  P.). 

Cubic  meters  X 35.315  = cu.  ft. 

Cubic  meters  X 1.308  = cu.  yd. 

Cubic  meters  X 264.2  = gal.  (231 
cu.  in.). 

Liters  X 61.022  = cu.  in.  (Act  Con- 
gress). 

Liters  X 33.84  = fluid  oz.  (U.  S.  Phar.). 
Liters  X .2642  = gal.  (231  cu.  in.). 
Liters  -f-  3.78  = gal.  (231  cu.  in.). 
Liters  28.316  = cu.  ft. 

Tonnes  X 1.102  = short  tons. 

Tonnes  X .9839  = long  tons. 


Hectoliters  X 3.531  = cu.  ft. 

Hectoliters  X 2.84  = bu.  (2,150.42 
cu.  in.). 

Hectoliters  X .131  = cu.  yd. 

Hectoliters  -t-  26.42  = gal.  (231 
cu.  in.). 

Grams  X 15.432  = gr.  (Act  Con- 
gress). 

Grams  -j-  981  = dynes. 

Grams  (water)  29.57  = fluid  oz. 

Grams  28.35  = oz.  avoir. 

Grams  per  cu.  cent.  27.7  = lb.  per 
cu.  in. 

Joule  X .7373  = ft.-lb. 

Kilograms  X 2.2046  = lb. 

Kilograms  X 35.3  = oz.  avoir. 

Kilograms  1,102.3  = ton  (2,000 lb.). 

Kilogr.  per  sq.  cent.  X 14.223  = lb. 
per  sq.  in. 

Kilogram-meters  X 7.233  = ft.-lb. 

Kilo  per  meter  X .672  = lb.  per  ft. 

Kilo  per  cu.  meter  X .026  = lb.  per 
cu.  ft. 

Kilo  per  cheval  X 2.235  = lb.  per 
H.  P. 

Kilowatts  X 1.34  = H.  P. 

Watts  ^ 746  = H.  P. 

Watts  -j-  .7373  = ft.-lb.  per  sec. 

Calorie  X 3.968  = B.  T.  U. 

Cheval  vapeur  X .9863  = H.  P. 

(Centigrade  X 1-8)  + 32  = degree  F. 

Franc  X .193  = dollars. 

Gravity  Paris  = 980.94  centimeters 
per  sec. 


MONEY. 

United  States  Currency. 


British  Money. 


10  mills  = 1 cent. 
10  cents  = 1 dime. 
10  dimes  = 1 dollar. 
10  dollars  = 1 eagle. 


4 farthings  = 1 penny. 

12  pence  = 1 shilling. 

20  shillings  = 1 pound  sterling. 

21  shillings  = 1 guinea. 


Standard  United  States  Coins. 


Gold. 

Silver. 

Denomination. 

Value. 

Weight. 

Denomination. 

Value. 

Weight. 

* Dollar 

Quarter  eagle 

* Three-dollar  piece 

Half  eagle 

Eagle  

Double  eagle  

i^l.OO 

2.50 

3.00 

5.00 
10.00 
20.00 

25.8  gr. 
64.5  gr. 
77.4  gr. 

129.0  gr. 

258.0  gr. 

516.0  gr. 

* Trade  dollar... 
Standard  silver 

dollar 

Half  dollar  

Quarter  dollar... 
Dime  

«1.00 

1.00 

.50 

.25 

.10 

420.0  gr. 

412.5  gr. 
192.9  gr. 
96.45  gr. 
38.58  gr. 

“ Fineness”  expresses  the  proportion  of  pure  metal  in  1,000  parts;  thus, 
“ 900  fine  ” means  that  900  of  every  1,000  parts  are  pure  metal.  Fineness  of 


* No  longer  coined. 


MONETARY  VALUES. 


11 


U.  S.  coins  = 900  pute  metal,  100  alloy;  alloy  of  gold  coin  is  copper  or  copper 
and  silver,  but  in  no  case  shall  silver  exceed  ^ of  total  alloy.  Alloy  of  silver 
coin  is  copper. 

Piece.  Weight.  Contents. 

5-cent( nickel) 77.16  grains 75^  copper,  25/^  nickel. 

*3-cent  30  grains 75^  copper,  25^  nickel. 

*2-cent 66  grains 95^  copper,  5^tin  and  zinc. 

1-cent  (copper)  48  grains .95^  copper,  5^  tin  and  zinc. 

»No  longer  coined. 


Space  Required  to  Store  U.  S.  Coins. 


Description. 

Amount. 

How  Put  Up. 

Space. 

Gold  coins 

$1,000,000 

$5,000  in  8-oz.  duck  bags 

Nearly  17  cu.  ft. 

Silver  dollars 

1,000,000 

1,000  in  8-oz.  duck  bags 

250  cu.  ft. 

Subsidiary  silver 

1,000,000 

1,000  in  8-oz.  duck  bags 

150  cu.  ft. 

A bag  of  standard  silver  dollars  occupies  a space  12  in.  X 9 in.  X 4 in. 


To  Convert  Value  of  U.  S.  Coins  Into  English  Values  and  Vice  Versa. 
Rule. — Cents  {U.  S.)  2.02771,  or  X .U9312  = English  pence. 

Example.—  100  cents  X .49312  = 49.312  pence  = 4s.  1.312d. 

English  pence  X 2.02771  = cents  {U.  S.). 

Example.—  lOOd.  X 2.02771  = 202.771  cents  = $2.0277. 

_ , Dollars  ^ ^ 7- 

Rule-—  = pounds  sterling. 

U.oboo 

Example.—  = £20.548.  £.548  X 240  = 131.5d.  = 10s.  11.5d. 

4.oboo 

Ru I e.— Pounds X U.8665  '=  dollars (U.S.).  Shillings X 2U.332-{-  = cents  {U.S.). 


VALUES  OF  FOREIGN  OOINS,  U.  S.  TREASURY  DEPT.,  JAN.  1,  1899. 


Argentine,  Argentine  Re- 
public   $ 4.824 

Bolivar,  Venezuela .193 

Boliviano,  Bolivia 439 

Centen,  Cuba 5.017 

Colon,  Costa  Rica  465 

Condor,  Chile  7.300 

Condor,  U.  S.of  Colombia  and 

Ecuador  9.647 

Copeck,  Russia 0075 

Crown,  Austria-Hungary 203 

Crown,  Denmark,  Norway, 

and  Sweden  268 

Crown,  Germany 1.06 

Crown,  Great  Britain 1.13 

Crown,  Sicily 96 

Crown,  Spain  (half  pistole)  1.95 

Dollar,  Bolivia .96 

t Dollar,  British  Honduras, 

British  Possessions,  N.  A. 

(except  Newfoundland), 

and  Liberia'. 1.000 

Dollar,  Chile,  Peru,  and 

Ecuador  93 

Dollar,  Mexican  (gold)  983 

Dollar,  Mexican  ( silver) 477 

Dollar,  Newfoundland 1.014 

Dollar,  U.  S.  of  Colombia .935 


Doubloon,  Central  America  $14.50 


Doubloon,  Chile 3.650 

Doubloon,  New  Granada 15.34 

Doubloon,  Spain  and  Mexico  15.65 

Drachma,  Greece  193 

Ducat,  Austria,  Bohemia, 

Hamburg,  Hanover 2.28 

Ducat,  Denmark 1.11 

Ducat,  Sweden 2.20 

Escudo,  Chile 1.825 

Florin,  Austria-Hungary 1.929 

Florin,  Hanover  (g-old)  1.66 

Florin,  Hanover  (silver) 56 

Florin,  Holland,  South  Ger- 
many  38 

Florin,  Netherlands  402 

Florin,  Prussia 55 

Florin,  Silesia  48 

Franc,  Belgium,  Bulgaria, 

France,  Italy,  Roumania, 

Switzerland  193 

Gourde,  Hayti  965 

Groschen,  Prussian  Poland  .024 

Guinea,  Great  Britain  5.11 

Gulden,  Baden. 40 

Imperial,  Russia 7.92 

Kran,  Persia 081 

Kreutzer,  Bavaria  .0067 


t The  British  dollar  has  the  same  legal  value  as  the  Mexican  dollar  in  Hongkong,  the  Straits 
Settlements,  and  Lahuan. 


12 


WEIGHTS  AND  MEASURES. 


VALUES  OF  FOREIGN  coxus.— {Continued.) 


Lira,  Italy  $ .193 

Mark,  Finland 193 

Mark,  German  Empire 238 

Maximilian,  Bavaria 3.30 

Milreis,  Brazil  546 

Milreis,  Portugal 1.080 

Mohur,  India 7.105 

Napoleon,  France  3.84 

Peseta,  Spain 193 

Peso,  Argentine  Republic ...  .965 

Peso,  Chile 365 

Peso,  U.  S.  of  Colombia 439 

Peso,  Cuba 926 

Peso,  Guatemala,  Honduras, 

Nicaragua,  Salvador 365 

Peso,  Uruguay 1.034 

Piaster,  Egypt  .049 

Piaster,  Turkey .044 

Piastre,  Spain  1.04 

Pistole,  Rome  3.37 

Pistole,  Spain 3.90 

Pound,  Egypt  4.943 

Pound  Sterling,  Great  Britain  4.8665 
Ruble,  Russia  515 


Rupee,  India $ .208 

Shilling,  Great  Britain 243 

Sol,  Peru 439 

Sou,  France  01 

Sovereign,  Great  Britain 4.8665 

Sucre,  Ecuador. .439 

f Amoy  .710 

Canton .708 

Chefoo 679 

Chin  Kiang 693 

Fuehau 656 

Haikwan  (Cus- 
toms)  722 

Tael,  China  ^ Hankow 664 

Hongkong f 

Niuchwang 665 

Ningpo 682 

Shanghai 648 

Swatow  655 

Takau  714 

^Tientsin  688 

Toman,  Persia 3.409 

Yen,  Japan 498 


t The  British  dollar  has  the  same  legal  value  as  the  Mexican  dollar  in  Hongkong,  the  Straits 
Settlements,  and  Labuan. 

The  carat  (a  24th  part)  is  used  to  express  the  proportion  of  gold  in  an 
alloy;  thus,  gold  18  carats  fine  is  pure.  The  carat  is  also  a unit  of  weight 
for  precious  stones.  Its  value  varies  according  to  different  authorities,  but 
the  international  carat  is  3.168  grains,  or  206  milligrams. 


Diamond  Weight  (Nystrom). 


Carats. 

1 = 

.25  = 

.015625  = 

.3125  = 

15.5  = 


Grains.  Parts. 


Grains, 

Troy. 


4 = 64  = 3.2 

1 ^ 16  _ ,8 

.0625  = 1 = .05 

12.5  = 20  = 1 

1 ounce 


TIMBER  AND  BOARD  MEASURE. 


TIMBER  MEASURE. 

Volume  of  Round  Timber.— The  volume  in  cubic  feet  equals  the  length 
multiplied  by  one-fourth  the  product  of  mean  girth  and  diameter,  all  dimen- 
sions being  in  feet.  If  length  is  given  in  feet  and  girth  and  diameter  in 
inches,  divide  by  144;  if  all  dimensions  are  in  inches,  divide  by  1,728. 

Volume  of  Square  Timber.— When  all  dimensions  are  in  feet: 

Multiply  the  breadth  by  the  depth  and  that  product  by  the  length,  and  the 
product  will  give  the  volume  in  cubic  feet. 

When  either  of  the  dimensions  is  in  inches: 

Rule. — Multiply  as  above  and  divide  by  12. 

When  any  two  of  the  dimensions  are  in  inches: 

Multiply  as  before  and  divide  by  Uh. 


TIMBER  AND  BOARD  MEASURE. 


v: 


Round  Timber.— Table  of  i Girths. 


i Girths. 
Inches. 

Area  in 
Feet. 

i Girths. 
Inches. 

Area  in 
Feet. 

i Girths. 
Inches. 

Area  in 
Feet. 

6 

.250 

12i 

1.04 

19 

2.50 

6i- 

.272 

m 

1.08 

19i 

2.64 

.294 

12f 

1.12 

20 

2.77 

6^ 

.317 

13 

1.17 

20i 

2.91 

7 

.340 

13i 

1.21 

21 

3.06 

7i 

.364 

13i 

1.26 

21i 

3.20 

n 

.390 

m 

1.31 

22 

3.36 

7^ 

.417 

14 

1.36 

22i 

3.51 

8 

.444 

14i 

1.41 

23 

3.67 

.472 

14i 

1.46 

23i 

3.83 

.501 

m 

1.51 

24 

4.00 

8^ 

.531 

15 

1.56 

24i 

4.16 

9 

.562 

15i 

1.61 

25 

4.34 

9i 

.594 

15i 

1.66 

25i 

4.51 

H 

.626 

15f 

1.72 

26 

4.69 

9f 

.659 

16 

1.77 

26| 

4.87 

10 

.694 

16i 

1.83 

27 

5.06 

lOi 

.730 

m 

1.89 

27i 

5.25 

m 

.766 

m 

1.94 

28 

5.44 

10^ 

.803 

17 

2.00 

28i 

5.64 

11 

.840 

I7i 

2.09 

29 

5.84 

Hi 

.878 

17i 

2.12 

29h 

6.04 

Hi 

.918 

17^ 

2.18 

30 

6.25 

IH 

.959 

18 

2.25 

12 

1.000 

18i 

2.37 

Area  corresponding  to  i girth  (mean)  in  inches  multiplied  by  length 
in  feet  equal  solidity  in  feet  and  decimal  parts. 


BOARD  MEASURE. 

In  measuring  boards,  they  are  assumed  to  be  1 inch  in  thickness.  The 
number  of  feet,  board  measure  (B.  M.),  in  a given  board  or  stick  of  timber, 
equals  the  length  in  feet  multiplied  by  the  breadth  in  feet  multiplied  by  the 
thickness  in  inches. 


Breadth. 

Inches. 

Area  of  a 
Lineal  Foot. 

Breadth. 

Inches. 

Area  of  a 
Lineal  Foot. 

Breadth. 

Inches. 

Area  of  a 
Lineal  Foot. 

i 

.021 

4i 

.354 

8i 

.688 

i 

.042 

4i 

.375 

8i 

.708 

1 

.063 

4i 

.396 

8i 

.729 

1 

.083 

5 

.417 

9 

.750 

li 

.104 

5i 

.438 

9i 

.771 

li 

.125 

5i 

.458 

9i 

.792 

li 

.146 

5i 

.479 

9i 

.813 

2 

.167 

6 

.500 

10 

.833 

2i 

.188 

6i 

.521 

lOi 

.854 

2i 

.208 

6i 

.542 

lOi 

.875 

• 2i 

.229 

6i 

.563 

lOi 

.896 

3 

250 

7 

.583 

11 

.917 

3i 

.271 

7i 

.604 

Hi 

.938 

3i 

.292 

7i 

.625 

Hi 

.958 

3i 

.313 

7i 

.646 

Hi 

.979 

4 

.333 

8 

.667 

12 

1.000 

Area  of  a lineal  foot  multiplied  by  length  in  feet  will  give  superficial  con- 
tents in  square  feet. 


14 


MATHEMATICS. 


MATHEMATICS. 


By  Edward  H.  Williams,  Jr.,  E.  M. 

Professor  of  Mining  Engineering  and  Geology  at  the  Lehigh  University. 


GENERAL  PRINCIPLES. 

Quantity  or  magnitude  is  anything  that  can  be  increased  or  decreased,  or 
that  is  capable  of  any  sort  of  measurement  or  calculation,  such  as  numbers, 
lines,  space,  time,  motion,  weight,  force,  power,  heat,  light,  electricity,  etc. 
We  can  measure  a quantity  by  applying  to  it  a portion  of  the  same  quantity, 
called  a unit.  If  the  quantities  are  of  different  kinds,  we  cannot  measure 
them  by  one  another,  but  we  can  compare  them  or  institute  a calculation 
between  them. 

Mathematics  treats  of  all  kinds  of  quantity  that  can  be  numbered  or  meas- 
ured. Arithmetic  is  that  part  that  treats  of  numbering,  and  is  called  the 
science  of  numbers.  Geometry  is  the  science  of  measuring.  These  two  are 
the  foundation  of  all  other  parts  of  mathematics,  and  are  called  pure  mathe- 
matics. We  can  also  reason  about  numbers  by  substituting  letters  for  num- 
bers, and  represent  their  relations  by  signs.  This  is  called  algebra,  and  it 
may  be  likened  to  a shorthand  arithmetic.  An  extension  of  arithmetic  to 
geometry,  by  which  angles  and  triangles  are  subjected  to  numerical  compu- 
tation, is  called  trigonometry,  and  pTane  trigonometry  treats  of  methods  of 
computing  plane  angles  and  triangles,  and  embraces  the  investigations  of  the 
relations  of  angles  in  general,  which  is  called  angular  analysis.  Another 
extension  of  arithmetic  to  geometry,  by  which  lines,  areas,  and  volumes  are 
computed,  is  called  mensuration.  Mensuration  of  large  portions  of  the  earth’s 
surface,  where  the  curvature  of  the  same  is  taken  into  calculation,  is  called 
geodesy.  If  the  portions  are  smaller  and  curvature  is  neglected,  the  science 
is  called  surveying,  and  mine  surveying  if  confined  to  underground  work. 


COMMONLY  USED  MATHEMATICAL  SIGNS  AND  ABBREVIATIONS. 


-f  means  plus,  or  addition. 

— means  minus,  or  subtraction. 

X means  multiplication. 

± means  plus  or  minus. 

T means  minus  or  plus. 

means  division. 

: means  ratio. 

: : means  proportion. 

2 : 3 ; : 4 : 6 shows  that  ^ is  to  3 
as  4 is  to  6. 

— means  equality. 

=0=  means  equivalency, 

y means  square  root, 

f means  cube  root,  etc. 

square  root  of  3. 

^ 5 cube  root  of  5. 

72  7 squared. 

83  8 cubed. 

^ = a/b,  a-^b.  15  16  = 

0 lb 

therefore. 

> greater  than. 

< less  than. 

□ square. 

□'  square  feet. 


□"  square  inches. 

O round. 

( ) [ 1 I } » vincula,  denoting  that 

the  numbers  enclosed  are 
to  be  taken  together;  as, 

(a  + 5)  c = 4 + 3 X 5 = 35. 
° degrees,  arc  or  thermometer. 

' minutes  or  feet. 

" seconds  or  inches. 

30°  40'  4"  is  30  degrees  AO 
minutes  A seconds. 

4'  6"  is  A feet  6 inches. 

' " accents  to  distinguish  letters, 

as  a',  a",  a'". 

ai,  02,  ai,  Oc,  read  osMft  1,  a sub  6,  etc. 
a-,  03  o squared,  a cubed. 

a\  = 1^^,  o^  = 1/ o3. 

sin  o = the  sine  of  a. 

log  = logarithm. 

l_  angle. 

L mght  angle. 

_L  perpendicular  to. 

sin  sine. 

cos  cosine. 


ARITHMETIC. 


15 


MATHEMATICAL  SIGNS  AND  ABBREVIATIONS— 


tan,  or  tang,  tangent. 
sec  secant. 

versin  versed  sine. 

cot  cotangent. 

cosec  cosecant. 

covers  coversed  sine. 

TT  pi,  ratio  of  circumference  of 

circle  to  diameter  3.14159. 
g acceleration  due  to  gravity 

= (32.16  ft.  per  sec.). 

R,  r radius. 

W,  w weight. 

H.  P.  horsepower. 


I.  H.  P.  indicated  horsepower. 

B.  H.  P.  brake  horsepower. 

A.  W.  G.  American  wire  gauge 

(Brown  & Sharpe). 

B.  W.  G.  Birmingham  wire  gauge. 

r.  p.  m.,  or  rev.  per  min.,  revolutions 
per  minute. 

A decimal  point  is  a period  (.)  pre- 
fixed to  a number  to  show 
that  the  number  is  less  than 
unity  (1);  thus,  .2  = 

.35  = 5.75  = or  5j. 


ARITHMETIC. 


To  Cast  the  Nines  Out  of  a Number.— Add  together  the  digits,  and  find  how 
many  nines  are  contained  in  their  sum.  Reject  these  nines  and  set  down  the 
remainder  to  the  right  of  the  number. 

Example.— Cast  the  nines  out  of  18,304.  18,304.  7.  Ans. 

To  Prove  Addition.— Cast  the  nines  out  of  each  row  of  figures  added,  and 
out  of  their  sum.  Add  together  the  remainder  and  cast  the  nines  from  its 
sum.  If  the  remainder  from  this  last  process  is  equal  to  the  remainder 
obtained  from  the  sum  of  the  numbers,  the  addition  is  correct. 

Example.— Prove  this  addition:  2,1  4 3,5  6 8 2 

8,5  6 0,3  9 1 5 

1 0,7  0 3,9  5 9 7.  Ans. 

To  Prove  Subtraction.— Add  the  remainder  to  the  lesser  number;  their  sum 
should  equal  the  larger  number. 

To  Prove  M uiti pi i cation.— Cast  the  nines  out  of  multiplicand  and  multi- 
plier, and  multiply  the  remainders  together.  Cast  the  nines  out  of  the 
product,  and  the  remainder  should  equal  the  remainder  obtained  by  cast- 
ing the  nines  from  the  original  product. 

Example.— Prove  this  multiplication:  3,542  X 6,196  = 21,946,232. 

3,5  4 2 5 
6,1  9 6 4 

21,946,232  2.  Ans. 

To  Prove  Division.— Subtract  the  remainder,  if  there  be  any,  from  the 
dividend,  and  divide  what  remains  by  the  quotient.  If  the  new  quotient 
equals  the  old  divisor,  the  work  is  right. 

Example.— Divide  31,046,835  by  56.  554,407f §.  Ans. 

Proof.— Take  43  from  31,046,835,  and  divide  the  remainder,  31,046,792,  by 
554,407.  56.  Ans. 

Ruie.— To  square  any  number  containing  the  fraction  i,  multiply  the  whole 
number  by  the  next  higher  whole  number,  and  add  i. 

Example.—  (8i)2  = 8 X 9 + i = 721. 


COMMON  FRACTIONS. 

A fraction  is  a part  of  a whole,  as  1,  §,  etc. 

The  numerator  of  a fraction  is  the  number  that  tells  how  many  parts  of  a 
whole  are  taken.  Thus,  2 is  the  numerator  of  §,  as  it  shows  that  two  of  the 
three  parts  into  which  the  whole  is  divided  are  taken. 

The  denominator  of  a fraction  is  the  number  that  shows  into  how  many 
parts  the  whole  is  divided.  Thus,  in  the  fraction  §,  the  3 is  the  denominator. 

A common  denominator  is  a denominator  common  to  two  or  more  fractions. 
Thus,  1 and  | have  common  denominators;  and  again,  12  is  a common  de- 
nominator for  I,  1,  1,  and  I,  as  they  each  are  respectively  equal  to 

and 

To  Add  Common  Fractions.— If  of  the  same  denominator,  add  together  the 
numerators  only.  Thus  ^ + + T6  — T%- 


16 


FRACTIONS. 


If  they  have  different  denominators,  change  them  to  fractions  with  com- 
mon denominators,  and  proceed  as  before. 

Example.— What  is  the  sum  of  § + 1 + ^ ? 

§ = iSa  = U,  and  ^ = U- 
le  + M M = U-  Ans. 

To  Multiply  Common  Fractions.— Multiply  the  numerators  together  for  the 
numerator,  and  the  denominators  for  the  denominator.  Thus,  | X X § 

==  TS* 

To  Divide  Common  Fractions.-Invert  the  divisor,  and  multiply. 

Example.— Divide  by  |. 

X t Ans. 

To  Reduce  Compound  Fractions  to  Simple  Fractions. — Multiply  the  integer 
by  the  denominator  of  the  fraction,  add  the  numerator  for  the  new  numera- 
tor, and  place  it  over  the  denominator. 

Example.— Reduce  5§  to  a simple  fraction. 

5 X 3 + 2 = 17,  or  the  numerator,  and  the  fraction  is  therefore  V-. 

To  Reduce  Simple  Fractions  to  Compound  Fractions. — Divide  the  numerator 
by  the  denominator,  and  use  the  remainder  as  the  numerator  of  the  remain- 
ing fraction. 

Example.— Reduce  to  a compound  fraction. 

9)64(7 

6 3 Compound  fraction  = 7^.  Ans. 

To  Reduce  Common  Fractions  to  Decimal  Fractions.— Annex  ciphers  to  the 
numerator,  and  divide  by  the  denominator,  and  point  off  as  many  decimal 
places  in  the  quotient  as  there  are  ciphers  annexed. 

Example.— Reduce  je  to  a decimal  fraction. 

16  ) 9.00  0 0 (.56  25  Ans. 

Note.— Ciphers  annexed  to  a deci- 
mal do  not  increase  its  value.  1.13  is 
the  same  as  1.1300.  Every  cipher 
placed  between  the  first  figure  of  a 
decimal  and  the  decimal  point  divides 
the  decimal  by  10.  Thus, 

.13  --  10  = .013. 


80 
100 
96 
40 
32 
80 
80 


Table  of  Fractions  Reduced  to  Decimals. 


ISi 

.015625 

.265625 

il 

.515625 

49 

67 

.765625 

TUf 

.03125 

.28125 

.53125 

.78125 

.046875 

19 

64 

.296875 

M 

.546875 

67 

.796875 

.0625 

16 

.3125 

9 

T6 

.5625 

e 

.8125 

.078125 

u 

.328125 

67 

.578125 

II 

.828125 

3^ 

.09375 

hh 

.34375 

.59375 

§1 

.84375 

.109375 

.359375 

if 

.609375 

II 

.859375 

5 

.125 

3 

.375 

5 

s 

.625 

1 

.875 

.140625 

if 

.390625 

u 

.640625 

II 

.890625 

.15625 

.40625 

ih 

.65625 

if 

.90625 

.171875 

if 

.421875 

.671875 

II 

.921875 

.1875 

T6 

.4375 

.6875 

1 5 

T6 

.9375 

.203125 

§1 

.453125 

.703125 

H 

.953125 

3^3 

.21875 

.46875 

§§ 

.71875 

u 

.96875 

.234375 

ii 

.484375 

II 

.734375 

II 

.984375 

.25 

.5 

3 

7 

.75 

1 

l.OOOO 

DECIMALS. 

Decimal  fractions  have  for  their  denominators  10  or  a power  of  10. 
but  the  denominator  is  usually  omitted.  Thus,  .1  ==  .01  = yio;  .001 

— To’&o.  etc.  n A r 

To  Add  Decimals.— Place  whole  numbers  under  .00 /o 

whole  numbers,  tenths  under  tenths,  hundredths  <>3 

under  hundredths,  etc.,  and  add,  placing  the  deci-  10  6 

mal  point  in  the  sum  directly  under  the  i>()ints  17.9312 

above.  Thus,  1 9.6  3 1 7 


DECIMALS. 


17 


To  Subtract  Decimals.— Arrange  the  figures  as  in 
addition,  and  proceed  as  in  simple  subtraction. 
Thus, 


5.9  6 9 7 8 
3.2  8 6 9 4 
2.6  8 2 8 4 


To  Multiply  Decimals.— Proceed  as  in 
simple  multiplication,  pointing  off  as 
many  decimal  places  in  the  result  as 
there  are  decimal  places  in  both  mul- 
tiplicand and  multiplier.  Thus, 

To  Divide  Decimals.- 


4.6  7 5 3 1 
.0  5 3 
1402593 
2337655 


(5  decimal  places.f 
(3  decimal  places.) 


0.247  79143  (8 decimal  places.) 

. . -Proceed  as  in  simple  division,  and  point  off  as  many 

decimal  places  in  the  quotient  as  the  number  of  decimal  places  in  the  divi- 
dend exceeds  those  in  the  divisor. 


Example  1.— Divide  4.756  by  3.3. 
3.3  ) 4.7  5 60  0 ( 1.441  2 Ans. 
33 
145 
132 
136 
132 
40 
33 
70 

4 


Example  2.— Divide  .006  by  20. 
20  ).0  0 60  (.0  0 03  Ans. 

60 


Note.— It  has  been  said  before  that  algebra  is  a shorthand  arithmetic. 
Before  proceeding  further  with  the  various  methods  of  arithmetic,  the 
principles  of  algebra  will  be  stated,  and,  after  the  subsequent  examples  are 
worked  out  by  arithmetical  rules,  an  example  will  be  given  of  the  algebraic 
method  of  doing  the  same.  In  every  example,  we  have  known  quantities 
from  which  we  seek  to  find  certain  unknown  ones.  While  there  is  no  way  of 
indicating  these  in  arithmetic,  we  can  readily  do  so  in  algebra,  by  placing  the 
first  letters  of  the  alphabet  as  representatives  of  the  known  quantities 
(as  a,  5,  c),  and  the  last  letters  {x,y,z)  of  the  unknown  ones.  The  signs  in 
algebra  are  those  just  given  for  arithmetic.  In  addition  to  them,  we  can 
indicate  multiplication  by  placing  a period  (.)  between  the  quantities,  as  a.b 
(read  a multiplied  by  b),  or  simply  by  placing  the  two  letters  together,  as  ab. 

We  can  indicate  division  as  in  common  fractions,  ^ being  read  a divided  by  b. 

To  illustrate  algebraic  symbols,  let  I denote  the  length,  b the  breadth,  and 
h the  height  of  a mine  car.  If  it  be  desired  to  divide  the  height  into  the 
product  of  the  length  and  breadth,  it  is  expressed  as  follows: 

lb 

h’ 

When  two  or  more  letters  are  placed  together,  without  anything  between 
them,  it  is  understood  that  the  quantities  represented  by  those  letters  should 
be  multiplied  together.  If  I represents  8 and  b represents  4,  then  4 and  8 are 
multiplied  together;  thus,  4 X 8 = 32. 

If  it  be  desired  to  divide  the  height  into  the  sum  of  the  length  and  breadth, 
it  is  expressed  thus: 

lAb 

h • 

The  square  of  the  length  multiplied  by  the  cube  of  the  breadth,  thus: 
l^bK 

The  square  root  of  the  length  divided  by  the  cube  root  of  the  breadth,  thus: 

V I 

fT' 

The  square  root  of  the  difference  of  the  length  and  breadth  divided  by  the 
height,  thus: 

i/T^ 

h * 


18 


PROPORTION, 


SIMPLE  PROPORTION,  OR  SINGLE  RULE  OF  THREE. 

A proportion  is  an  expression  of  equality  between  equal  ratios;  thus,  the 
ratio  of  10  to  5 = the  ratio  of  4 to  2,  and  is  expressed  thus: 

10  : 5 ; : 4 : 2. 

There  are  four  terms  in  proportion.  The  first  and  last  are  the  extremes, 
and  the  second  and  third  are  the  means. 

Quantities  are  in  proportion  by  alternation  when  antecedent  is  compared 
with  antecedent  and  consequent  with  consequent.  Thus,  if  10  ; 5 : : 4 : 2, 
then  10  : 4 : : 5 : 2. 

Quantities  are  in  proportion  by  inversion  when  the  antecedents  are  made 
consequents  and  the  consequents  antecedents.  Thus,  if  10  : 5 : : 4 : 2,  then 
5 : 10  : : 2 : 4. 

In  any  proportion,  the  product  of  the  means  will  equal  the  product  of  the 
extremes.  Thus,  if  10  : 5 : : 4 : 2,  then  5 X 4 = 10  X 2. 

A mean  proportional  between  two  quantities  equals  the  square  root  of  their 
product.  Thus,  a mean  proportional  between  12  and  3 = the  square  root  of 
12  X 3,  or  6. 

If  the  two  means  and  one  extreme  of  a proportion  are  given,  we  find  the 
other  extreme  by  dividing  the  product  of  the  means  by  the  given  extreme. 
Thus,  10  : 5 : : 4 : ( ),  then  (4  X 5)  10  = 2,  and  the  proportion  is  10  : 5 : : 4 : 2. 

If  the  two  extremes  and  one  mean  are  given,  we  find  the  other  mean  by 
dividing  the  product  of  the  extremes  by  the  given  mean.  Thus,  10  : ( ) : : 4 : 2, 
then  (10  X 2)  -f-  4 = 5,  and  the  proportion  is  10  : 5 : : 4 : 2. 

Example.— If  6 men  load  30  wagons  of  coal  in  a day,  how  many  wagons 
will  10  men  load  ? (They  will  evidently  load  more,  so  the  second  term  of  the 
proportion  must  be  greater  than  the  first.) 

6 : 10  : : 30  ; ( );  then,  (10  X 30)  6 = 50.  Ans. 


COMPOUND  PROPORTION,  OR  DOUBLE  RULE  OF  THREE. 

Principles. 

1.  The  product  of  the  simple  ratios  of  the  first  couplet  equals  the  product 
of  the  simple  ratios  of  the  second  couplet.  Thus, 


2.  The  product  of  all  the  terms  in  the  extremes  equals  the  product  of  all 
the  terms  in  the  means.  Thus,  in 


f4  : 12)  . 

. f5  : 10) 

17  : 14/  • 

• 16:18; 

we  have  4 X 7 X 10  X 18  = 12  X 14  X 5 X 6. 

3.  Any  term  in  either  extreme  equals  the  product  of  the  means  divided 
by  the  product  of  the  other  terms  in  the  extremes.  Thus,  in  the  same 
proportion,  we  have 

4 = 5 X 6 X 12  X 14 
7X10X18  * 

4.  Any  term  in  either  mean  equals  the  product  of  the  extremes  divided 
by  the  product  of  the  other  terms  in  the  means.  Thus,  in 


f4  : 12)  . 

. r5: 

: 10) 

17  : 14;  • 

• 16: 

: 18/ 

we  have  5 = (4  X 7 X 10  X 18)  (6  X 12  X 14). 

Rule. — I.  Put  the  required  quantity  for  the  first  term  and  the  similar  known 
quantity  for  the  second  term,  and  form  ratios  with  each  pair  of  similar  quantities 
for  the  second  couplet,  as  if  the  result  depended  on  each  pair  and  the  second  term. 

1 1 . Find  the  required  term  by  dividing  the  product  of  the  means  by  the  product 
of  the  fourth  terms. 

Example  1.— If  4 men  can  earn  S24  in  7 days,  how  much  can  14  men  earn 
in  12  days  ? 

The  sum  : $24  : : | ^2  • 7 } 5 the  sum  ^ ^ ^ 

Example  2.— If  12  men  in  35  days  build  a wall  140  rd.  long,  6 ft.  high,  how 


EVOLUTION. 


19 


many  men  can,  in  40  days,  build  a wall  of  the  same  thickness  144  rd.  long, 
5 ft.  high? 


r 40  : 35  ) 

^ 140  : 144  y : : 
I 6:5  j 


12  : ( ) = 


35  X 144  X 5 X 12 
40  X 140  X 6 


= 9.  Ans. 


INVOLUTION. 

To  Square  a Number.— Multiply  the  number  by  itself.  Thus,  the  square  of 
4 = 4 X 4,  or  16. 

To  Cube  a Number.— Multiply  the  square  of  the  number  by  the  number. 
Thus,  the  cube  of  4 = 16  X 4 = 64. 

To  Find  the  Fourth  Power  of  a Number. — Multiply  the  cube  by  the  number. 
Thus,  the  fourth  power  of  4 = 64  X 4 = 256. 

To  Raise  a Number  to  the  Sixth  Power.— Square  its  cube. 

To  Raise  a Number  to  the  Twelfth  Power. — Square  its  sixth  power. 

(See  logarithms  for  shorter  method.) 


EVOLUTION. 

To  Find  the  Square  Root  of  a Number: 

Rule.— I.  Separate  the  given  number  into  periods  of  two  figures  each,  beginning 
at  the  units  place. 

11.  Find  the  greatest  number  whose  square  is  contained  in  the  period  on  the 
left:  this  will  be  the  first  figure  in  the  root.  Subtract  the  square  of  this  figure  from 
the  period  on  the  left,  and  to  the  remainder  annex  the  next  period  to  form  a 
dividend. 

HI.  Divide  this  dividend,  omitting  the  figure  on  the  right,  by  double  the  part  of 
the  root  already  found,  and  annex  the  quotient  to  that  part,  and  also  to  the  divisor; 
then,  multiply  the  divisor  thus  completed  by  the  figure  of  the  root  last  obtained, 
and  subtract  the  product  from  the  dividend. 

IV.  If  there  are  more  periods  to  be  brought  down,  continue  the  operation  as 
before. 

Example.— Find  the  square  root  of  8 7'4  2'2  5 ( 9 3 5 Ans. 

874,225.  8 1 


OPEKATION. 


18  3r6T2' 

^ 549 
186  519325 
9325 


9 X 2 = 18.  18  into  64  goes  3 times,  hence 
new  divisor  = 183.  93  X 2 = 186.  186  into 
932  goes  5 times,  hence  new  divisor  = 1,865. 

(See  logarithms  for  shorter  method.) 

The  square  root  of  a fraction  is  found  by  extracting  the  square  root  of  the 
numerator  and  denominator  separately.  Thus,  the  square  root  of  g?  = f . 

When  decimals  occur,  the  number  is  pointed  off  into  periods  both  right 
and  left  from  the  decimal  point,  and  there  will  be  as  many  decimal  places  in 
the  root  as  there  are  periods  to  the  right  of  the  decimal  point  in  the  number. 

Example  1.— Find  the  square 
root  of  874.225.  ^ 

S'7  4 9 r 9 q ^ fi-u  EXAMPLE  2.— Find  the  square 

8 7 4.2  2 5 ( 2 9.5  6+  root  of  .00874225. 

.0  0'8  7'4  2'2  5 (.0  9 3 5 
81 

18  31' 


58  5r3322 
2 9 2 5 

5M«71  1 9 ^ 6 a 


642 

549 
186  51  93  25 
9325 


4 3 08+ 

To  Find  the  Cube  Root  of  a Number: 

Rule. — I.  Separate  the  given  number  into  periods  of  three  figures  each,  beginning 
at  the  units  place. 

II.  Find  the  greatest  number  whose  cube  is  contained  in  the  period,  on  the  left; 
this  will  be  the  first  figure  in  the  root.  Subtract  the  cube  of  this  figure  from  the 
period  on  the  left,  and  to  the  remainder  annex  the  next  period  to  form  a dividend. 


20 


PERCENTAGE. 


III.  Divide  this  dividend  by  the  partial  divisor,  which  is  3 times  the  square  oj 
the  root  already  found,  considered  as  tens;  the  quotient  is  the  second  figure  of  the 
root. 

IV.  To  the  partial  divisor  add  3 times  the  product  of  the  second  figure  of  the 
root  by  the  first  considered  as  tens,  also  the  square  of  the  second  figure;  the  result 
will  be  the  complete  divisor. 

Y.  Multiply  the  complete  divisor  by  the  second  figure  of  the  root,  and  subtract 
the  product  from  the  dividend. 

VI.  If  there  are  more  periods  to  be  brought  down,  proceed  as  before,  using  the 
part  of  the  root  already  found,  the  same  as  the  first  figure  in  the  previous  process. 

Example.— Find  the  cube  root  of  12,812,904. 

OPERATION. 

1 2,8  1 2,9  0 4 ( 2 3 4 Ans. 

2‘^=  8 


1st  partial  divisor,  3 X 202  = 

1,2  0 0 

4,812 

3X20X3  = 

180 

32 

9 

4,1  6 7 

1st  complete  divisor, 

1,3  8 9 

6 4 5,9  0 4 

2d  partial  divisor,  3 X 2302  = 

1 5 8,7  0 0 

3 X 230  X 4 = 

2,7  6 0 

42  = 

16 

6 4 5,9  0 4 

2d  complete  divisor. 

1 6 1,4  7 6 

The  cube  root  of  a fraction  is  found  by  extracting  the  cube  root  of  the 
numerator  and  denominator  separately.  Thus,  the  cube  root  of  f . 

(See  logarithms  for  shorter  method.) 


PERCENTAGE. 

Percentage  means  by  or  on  the  hundred.  Thus,  1^  = = .01,  ^ 

= .03. 

To  Find  the  Percentage,  Having  the  Rate  and  the  Base.— Multiply  the  base 
by  the  rate  expressed  in  hundredths.  Thus  6^  of  1,930  is  found  as  follows: 

1,930  X .06  = 115.80. 

To  Find  the  Amount,  Having  the  Base  and  the  Rate.— Multiply  the  base  by  1 
plus  the  rate.  Thus,  the  amount  of  $1,930  for  one  year  at  6^  is  $1,930  X 1.06 
= $2,045.80. 

To  Find  the  Base,  Having  the  Rate  and  the  Percentage.— Divide  the  percent- 
age by  the  rate.  Thus,  if  the  rate  is  6^  and  the  percentage  is  115.80,  the  base 
= 115.80  --  .06  = 1,930. 

To  Find  the  Rate,  Having  the  Percentage  and  the  Base. — Divide  the  percent- 
age by  the  base.  Thus,  if  the  percentage  is  115.80  and  the  base  1,930,  the  rate 
equals  115.80  ^ 1,930  = .06,  or  6/.. 


ARITHMETICAL  PROGRESSION. 

Quantities  are  said  to  be  in  arithmetical  progression  when  they  increase  or 
decrease  by  a common  difference.  The  following  is  an  increasing  series  in 
arithmetical  progression:  1,  3,  5,  7,  9, 11, 13.  If  the  figures  be  read  backward, 
13,  11,  9,  etc.,  it  becomes  a decreasing  series.  In  the  first  series,  the  first  term 
is  1;  the  last  term  13;  the  number  of  terms  7;  the  common  difference  2;  and  the 
sum  of  the  terms  49. 

In  any  arithmetical  progression. 

Let  / = first  term; 

I = last,  or  nth  term; 
d = common  difference; 
n — number  of  terms;  and 
s = their  sum. 

The  second  term  =/  -f  (2  — l)d  ==/  -|-  d;  the  fourth  term  =/  H-  (4  — l)d; 
and  the  nth  term  = 

f+{n-l)d.  (1) 

From  equation  (1)  we  obtain 

f = I ±{n-  l)d.  (2)  a = (4) 

'll ' ' 

“ = -^  + 1-  «=|C/'  + 0.  (6) 


GEOMETRICAL  PROGRESSION. 


21 


Substituting  the  value  of  I from  ( 1 ) , 

« = (6) 


Example  1.— A company  contracts  to  put  down  a bore  hole  at  one  dollar 
($1)  per  foot  for  the  first  100  ft.;  three  dollars  ($3)  per  foot  for  the  second  100 
ft.;  and  two  dollars  (|2)  per  foot  additional  for  each  successive  100  ft.  The 
hole  was  800  ft.  deep.  What  was  the  cost  ? 

« = §;/=  100;  and  d = 2.  Substitute  these  values  in  formula  (6). 
s = f [2  X 100  + (8  — 1)  200]  = i|6,400.  Ans. 

Example  2.— If  water  fiowing  10.12  gal.  per  min.  be  struck  in  a shaft  30  ft. 
below  the  surface,  and  the  increase  in  flow  be  .02  gal.  per  ft.  till  the  depth  be 
200  ft.,  and  thence  the  flow  decreases  .02  gal.  per  ft.  till  the  rock  be  dry,  how 
deep  was  the  shaft  at  the  last  point,  and  what  was  the  total  amount  of  water 
flowing  into  it  per  minute  ? 

Dunng  the  increase  of  flow,  n = 170;  / = 10.12;  and  d = .02.  I [by 
formula  (1)]  = 10.12  + (170  — 1).02  = 13.50,  or  13.50  gal.  flow  at  a depth  of  200 
ft.,  and  s = [2  X 10.12  + (170  — 1)  .02]  = 2,007.7  gal.  flowing  in  along  the  first 
200  ft.  in  depth. 

During  the  decrease  in  flow / = 13.50;  d = .02,  and  I = .02. 

n [formula  (3)]  = — ^ + 1,  for  a decreasing  progression 


^3  50 02 

Then, * + 1 = 675,  the  depth  at  which  the  rock  will  run  dry, 

and  s = [2  X .02  + (675  — 1)  .02],  or  4,563  gal.,  the  amount  of  water  that 

will  flow  in  per  minute  along  the  last  675  ft.  The  total  amount  of  water 
flowing  in  along  the  total  depth  of  875  ft.  is  2,007.7  + 4,563,  or  6,570.7  gal.  Ans. 


GEOMETRICAL  PROGRESSION. 

A series  of  quantities,  in  which  each  is  derived  from  that  which  precedes 
it,  by  multiplication  by  a constant  quantity,  is  called  a geometrical  progression. 
If  the  multiplier  be  a whole  number,  the  progression  is  styled  increasing;  if 
it  be  a fraction,  the  progression  is  styled  decreasing.  The  series 
1,  2,  4,  8,  16,  32 

has  2 for  a multiplier,  and  is  an  increasing  progression.  The  series 
32,  16,  8,  4,  2,  1, 

have  ^ for  a multiplier,  and  are  decreasing  progressions. 

The  common  multiplier  in  a geometrical  progression  is  called  the  common 
ratio;  or,  briefly,  the  ratio. 

Let  / = first  term; 

I = last  term,  whose  number  from /is  n; 
n = number  of  terms; 
r = ratio; 
s = sum  of  terms. 

(1)  (4) 

» - ~ (2)  / = s _ r (s  - 1).  (5) 


(3) 


(6) 


r — 1 
Zr-/ 

‘~s~l 

Example.— If  a man  should  contract  to  sink  a shaft  to  the  base  of  the  coal 
measures  at  the  rate  of  cent  for  the  first  50  ft.;  | cent  for  the  second  50  ft.; 
4 cent  for  the  third  50  ft.;  and  so  on  at  the  same  rate,  how  much  would  be 
due  if  the  shaft  were  1,500  ft.  deep? 

/ = n = 30;  and  r = 2. 

Substituting  in  formula  (1), 

33,554,432  X 2 — 

2-T 

^ ^671,088.63^1.  Ans, 


/ = X (229)  33,554,432,  and  s [formula  (3)] 


22 


LOGARITHMS, 


LOGARITHMS. 


USE  OF  LOGARITHMS. 

Logarithms  are  designed  to  diminish  the  labor  of  multiplication  and  divi- 
sion, by  substituting  in  their  stead  addition  and  subtraction.  A logarithm  is 
the  exponent  of  the  power  to  which  a fixed  number,  called  the  base,  must  be 
raised  to  produce  a given  number.  The  base  of  the  common  system  is  10, 
and,  as  a logarithm  is  the  exponent  of  the  power  to  which  the  base  must  be 
raised  in  order  to  be  equal  to  a given  number,  all  numbers  are  to  be  regarded 
as  powers  of  10;  hence, 

100=  we  have  logarithm  of  1 = 0. 

101  = 10,  we  have  logarithm  of  10  = 1. 

102  = 100,  we  have  logarithm  of  100  = 2. 

10^  = 1,000,  we  have  logarithm  of  1,000  = 3. 

104  = 10,000,  we  have  logarithm  of  10,000  = 4. 

The  logarithms  of  numbers  between  1 and  10  are  less  than  unity,  and  are 
expressed  as  decimals.  The  logarithm  of  any  number  between  10  and  100  is 
more  than  1 and  less  than  2,  hence  it  is  equal  to  1 plus  a decimal.  Between 
100  and  1,000,  it  is  equal  to  2 plus  a decimal,  etc. 

The  integral  part  of  a logarithm  is  its  characteristic,  the  decimal  part  is 
its  mantissa. 

Example.— The  log  of  67.7  is  1.83059,  the  characteristic  of  this  logarithm 
is  1 and  the  mantissa  is  .83059. 

The  characteristic  of  a logarithm  is  always  1 less  than  the  number  of  whole 
figures  expressing  that  number , and  may  be  either  negative  or  positive. 

The  characteristic  of  the  logarithm  of  7 is  0;  of  17  is  1;  of  717  is  2;  etc. 

The  mantissa  is  the  decimal  portion  of  a logarithm^  and  is  always  considered 
positive. 

To  Find  the  Logarithm  of  Any  Number  Between  I and  100. — Look  on  the  first 
page  of  the  table,  along  the  column  marked  “No.,”  for  the  given  number; 
opposite  it  will  be  found  the  logarithm  with  its  characteristic. 

To  Find  the  Logarithm  of  Any  Number  Consisting  of  Three  Figures.— Proceed 
in  the  same  manner  and  find  the  decimal  in  the  first  column  to  the  right 
of  the  number;  prefix  to  this  the  characteristic  2.  Thus,  the  logarithm 
of  327  is  2.51455.  As  the  first  two  figures  of  the  decimal  are  the  same  for 
several  successive  figures,  they  are  only  given  where  they  change.  Thus, 
the  decimal  part  of  the  logarithm  of  302  is  .48001.  The  first  two  figures 
remain  the  same  up  to  310,  and  are  therefore  to  be  supplied. 

To  Find  the  Logarithm  of  Any  Number  of  Four  Figures. — Look  in  the  column 
headed  “ No.”  for  the  first  three  figures,  r.nd  then  along  the  top  of  the  page 
for  the  fourth  figure.  Down  the  colamn  headed  by  the  fourth  figure,  and 
opposite  the  first  three,  will  be  found  the  decimal  part.  To  this  prefix  the 
characteristic  3. 

To  Find  the  Logarithm  of  Any  Number  Containing  More  Than  Four  Figures. 

Place  a decimal  point  after  the  fourth  figure  from  the  left,  thus  changing  the 
number  into  an  integer  and  a decimal.  If  the  decimal  part  contains  more 
than  two  figures,  and  its  second  figure  is  5 or  greater,  add  1 to  the  first  figure 
in  the  decimal.  Find  the  mantissa  of  the  first  four  figures  and  subtract  it 
from  the  next  greater  mantissa  in  the  table.  Under  the  heading  “P.  P.” 
find  a column  headed  by  the  difference  first  found;  find  in  this  column  the 
number  opposite  the  number  corresponding  to  the  first  figure  of  the  decimal, 
or  the  first  figure  increased  by  one,  and  add  it  to  the  mantissa  already  found 
for  the  first  four  figures  of  the  given  number. 

Example.— What  is  the  logarithm  of  234,567? 

Placing  a decimal  point  after  the  fourth  figure  from  the  left,  we  have 
2,345.67.  The  mantissa  of  2,345  is  .37014;  the  difference  between  .37014  and  the 
next  higher  logarithm  .37033  is  19.  Add  1 to  the  first  figure  of  the  decimal  6, 
and  in  the  column  headed  19,  under  “ P.  P.,”  opposite  7,  we  find  13.3,  which, 
added  to  the  portion  of  the  mantissa  already  found,  .37014,  gives  .37027.  The 
characteristic  is  5,  hence  the  logarithm  is  5.37027. 

To  Find  the  Logarithm  of  a Decimal  Fraction.- Proceed  according  to  previous 
rules,  except  in  regard  to  the  characteristic.  Where  the  number  consists 


LOGARITHMS. 


23 


of  a whole  number  and  a decimal,  the  characteristic  is  1 less  than  the  whole 
number.  Where  it  is  a simple  decimal,  or  when  there  are  no  ciphers  between 
the  decimal  point  and  the  first  numerator,  the  characteristic  is  negative, 
and  is  expressed  by  1,  with  a minus  sign  over  it.  Where  there  is  one  cipher 
between  the  decimal  point  and  first  numerator,  the  characteristic  is  2,  with 
a minus  sign  over  it.  Where  there  are  2 ciphers,  the  characteristic  is  3,  with 
a minus  sign  over  it.  Thus: 

The  logarithm  of  67.7  is  1.83059. 

The  logarithm  of  6.77  is  0.83059. 

The  logarithm  of  .677  isL83059. 

The  logarithm  of  .0677  is  2.83059. 

The  logarithm  of  .00677  is  3.83059. 

The  characteristic  only  is  negative.  The  decimal  part  is  positive. 

To  Find  the  Logarithm  of  a Vulgar  Fraction.— Subtract  the  logarithm  of  the 
denominator  from  the  logarithm  of  the  numerator.  The  difference  is  the 
logarithm  of  the  fraction. 

Example.— Find  logarithm  of 

Log  4 = 0.60206 
Log  10  = L 

_ 1.60206 

1.60206  is  the  logarithm  of  .4. 

To  Find  the  Natural  Number  Corresponding  to  Any  Logarithm.— Look  in  the 
column  headed  “ 0 ” for  the  first  two  figures  of  the  decimal  part;  the  other  four 
figures  are  to  be  looked  for  in  the  same  or  in  one  of  the  nine  following  col- 
umns. If  they  are  exactly  found,  the  number  must  be  made  to  correspond 
with  the  characteristic  by  pointing  off  decimals  or  annexing  ciphers. 

If  the  decimal  portion  cannot  be  found  exactly,  find  the  next  lower  loga- 
rithm, subtract  it  from  the  given  logarithm,  divide  the  difference  by  the 
difference  between  the  next  lower  and  the  next  higher  logarithm,  and  annex 
the  quotient  to  the  natural  number  found  opposite  the  lower  logarithm. 

To  Multiply  by  the  Use  of  Logarithms.— Add  the  logarithms  of  the  factors 
together;  the  sum  will  be  the  logarithm  of  their  product. 

Example.—  67.7  X -677. 

Log  67.7  = 1.83059 
Log  .677  = 1.83059 

1.66118 

1.66118  is  the  logarithm  of  45.833. 

To  Divide  by  the  Use  of  Logarithms.— Subtract  the  logarithm  of- the  divisor 
from  the  logarithm  of  the  dividend;  the  difference  will  be  the  logarithm  of 
the  quotient. 

Example.— Divide  67.7  by  .0677. 

Log  67.7  = 1.83059 
Log  .0677  = 2.83059 
3.00000 

3 is  the  logarithm  of  1,000. 

To  Square  a Number  by  the  Use  of  Logarithms.— Multiply  the  logarithm  of 
the  number  by  2.  The  product  will  be  the  logarithm  of  the  square  of  the 
number. 

Example.— Square  .677.  _ 

Log  .677  = L83059 
2 

1.66118 

1.66118  is  the  logarithm  of  .45833. 

To  Cube  a Number.— Multiply  the  logarithm  of  the  number  by  3.  The 
product  will  be  the  logarithm  of  the  cube  of  the  number. 

To  Raise  a Number  to  Any  Power,  as  4th,  5th,  6th,  or  7th,  multiply  the  loga- 
rithm of  the  number  by  4,  5,  6,  or  7,  and  the  results  will  be  the  logarithms  of 
the  4th,  5th,  6th,  or  7th  powers,  respectively.  Thus,  a number  can  readily  be 
raised  to  any  power  required. 


24 


GEOMETRY, 


To  Extract  the  Square,  Cube,  Fourth,  Fifth,  or  Any  Root  of  a Number.— Divide 
the  logarithm  of  the  number  by  the  index  of  the  root  required,  and  the 
quotient  will  be  the  logarithm  of  the  required  root. 

Thus,  to  find  the  square  root  of  625: 

Logarithm  of  625  = 2.79588. 

2.79688^2  = 1.39794. 

1.39794  = logarithm  of  25. 

Therefore,  the  square  root  of  625  is  25. 

To  Find  the  Cube,  Fourth,  or  Any  Root. — Proceed  in  the  same  way,  using 
the  index  of  the  required  root  as  a divisor. 

To  Divide  a Logarithm  Having  a Negative  Characteristic.— If  the  characteristic 
is  evenly  divisible  by  the  divisor,  divide  in  the  usual  manner  and  retain  the 
negative  sign  for  the  characteristic  in  the  quotient.  But  if  the  negative 
characteristic  is  less  than,  or  not  evenly  divisible  by,  the  divisor,  add  such  a 
negative  number  to  it  as  will  make  it  evenly  divisible,  and  prefix  an  equal 
positive  number  to  the  decimal  part  of  the  logarithm;  then  divide  the 
increased  negative  characteristic  by  the  divisor,  to  obtain  the  characteristic 
of  the  quotient  desired.  To  obtain  the  decimal  part  of  the  quotient,  divide 
the  decimal  part  of  the  logarithm,  with  the  positive  number  prefixed,  in  the 
usual  manner.  To  this  quotient  prefix  the  negative  characteristic  already 
found,  and  this  will  be  the  quotient  desired. 

Example  1.—  ^^68^  ^ 2.1082282. 

Example  2.— 

14.3268472  ^ (14  + 4 = 18)  + (4  + .3268472)^^  + 4.3268472  ^ 2.4807608. 

Example  3.— 

i/Wl  = M ; I + " = T.966U78  = .9249+. 


GEOMETRY. 


PRINCIPLES  OF  GEOMETRY. 

1.  The  sum  of  all  the  angles  formed  on  one  side  of  a straight  line  equals 
two  right  angles,  or  180°. 

2.  The  sum  of  all  the  angles  formed  around  a point  equals  four  right 
angles,  or  360°. 

3.  When  two  straight  lines  intersect  each  other,  the  opposite  or  vertical 
angles  are  equal. 

4.  If  two  angles  have  their  sides  parallel,  they  are  equal. 

5.  If  two  triangles  have  two  sides,  and  the  included  angle  of  the  one 
equal  to  two  sides  and  the  included  angle  of  the  other,  they  are  equal  in  all 
their  parts. 

6.  If  two  triangles  have  two  angles,  and  the  included  side  of  the  one  equal 
to  two  angles  and  the  included  side  of  the  other,  they  are  equal  in  all  their 
parts. 

7.  In  any  triangle,  the  greater  side  is  opposite  the  greater  angle,  and  the 
greater  angle  is  opposite  the  greater  side. 

8.  The  sum  of  the  lengths  of  any  two  sides  of  a triangle  is  greater  than 
the  length  of  the  third  side. 

9.  In  an  isosceles  triangle,  the  angles  opposite  the  equal  sides  are  equal. 

10.  In  any  triangle,  the  sum  of  the  three  angles  is  equal  to  two  right 
angles,  or  180°. 

11.  If  two  angles  of  a triang:le  are  given,  the  third  may  be  found  by 
subtracting  their  sum  from  two  right  angles,  or  180°. 

12.  A triangle  must  have  at  least  two  acute  angles,  and  can  have  but  one 
obtuse  or  one  right  angle. 

13.  In  any  triangle,  a perpendicular  let  fall  from  the  apex  to  the  base  is 
shorter  than  either  of  the  two  other  sides. 


GEOMETRY. 


25 


14.  In  any  parallelogram,  the  opposite  sides  and  angles  are  equal  each  to 
each. 

15.  The  diagonals  divide  any  paralellogram  into  two  equal  triangles. 

16.  The  diagonals  of  a parallelogram  bisect  each  other;  that  is,  they 
divide  each  other  into  equal  parts. 

17.  If  the  sides  of  a polygon  be  produced  in  the  same  direction,  the  sum 
of  the  exterior  angles  will  equal  four  right  angles. 

18.  The  sum  of  the  interior  angles  of  a polygon  is  equal  to  twice  as  many 
right  angles  as  the  polygon  has  sides,  less  four  right  angles. 

Example.— The  sum  of  the  interior  angles  of  a quadrilateral  = (2X4) 
— 4 = 4 right  angles.  The  sum  of  the  interior  angles  of  a pentagon  = 
(2  X 5)  — 4 = 6 right  angles.  The  sum  of  the  interior  angles  of  a hexagon 
= (2  X 6)  — 4 = 8 right  angles. 

19.  In  equiangular  polygons,  each  interior  angle  equals  the  sum  divided 
by  the  number  of  sides. 

20.  The  square  described  on  the  hypotenuse  of  a right-angled  triangle  is 
equal  to  the  sum  of  the  squares  described  on  the  other  two  sides.  Thus,  in  a 
right-angled  triangle  whose  base  is  20  ft.  and  altitude  10  ft.,  the  square  of 
the  hypotenuse  equals  the  square  of  20  + the  square  of  10  , or  500.  Then  the 
hypotenuse  equals  the  square  root  of  500,  or  22.3607  ft. 

21.  Having  the  hypotenuse  and  one  side  of  a right-angled  triangle,  the 
other  side  may  be  found  by  subtracting  from  the  square  of  the  hypotenuse 
the  square  of  the  other  known  side.  The  remainder  will  be  the  square  of 
the  required  side. 

22.  Triangles  that  have  an  angle  in  each  equal,  are  to  each  other  as  the 
product  of  the  sides  including  those  equal  angles. 

23.  Similar  triangles  are  to  each  other  as  the  squares  of  their  correspond- 
ing sides. 

24.  The  perimeters  of  similar  polygons  are  to  each  other  as  any  two 
corresponding  sides,  and  their  areas  are  to  each  other  as  the  squares  of 
those  sides. 

25.  The  diameter  of  a circle  is  greater  than  any  chord. 

26.  Any  radius  that  is  perpendicular  to  a chord,  bisects  the  chord  and  the 
arc  subtended  by  the  chord. 

27.  Through  three  points  not  in  the  same  line,  a circumference  may  be 
made  to  pass. 

Directions.— Draw  two  lines  connecting  the  three  points.  Erect  perpen- 
diculars from  the  centers  of  each  of  these  two  lines,  and  the  point  of  inter- 
section of  the  perpendiculars  will  be  the  center  of  the  circle. 

28.  The  circumferences  of  circles  are  to  each  other  as  their  radii,  and 
their  areas  are  to  each  other  as  the  squares  of  their  radii. 

Example  1.— If  the  circumference  of  a circle  is  62.83  in.  and  its  radius  is 
10  in.,  what  is  the  circumference  of  a circle  whose  radius  is  15  in.  ? 

10  : 15  : : 62.83  ; 94.245  in.  Ans. 

Example  2.— If  a circle  6 in.  in  diameter  has  an  area  of  28.274  sq.  in.,  what 
is  the  area  of  a circle  12  in.  in  diameter  ? 

32  : 62  ; : 28.274  : 113.096  sq.  in.  Ans. 


PRACTICAL  PROBLEMS  IN  GEOMETRICAL  CONSTRUCTION. 

^ To  Bisect  a Given  Straight  Line  A 5. —From 

y A and  B as  centers,  with  a radius  greater  than 

I one-half  of  A B,  describe  arcs  intersecting  at  E 

^ j B and  F.  Draw  E F.  It  will  bisect  A B.  C will 

be  the  middle  point,  and  EF  will  be  perpendic- 
! ular  to  A B.  The  points  E and  F will  be  equi- 

)|;F  distant  from  A,  B,  or  C. 


From  a Given  Point  C,  Without  a Straight  Line  AB^ 
to  Draw  a Perpendicular  to  the  Line.— From  0 as  a 
center,  with  a radius  sufficiently  great,  describe 
an  arc  cutting  A ^ in  points  A and  B\  then  from 
A and  B as  centers,  with  a radius  greater  than 
one-half  of  A B,  describe  two  arcs  cutting  each 
other  at  D,  and  draw  CD. 


€ 


E 


A* 


26 


GEOMETRY. 


'>fD 


A^r 


C 


At  a Given  Point  C in  a Straight  Line  AB,  to 
Erect  a Perpendicular  to  That  Line.— Take  the  points 
A and  B equally  distant  from  C,  and,  with  A and 
B as  centers,  and  a radius  greater  than  one-half 
of  A B,  describe  two  arcs  cutting  each  other  at 
B,  and  draw  the  line  D C. 


At  a Point  -4  on  a Given  Straight  Line  A B, 
to  Make  an  Angle  Equal  to  a Given  Angle  EFG. 
From  jP  as  a center,  with  any  radius  F G, 
describe  the  arc  E G.  From  J.  as  a center, 
with  the  same  radius,  describe  the  arc  CB; 
then  with  a radius  equal  to  the  chord  E G, 
describe  an  arc  from  £ as  a center,  cutting 
CB  at  Z),  and  draw  A D 


To  Bisect  a Given  Arc  .4(75.— With  the  same 
radii  and  the  extremities  .4  5 as  centers,  describe 
arcs  intersecting  at  D and  E.  The  line  DE 
bisects  the  arc  at  C, 


To  Bisect  an  Angle  A B (7.— With  any  radius  and 
5 as  a center,  describe  an  arc  cutting  the  sides  at 
A and  C.  With  these  points  as  centers,  describe 
arcs  of  equal  ^^dius  intersecting  at  5.  The  line 
5 is  the  biseccor,  and  the  LA  B D = LB  B C.  ^ 


To  Bisect  an  Open  Angle  {Method  by  L.  L. 
Logan).— Let  AB  and  CZ)  be  the  sides  of 
an  open  angle.  With  any  point  0 as  a cen- 
ter, describe  a circle  cutting  the  sides  at 
e,/,  g,  and  h,  and  with  e and/,  and  g and  h 
as  centers  and  any  radius,  describe  arcs 
intersecting  at  k and  I,  respectively.  Draw 
Ok  and  01  and  mn.  With  p and  q as  cen- 
ters, and  any  radius,  describe  arcs  intersect- 
ing at  R and  S.  The  line  drawn  through 
RSis  the  required  bisector. 


Through  a Given  Point  A,  to  Draw  a Straight 
Line  Parallel  to  a Given  Straight  Line  (7  A— From 
.4  as  a center,  with  a radius  greater  than 
the  shortest  distance  from  A to  CB,  describe 
an  indefinite  arc  B E.  From  D as  a center, 
with  the  same  radius,  describe  the  arc  A F. 
Take  B E equal  to  A F,  and  draw  A B. 


-4E- 


\ B 


To  Find  the  Center  of  a Given  Circumference  or  Arc. 

Take  any  three  points  A,  B,  and  C on  the  circumfer- 
ence, and  unite  them  by  the  lines  A B and  B C.  Bisect 
these  chords  by  the  perpendiculars  B O and  E 0\  their 
intersection  is  the  center  of  the  circle. 


GEOMETRY. 


27 


Through  a Given  Point  P,  to  Draw  a Tangent  to  a Given 
Circle.— 1.  If  P be  in  the  circumference:  Find  C the 
center  of  the  circle,  draw  the  radius  G P,  and  draw 
D E perpendicular  to  C P. 


2.  If  P be  without  the  circle:  Join  P and 
the  center  of  the  circle.  Bisect  P C in  P;  with 
P as  a center,  and  a radius  P (7,  describe  the  cir- 
cumference intersecting  the  given  circumference 
at  A and  B.  From  the  intersections  A and  P, 
draw  B P and  A P. 


An  acute  angle  having  its  vertex  in  the  circumference  and 

subtended  by  an  arc  is  equal  to  one-half  the  central 
angle  subtended  by  the  same  arc.  Thus,  the  A B 0 
^ k L AO  C. 


An  acute  angle  included  between  a chord  and  a tangent  is 

equal  to  one-half  the  central  angle  subtended  by  the 
chord.  Thus,  [_  AB  G = \ L_  GOB. 


If,  from  a point,  two  tangents  be  drawn  to  a circle,  they 
will  be  equal,  and  their  angle  of  intersection  will  be 
equal  to  the  central  angle  subtended  by  the  chord 
joining  the  two  points  of  tangency.  Thus,  AB  = A G^ 
and  [_  D AG  = L BOG. 


To  Divide  a Straight  Line  Into  Any  Number 
of  Equal  Parts. — To  divide  the  line  AB 
into,  say,  6 parts,  draw  the  line  A G from 
A,  making  any  angle  with  A B;  measure 
off  6 equal  spaces  on  A C;  draw  6 B,  and 
from  1,  S,  4,  5 on  ^ C draw  parallels  to 
6 B.  These  divide  ^ P as  required  into 
6^  equal  parts. 

By  a similar  process  a line  may  be 
divided  into  a number  of  unequal  parts. 
Set  off  on  A G divisions  proportional  to 
the  required  divisions,  and  draw  the 
parallel  lines  as  explained  above. 


23 


MENSVRATION. 


MENSURATION. 

MENSURATION  OF  SURFACES. 


PARALLELOGRAMS. 

A parallelogram  is  a four-sided  figure  whose  opposite  sides  are  parallel. 


V Square.  Rectangle.  Rhombus.  Rhomboid. 

{Four  equal  sides  {Four  right  angles  {Four  equal  sides  {Four  oblique  angles  and 

and  four  right  an-  and  opposite  sides  and  oblique  angles.)  opposite  sides  equal.) 

gles.)  equal.) 

T#  Find  the  Area  of  Any  Parallelogram.— Multiply  the  length  of  any  side 
by  the  length  of  a perpendicular  line  from  that  side  to  the  opposite  one. 
Thus,  in  the  foregoing  figures,  the  areas  of  the  square  and  rectangle  are 
found  by  multiplying  the  length  A 5 by  the  height  B C.  The  areas  of  the 
rhombus  and  rhbmfed  are  found  by  multiplying  the  length  A B by  the 
height  C D. 

To  Find  the  Diagonal  of  a Square.— Multiply  the  length  of  a side  by  1.41421. 

Having  the  Diagonal,  to  Find  the  Side  of  a Square. — Divide  the  diagonal  by 
1.41421,  or  multiply  it  by  .707107. 

Ti  Find  a Square  Equal  in  Area  to  a Given  Circle.— Multiply  the  diameter  of 
the  circle  by  .886227,  and  the  result  will  be  the  side  of  the  required  square. 

T«  Find  the  Area  of  the  Largest  Square  That  May  be  Inscribed  in  a Circle. 
Square  the  radius  of  the  circle,  and  multiply  by  2. 

To  Find  the  Side  of  the  Largest  Square  that  May  be  inscribed  in  a Circie. 
Divide  the  diameter  of  the  circle  by  1.41421,  or  multiply  it  by  .707107. 


TRIANGLES. 

Atriangieisa  figure  having  three  straight  sides. 


Equilateral.  Isosceles.  Scalene. 

{Three  equal  {Two  equal  {Three  un- 
sides.) sides.)  equal  sides.) 


T#  Find  the  Area  of  a Triangle.— Multiply  its  base  by  one-half  the  perpen- 
dicular height,  or  altitude. 

To  Find  the  Perpendicular  Height  of  an  Equilateral  Triangle.— Multiply  the  length 
of  one  of  its  sides  by  .866025. 

To  Find  the  Length  of  Each  Side  of  an  Equilateral  Triangle.— Divide  the  per- 
pendicular height  by  .866025,  or  multiply  the  perpendicular  height  by  1.1547. 
Or,  take  the  square  root  of  the  area  and  multiply  it  by  1.51967. 

To  Find  the  Side  of  a Square  of  Same  Area  as  an  Equilateral  Triangle.— Mul- 
tiply the  length  of  one  of  its  sides  by  .658037. 


TRIANGLES. 


29 


To  Find  the  Diameter  of  a Circle  of  Same  Area  as  an  Equilateral  Triangle. 

Divide  the  length  of  one  of  its  sides  by  1.34677. 

The  following  rules  apply  to  any  triangle: 

Having  Two  Sides  and  the  Included  Angle,  to  Find  the  Area.— Multiply  together 
the  two  sides  and  the  natural  sine  of  the  included  angle,  and  divide  the 
product  by  2.  Or,  by  logarithms,  add  together  the  logarithms  of  the  two 


sides  and  the  logarithmic  sine  of  the  included  angle,  and  from  the  sum 
subtract  the  logarithm  of  2,  and  the  result  will  be  the  logarithm  of  the  area. 

Having  Three  Sides  of  a Triangle,  to  Find  the  Area.— Add  the  three  sides 
together,  divide  the  sum  by  2;  from  the  half  sum,  subtract  each  side  sep- 
arately; multiply  the  half  sum  and  the  three  remainders  continuously 
together,  and  extract  the  square  root  of  the  product.  Thus,  if  the  triangle 

has  three  sides  whose  lengths  are  30,  40,  and  50  ft.,  then  ^ 


Then,  subtracting  from  this  60  each  side  separately,  we  have:  60  — 30  = 30; 
60  — 40  = 20;  60  — 50  = 10.  Then,  60  X 30  X 20  X 10  = 360,000.  The  square 
root  of  360,000  = 600  sq.  ft.,  or  area. 

Having  the  Three  Sides  of  a Triangle,  to  Find  Its  Angles.— In  the  triangle 
A B C,  A B ^ 21  ft.,  B C = 17.25  ft.,  and  A C = S2  ft.  Draw  BD  per- 
pendicular io  A C\  then, 

32  : 21  + 17.25  = 21  — 17.25  : AD  — DC; 
or,  AD  — DC  = 4.48 

But  AD  A DC  = 32 

Adding, 


Subtracting, 


2AD  = 36.48 
A Z>  = 18.24 
2 D (7  = 27.52 
DC  = 13.76 


cos  A = = .86857,  or  A = 29°  42'  25.7". 

cos  C = = .79768,  ox  C = 37°  5'  26.7". 

B = 180°  — (A  + C)  = i80  — (29°  42'  25.7"+  37°  5'  26.7")  = 113°  12'  7.6". 
Having  Two  Sides  and  Included  Angle,  to  Find  Third  Side  and  the  Other  Angles. 

In  the  triangle  ABC,  let  A ^ = 19  ft.,  AC  = 2?  ft.,  and  A = 36°  3'  29". 
Draw  B D perpendicular  to  A a ^ D = 19  X sin  A = 19  X .58861  = 11.18  ft. 

A D = 19  X cos  A 19  X .80842  = 15.36  ft.  D C = 2d  — 15.36  = 7.64  ft. 

Tan  C = = 1.46335,  or  C = 55°  39'  10".  .B  = 180  — (A  -f  (7)  = 180 

7?  D 11  18 

- (36°  3'  29"  + 55°  39'  10")  = 88°  17'  21".  BC  = = 13.54  ft. 

sin  (7  .82562 

Having  One  Side  and  the  Two  Adjacent  Angles,  to  Find  the  Other  Two  Sides. 

The  third  angle  equals  180°  minus  the  sum  of  the  other  two  angles.  This 
third  angle  will  be  the  one  opposite  the  given  side.  Then  the  sine  of  the 
angle  opposite  the  given  side  is  to  the  given  side  as  the  sine  of  either  of  the 
other  angles  is  to  its  opposite  side.  Thus,  in  the  triangle  A B (7,  let  A = 60°, 
B = 70°,  and  the  side  A B = 200  ft.  Then  the  angle  C = 180°—  (60°  + 70°) 
= 50°. 

Then,  sin  50°  : 200  : : sin  60°  : B C, 

and  sin  50°  : 200  : : sin  70°  : A C. 

To  Find  the  Area.— Either  find  the  three  sides  as  above,  and  follow  rule 
already  given,  or  multiply  the  natural  sines  of  the  two  given  angles  together. 


30 


MENSURATION. 


Then,  as  the  natural  sine  of  the  single  angle  is  to  the  product  of  the  sines  of 
the  given  angles,  so  is  the  square  of  the  given  side  to  twice  the  required  area. 
Thus,  sin  C : sin  AXsin  B ::  AB^ : to  twice  the  area  of  the  triangle. 

The  area  of  any  triangle  is  equal  to  half  the  area  of  a parallelogram 
having  the  same  base  and  perpendicular  height. 


TRAPEZOIDS. 

A trapezoid  has  four  straight  sides,  only  two  of  which  are  parallel. 


To  Find  the  Area  of  a Trapezoid.— Add  together  the  two  parallel  sides,  and 
divide  by  2.  Multiply  the  quotient  by  the  perpendicular  height. 

Thus,  ABj^_C^  X EF  = area. 


TRAPEZIUMS. 

A trapezium  has  four  sides,  no  two  of  which  are  parallel. 

To  Find  the  Area  of  a Trapezium.— Divide  the  trape- 
zium into  two  triangles,  and  find  the  area  of  each 
according  to  the  rules  given  under  the  head  of 
“ Triangles.”  Add  together  the  areas  of  the  two 
triangles,  and  the  sum  will  equal  the  area  of  the 
trapezium.  The  sides  and  angles  can  be  found  in 
the  same  manner. 

If  the  diagonals  and  the  perpendiculars  from  them  to  the  opposite  angles 
are  given,  add  together  the  two  perpendiculars,  multiply  the  sum  by  the 
diagonal,  and  divide  by  2. 

The  sum  of  the  four  angles  included  in  a trapezium  always  equals  four 
right  angles.  


POLYGONS. 

All  figures  bounded  by  more  than  four  straight  lines  are  called  pcriygons. 

ooo 

Pentagon.  Hexagon.  Heptagon. 

If  all  the  sides  and  angles  are  equal,  it  is  a regular  polygon.  If  not,  it  is 
an  irregular  polygon. 

The  sum  of  the  interior  angles  of  any  polygon  is  equal  to  twice  as  many 
right  angles  as  the  polygon  has  sides,  less  four  right  angles. 

To  Find  the  Area  of  Any  Regular  Polygon.— Square  one  of  its  sides  and 
multiply  by  the  number  given  in  the  column  of  areas  in  the  following 
table.  Or,  multiply  the  length  of  one  of  the  sides  by  one-half  the  length 
of  a perpendicular  drawn  to  the  center  of  the  figure,  and  this  product  by 
the  number  of  sides. 

Having  the  Side  of  a Regular  Polygon,  to  Find  the  Radius  of  a Circumscribing 
Circle.— Multiply  the  side  by  the  corresponding  number  in  following 
column  of  outer  radii.  If  the  radius  of  the  circumscribing  circle  be  given. 


Octagon. 


CIRCLES. 


31 


divide  it  by  the  number  in  column  of  outer  radii,  and  the  quotient  will  be 
the  side  of  the  polygon. 

To  Find  the  Area  of  an  Irregular  Polygon. — Divide  it  into  triangles,  find  the 
Table  of  Regular  Polygons  Whose  Sides  Are  Unity. 


Number 

of 

SideS. 

Name  of  Polygon. 

Areas. 

Outer 

Radii. 

Angles  Contained 
Between 

Two  Sides. 

Angle  at  Center 
of 

Circle. 

3 

Equilateral  triangle 

.4330 

.5774 

60° 

120° 

4 

Square  

1.0000 

.7071 

90° 

90° 

5 

Pentagon 

1.7205 

.8507 

108° 

72° 

6 

Hexagon 

2.5981 

1.0000 

120° 

60° 

7 

Heptagon  

3.6339 

1.1524 

128°  34'  17"  + 

51°  25'  43"— 

8 

Octagon  

4.8284 

1.3066 

135° 

45° 

9 

Nonagon 

6.1818 

1.4619 

140° 

40° 

10 

Decagon  

7.6942 

1.6180 

144° 

36° 

11 

Undecagon 

9.3656 

1.7747 

J 

O 

32°  43'  38"  + 

12 

Dodecagon  

11.1962 

1.9319 

150° 

30° 

area  of  each  triangle,  and  add  them  together.  The  sum  will  be  the  area 
of  the  polygon. 

To  Find  the  Area  of  a Figure  Whose  Outlines  Are  Very  Irregular.— Draw  straight 
lines  around  it  that  will  enclose  within  them  (as  nearly  as  can  be  judged) 
as  much  space  not  belonging  to  the  figure  as  they  exclude  space  belong- 
ing to  it.  The  area  of  the  figure  thus  formed  may  be  easily  found  by 
dividing  into  triangles. 


CIRCLES. 

{See  Table  of  Areas  of  Circles,  Etc.) 

A circle  is  a figure  bounded  by  a curved  line,  every  point  of  which  is  equi- 
distant from  the  center.  Or,  a circle  is  a regular  poly- 
gon of  an  infinite  number  ol  sides. 

The  circumference  of  a circle  equals  the  diameter 
multiplied  by  3.1416,  or  the  square  root  of  the  product 
of  the  area  multiplied  by  12.566. 

To  Find  the  Diameter.— Divide  the  circumference  by 
3.1416,  or  multiply  it  by  .31831. 

To  Find  the  Area  of  a Circle. — Multiply  the  circumfer- 
ence by  one-fburth  of  the  diameter,  or  the  square  of  the 
radius  by  3.1416.  Multiply  the  square  of  the  diameter 
by  .7854,  or  the  square  of  the  circumference  by  .07958. 

To  Find  the  Diameter  of  a Circle  Equal  in  Area  to  a Given  Square.— Multiply 
one  side  of  the  square  by  1.12838. 

To  Find  the  Radius  of  a Circle  to  Circumscribe  a Given  Square.— Multiply 
one  side  by  .7071;  or  take  one-half  the  diagonal. 

To  Find  the  Side  of  a Square  Equal  in  Area  to  a Given  Circle.— Multiply  the 
diameter  by  .88623. 

To  Find  the  Side  of  the  Greatest  Square  in  a Given  Circle. — Multiply  the 
diameter  by  .7071. 

To  Find  the  Area  of  the  Greatest  Square  in  a Given  Circle.— Square  the  radius 
and  multiply  by  2. 

To  Find  the  Side  of  an  Equilateral  Triangle  Equal  in  Area  to  a Given  Circle. 

Multiply  the  diameter  by  1.3468. 

Having  the  Chord  and  Rise  of  an  Arc,  to  Find  the  Radius.— Square  half  the 
chord,  and  divide  by  the  rise.  To  the  quotient  add  the  rise,  and  divide  by  2. 
Or,  radius  = the  square  of  the  chord  of  half  the  arc  divided  by  twice  the 
rise  of  the  whole  arc. 

Having  the  Chord  and  Radius,  to  Find  the  Rise.— Square  the  radius,  also 
square  half  the  chord.  Take  the  last  square  from  the  first.  Extract  square 
root  of  the  remainder,  and  subtract  it  from  the  radius  if  the  radius  is  greater; 
if  not,  add  it  to  the  radius. 

Having  the  Radius  and  Rise,  to  Find  the  Chord.— From  the  radius  subtract 
the  rise  (or  from  the  rise  subtract  the  radius,  if  rise  is  the  greater),  square 


32 


MENSURATION. 


the  remainder,  and  subtract  it  from  the  square  of  the  radius.  Extract  the 
square  root  of  the  remainder,  and  multiply  by  2. 

Having  the  Rise  of  the  Arc  and  Diameter  of  Circle,  to  Find  the  Chord.— Sub- 
tract the  rise  from  the  diameter,  and  multiply  the  remainder  by  the  rise. 
Extract  the  square  root  of  the  product,  and  multiply  by  2. 

To  Find  the  Breadth  of  a Circular  Ring,  Having  Its  Area  and  the  Diameter  of 
the  Outer  Circle. — Find  the  area  of  the  whole  circle,  and  from 
it  take  the  area  of  the  ring.  Multiply  the  remainder  by 
1.2732,  and  the  square  root  of  the  product  will  be  the  diam- 
eter of  the  inner  circle.  Take  it  from  the  diameter  of  the 
outer  one,  and  the  remainder  will  be  twice  the  breadth. 

To  Find  the  Area  of  a Circular  Ring.— Take  the  difference  of 
the  squares  of  the  radii,  and  multiply  it  by  3.1416. 

To  Find  the  Length  of  an  Arc  When  Its  Degrees  and  Radius  Are 
Given.— Multiply  the  number  of  degrees  by  .01745,  and  the  product  by  the 
radius. 

To  Find  the  Area  of  a Sector.— Multiply  the  arc  by  one-half  the  radius. 
The  area  of  the  sector  is  to  the  area  of  the  circle  ^ the  number  of  degrees 
in  the  sector  is  to  360°. 

To  Find  the  Area  of  a Segment.— Find  the  area  of  the  sector  having  the 
same  arc,  and  also  the  area  of  the  triangle  formed  by  the  chord  of  the  segment 
and  the  radii  of  the  sector.  If  the  segment  is  greater  than  a semicircle,  add 
the  two  areas;  if  less,  subtract  them. 


THE  ELLIPSE. 

To  Find  the  Area  of  an  Elllpse.—Multiply  one-half  of  the  two  axes  and 
CD  together,  and  multiply  the  product  by  3.1416. 

To  Find  the  Perimeter  of  an  Ellipse. — Multiply  one-half 
the  sum  of  the  two  axes  by  3.1416. 

To  Draw  an  Approximate  Ellipse  {Methodby  Three  Squares). 
Let  a be  the  center,  h c the  major,  and  a e half  the  minor 
axis  of  an  ellipse.  Draw  the  rectangle  bfgc,  and  the 
diagonal  line  be;  at  a right  angle  to  b e,  draw  linefh  cut- 
ting J5  .Bat  f.  With  radius  ae,  and  from  a as  a center, 
draw  the  dotted  arc  ej,  giving  the  pointy’  on  the  line  B B.  From  k,  which  is 
central  between  b and  j,  draw  the  semicircle  b mj,  cutting  A A ail.  Draw 
the  radius  of  the  semicircle  b mj,  cutting  fg  at  n.  With  radius  m n,  mark 
on  A A,  at  and  from  a as  a center,  the  point  o.  With  radius  ho,  and  from 
center  h,  draw  the  arc  poq.  With  radius  a I, 
and  from  b and  c as  centers,  draw  arcs  cut- 
ting poq  at  the  points  p and  q.  Draw  the 
lines  hpr  and  hqs,  and  also  the  lines  p i t 
and  qvw.  From  A as  a center,  draw  that 
part  of  the  ellipse  lying  between  r and  s 
with  radius  hr.  From  p as  a center  draw 
that  part  of  the  ellipse  lying  between  r and 
t with  the  radius  pr.  From  q,  draw  the 
ellipse  from  s to  w.  With  radius  i t,  from  i as 
a center,  draw  the  ellipse  from  t to  5 with 
radius  i t,  and  from  as  a center,  draw  the 
ellipse  from  w to  c,  and  one-half  the  ellipse 
will  be  drawn.  It  will  be  seen  that  the  whole 
construction  has  been  performed  to  find  the 
centers  h,  p,  q,  i,  and  v,  and  that  while  v and  i 
may  be  used  to  carry  the  curve  around  the  other  side  or  half  of  the  ellipse, 
new  centers  must  be  provided  for  h,  p,  and  q;  these  new  centers  correspond 
in  position  to  h,  p,  q. 


A 


V 1 

hy  ' 

Rv"  \ i 

R \ {k 

a / 

\ 

/ 

1 

\ 

I 


\v| 


Straightedge  Method.— On  a straightedge,  lay  off  ^.B 
equal  to  one-half  the  short  diameter  and  A C equal  to 
one-half  the  long  diameter.  Determine  points  on  the 
circumference  of  the  ellipse  by  marking  positions  of 
A.  as  the  point  B is  moved  along  the  major  axis  and,  at 
the  same  time,  the  point  C along  the  minor  axis. 


MENSURATION  OF  SOLIDS. 


33 


MENSURATION  OF  SOLIDS. 


THE  CUBE  AND  THE  PARALLELOPI PED. 

To  Find  the  Surface  of  a Cube.— Multiply  the  area  of  one  side  by  6. 

To  Find  the  Surface  of  a Paralleiopiped.— Add  together  t.wice  the  area  of 
the  base,  twice  the  area  of  the  side,  and  twice  the  area  of  the  end. 

To  Find  the  Cubicai  Contents  of  a Cube  or  Paralleiopiped.— Multiply  the  area 
of  the  base  by  the  perpendicular  height. 


THE  PRISM. 

To  Find  the  Convex  Surface  of  a Right  Prism.— Multiply  the 

perimeter  of  the  base  by  the  altitude. 

To  find  the  entire  surface,  add  the  areas  of  the  bases. 

To  Find  the  Contents  of  a Prism.— Multiply  the  area  of  the 
base  by  the  altitude  of  the  prism. 


THE  CYLINDER. 

To  Find  the  Convex  Surface  of  a Cylinder. — Multiply  the  circum- 
ference of  the  base  by  the  altitude. 

To  find  the  entire  surface,  add  the  areas  of  the  ends. 

To  Find  the  Contents  of  a Cylinder.— Multiply  the  area  of  the 
base  by  the  altitude. 


THE  SPHERE. 

To  Find  the  Surface  of  a Sphere.— Multiply  the  diameter  by  the  circum- 
ference; or,  square  the  radius  and  multiply  it  by  4 and  3.1416. 

To  Find  the  Contents  of  a Sphere.— Multiply  the  surface  by 
one-third  of  the  radius;  or,  multiply  the  cube  of  the  diam- 
eter by  .5286. 

To  Find  the  Surface,  of  a Zone.— Multiply  the  height  of  the 
zone  by  the  circumference  of  a great  circle  of  the  sphere. 

To  Find  the  Contents  of  a Spherical  Segment  of  One  Base. 
Add  the  square  of  the  height  to  three  times  the  square  of 
the  radius  of  the  base;  multiply  this  sum  by  the  height, 
and  the  product  by  .5236. 

The  curved  surface  on  a hemisphere  is  equal  to  twice  its  plane  surface,  and 
the  curved  surface  on  a quarter  of  a sphere  is  equal  to  its  plane  surface. 


THE  PYRAMID. 

To  Find  the  Convex  Surface  of  a Pyramid. — Multiply  the  per- 
imeter of  the  base  by  one-half  the  slant  height. 

To  find  the  entire  surface,  add  the  area  of  the  base. 

To  Find  the  Contents  of  a Pyramid.— Multiply  the  area  of  the 
base  by  one-third  of  the  altitude. 


THE  CONE. 


To  Find  the  Convex  Surface  of  a Cone.— Multiply 
the  circumference  of  the  base  by  one-half  the 
slant  height. 

To  find  the  entire  surface,  add  the  area  of  the 
base. 

To  Find  the  Contents  of  a Cone.— Multiply  the  area 
of  the  base  by  one-third  of  the  altitude. 


34 


MENSURATION, 


THE  FRUSTUM  OF  A PYRAMID  OR  CONE. 

To  Find  the  Convex  Surface.— Multiply  one-half  of  the  sum  of  the  perim- 
eters or  circumferences  of  the  two  bases 
by  the  slant  height. 

The  entire  surface  is  found  by  adding 
the  areas  of  the  two  bases. 

To  Find  the  Contents  of  a Frustum. — Add 
together  the  sum  of  the  two  bases  and 
the  square  root  of  their  product,  and  mul- 
tiply the  sum  by  one-third  of  the  altitude  of  the  frustum. 


CYLINDRICAL  RINGS. 

A cylindrical  ring  is  formed  by  bending  a cylinder  or  pipe  until  its  two 
ends  meet. 

To  Find  the  Surface  of  a Cyiindrical  Ring. — To  the  thickness 
of  the  ring,  add  the  inner  diameter,  multiply  this  sum  by  the 
thickness  of  the  ring,  and  the  product  by  9.8696. 

To  Find  the  Contents  of  a Cylindrical  Ring.— To  the  thickness 
of  the  ring  add  the  inner  diameter,  multiply  this  sum  by 
the  square  of  one-half  the  thickness. 

To  Find  the  Volume  of  an  Irregular  Body.— Fill  a vessel  of 
known  dimensions  with  water,  and  immerse  the  body.  The  contents  will 
equal  the  volume  of  water  displaced. 


THE  PRISMOIDAL  FORMULA. 

This  formula  is  the  invention  of  Mr.  El  wood  Morris,  C.  E.,  of  Philadelphia, 
and  is  extensively  used  in  calculating  the  cubical  contents  of  cuttings, 
embankments,  etc. 

It  embraces  all  parallelepipeds,  prisms,  pyramids,  cones,  wedges,  etc., 
whether  regular  or  irregular,  right  or  oblique,  with  their  frustums  when  cut 
parallel  to  their  bases.  In  fact,  it  embraces  all  solids  having  two  parallel 
faces  or  sides,  provided  these  two  faces  are  united  by  surfaces,  whether  plane 
or  curved,  on  which,  and  through  every  point  of  which,  a straight  line  may 
be  drawn  from  one  of  the  parallel  faces  to  the  other. 

To  Find  the  Contents  of  Any  Prismoid.— Add  together  the  areas  of  the  two 
parallel  surfaces,  and  four  times  the  area  of  the  section  taken  half  way 
between  them,  and  parallel  to  them;  multiply  the  sum  by  the  perpendicular 
distance  between  the  two  parallel  sides,  and  divide  the  product  by  6. 


PLANE  TRIGONOMETRY. 


Plane  trigonometry  treats  of  the  solution  of  plane  triangles. 

In  every  triangle,  there  are  six  parts — three  sides  and  three  angles.  These 
parts  are  so  related  that  when  three  of  the  parts  are  given,  one  being  a side, 
the  other  parts  may  be  found. 

An  angle  is  measured  by  the  arc  included  between  its  sides,  the  center  of 
the  circumference  being  at  the  vertex  of  the  angle. 

For  measuring  angles,  the  circumference  is  divided  into  360  equal  parts, 
called  degrees;  each  degree  into  60  equal  parts  called 

minutes. 

A quadrant  is  one-fourth  the  circumference  of  a cir- 
cle, or  90°. 

The  complement  of  an  arc  is  90°  minus  the  arc;  D C 
is  the  complement  of  B C,  and  the  angle  D 0 C is  the 
complement  of  B 0 C. 

The  supplement  of  an  arc  is  180°  minus  the  arc;  AE 
is  the  supplement  of  the  arc  B D E,  and  the  angle  B 0 E. 

In  trigonometry,  instead  of  comparing  the  angles  of 
triangles  or  the  arcs  that  measure  them,  we  compare 
the  trigonometric  functions  known  as  the  sine,  cosine^  tangent,  cotangent, 
secant,  and  cosecant. 

The  sine  of  an  arc  is  the  perpendicular  let  fall  from  one  extremity  of  the 


PLANE  TRIGONOMETRY. 


35 


arc  on  the  diameter  that  passes  through  the  other  extremity.  Thus,  CD  is 
the  sine  of  the  arc  A C. 

The  cosine  of  an  arc  is  the  sine  of  its  complement;  or  it  is  the  distance 
from  the  foot  of  the  sine  to 
the  center  of  the  circle. 

Thus,  CE  or  OD  equals  the 
cosine  of  arc  A C. 

The  tangent  of  an  arc  is  a 
line  that  is  perpendicular  to 
the  radius  at  one  extremity 
of  an  arc  and  limited  by  a 
line  passing  through  the  cen- 
ter of  the  circle  and  the  other 
extremity.  Thus,  T is  the 
tangent  of  A C. 

The  cotangent  of  an  arc  is 
equal  to  the  tangent  of  the 
compl-ement  of  the  arc. 

Thus,  B T'  is  the  cotangent 

of^a 

The  secant  of  an  arc  is  a 
line  drawn  from  the  center 
of  the  circle  through  one  extremity  of  the  arc,  and  limited  by  a tangent  at 
the  other  extremity.  Thus,  0 T is  the  secant  of  A C. 

The  cosecant  of  an  arc  is  the  secant  of  the  complement  of  the  arc.  Thus, 
0 T'  is  the  cosecant  of  A C. 

The  versed  sine  of  an  arc  is  that  part  of  the  diameter  included  between  the 
extremity  of  the  arc  and  the  foot  of  the  sine.  DA  is  the  versed  sine  of  A C. 

The  coversed  sine  is  the  versed  sine  of  the  complement  of  the  arc.  Thus, 
5 jE  is  the  CO  versed  sine  of  A C. 

From  the  above  definitions,  we  derive  the  following  simple  principles: 

1.  The  sine  of  an  arc  equals  the  sine  of  its  supplement,  and  the  cosine  of  an 
arc  equals  the  cosine  of  its  supplement. 

2.  The  tangent  of  an  arc  equals  the  tangent  of  its  supplement,  and  the  cotan- 
gent of  an  arc  equals  the  cotangent  of  its  supplement. 

3.  The  secant  of  an  arc  equals  the  secant  of  its  supplement,  and  the  cosecant 
equals  the  cosecant  of  its  supplement. 

Thus, 

sine  of  70°  = sine  of  110°.  cosine  of  70°  = cosine  of  110°. 

tangent  of  70°  = tangent  of  110°.  cotangent  of  70°  = cotangent  of  110°. 

secant  of  70°  = secant  of  110°.  cosecant  of  70°  ==  cosecant  of  110°. 

Thus,  if  you  want  to  find  the  sine  of  an  angle  of  120°  30',  look  for  the  sine 
of  180  — 120°  30',  or  59°  30',  etc. 

In  the  rt.  l\xyz,  the  following  relations  hold: 


Functions  of  the  sum  and  difference  of  two  angles: 

sin  {A  A B)  = sin  A cos  B + cos  A sin  B. 

cos  {a  B)=  cos  A cos  ^ — sin  ^ sin  B. 

sin  \A  — B)  — sin  A cos  B — cos  A sin  B. 

cos  {A  — B)  ^ cos  A cos  jB  + sin  ^ sin  B. 

Natural  sines,  tangents,  etc.  are  calculated  for  a circle  whose  radius  is 
unity,  and  logarithmic  sines,  tangents,  etc.  are  calculated  for  a circle  whose 
radius  is  10,000,000,000. 


PRACTICAL  EXAMPLES  IN  THE  SOLUTION  OF  TRIANGLES. 

Case  1.  To  Determine  the  Height  of  a Vertical  Object  Standing  on  a Horizon- 
tal Plane.— Measure  from  the  foot  of  the  object  any  convenient  horizontal 


36 


PLANE  TRIGONOMETRY. 


distance  A B;  at  the  point  A,  take  the  angle  of  elevation  B AC.  Then,  as  B 
is  known  to  be  a right  angle,  we  have  two  angles  and  the  included  side  of  a 
triangle. 

Assuming  that  the  line  A Bis  300  ft.  and  the  angle  BAC==  40°,  the  angle 
C = 180°  - (90°  + 40°)  = 50°.  Then, 
sin  C : A B ::  sin  A : B C, 
or  .766044  : 300  : : .642788  or  251.73+  ft. 

Or,  by  logarithms: 

Log  300  = 2.477121 
Log  sin  40°  = 9.808067 
12.285188 
Log  sin  50°  = 9.884254 

2.400934  or  log  of  251.73+  ft. 
Hence,  BC=  251.73+  ft. 

Case  2.  To  Find  the  Distance  of  a Vertical  Object  Whose  Height  is  Known.— At  a 
point  A,  take  the  angle  of  elevation  to  the  top  of  the  object.  Knowing  that 
the  angle  ^ is  a right  angle,  we  have  the  angles  B and  A and  the  side  B C. 

Assuming  that  the  side  B C = 200  ft.  and  the  angle 
A = 30°,  we  have  a triangle  as  follows:  Angle  A = 

300,  ^ ^ 90°^  (7  = 60°,  and  the  side  B C — 200  ft. 

Then,  sin  A:  B Gw  sin  0 : A B, 
or  .5  : 200 : : .866025  : ( ),  or  346.41  ft. 


By  logarithms: 

Log  200  = 
Log  sin  60°  = 

Log  sin  30°  = 


2.301030 
9.937531 
12.238561 
^ 9.698970 


2.539591  or  log  of  346.41  ft. 

Case  3.  To  Find  the  Distance  of  an  Inaccessible  Object.— Measure  a hori- 
zontal base  line  A By  and  take  the  angles  formed  by  the  lines  B AC  and  ABC. 

We  then  have  two  angles  and  the  included 
side.  Assuming  the  angle  A to  be  60°,  the 
angle  B 50°,  and  the  side  AB  = 500  ft.,  we 
have  the  angle  C=  180°  — (60°  + 50°)  = 70°. 
Then, 

sin  70°  : A .B  : : sin  A : B C, 
and  sin  70°  : AB  w sin  B . AC', 
or,  .939693  : 500  : : .866025 


B C,  or  460.8+, 
.766044  : A C,  or  407.6+. 


and  .939693  : 500 
By  logarithms: 

Log  500=  2.698970 
Logsin60°=  9.937531 
12.636501 
Log  sin 70°=  9.972986 

2.663515=  log  of 460.8+. 

Log500=  2.698970 
Log  sin  50°=  9.884254 
12.583224 
Logsin70°=  9.972986 

2.610238  = log  of  407.6 +. 

Case  4.  To  Find  the  Distance  Between  Two  Objects  Separated  by  an  Impassa- 
ble Barrier.— Select  any  convenient  station,  as 
C,  measure  the  lines  C A and  C B.  and  the  angle 
included  between  these  sides.  Then  we  have 
two  sides  and  the  included  angle. 

Assuming  the  angle  Cto  be  60°,  the  side  CA, 

600  ft.,  and  the  side  CB,  500  ft.,  we  have  the 
following  formula: 

CA  + CB : CA  — CB : : tan  ; tan  ^ , 

A + B _ 180°  - 60° 

^ 2 ' “ 2 


Then, 


, or  60°. 


Then,  1,100  : 100  : : tan  60°  : tan 


7^- A. 
2 * 


PLANE  TRIGONOMETRY. 


37 


or,  1,100 : 100  : : 1.732050  ; .157459,  or  tangent  of  , or  8°  57'. 

Then,  60°  + 8°  57'  = 68°  57',  or  angle  B, 

and  60°  — 8°  57'  = 51°  03',  or  angle  A. 

Having  found  the  angles,  find  the  third  side  by  the  same  method  as  Case  1. 
The  above  formula,  'worked  out  by  logarithms,  is  as  follows: 

Log  100  = 2.000000 
Log  tan  60°  = 10.238561 
12.238561 
Log  1,100  = 3.041393 

9.197168  = log  tan  of  or  8°  hT. 


Then, 

and 


(S) 


60°  + 8°  57'  = 68°  57',  or  angle  B, 

60°  — 8°  57'  = 51°  03',  or  angle  A. 

Note.— The  greater  angle  is  always  oppo- 
site the  greater  side. 

Case  5.  To  Find  the  Height  of  a Vertical 
Object  Standing  Upon  an  Inclined  Plane. — Meas- 
ure any  convenient  distance  DC  on  a line 
from  the  foot  of  the  object,  and,  at  the  point 
D,  measure  the  angles  of  elevation  EDA 
and  ED  B to  foot  and  top  of  tower.  We 
then  have  two  triangles,  both  of  which  may 
be  solved  by  Case  1,  and  the  height  above 
D of  both  the  foot  and  top  will  be  known. 

The  difference  between  them  is  the  height 
of  the  tower. 

Case  6.  To  Find  the  Height  of  an  Inaccessible  Object  Above  a Horizontal  Plane. 

Measure  any  convenient  horizontal  line  A B directly  toward  the  object,  and 
take  the  angles  of  elevation  at  A and  B.  We  will  then  have  sufficient  data 
to  work  with.  Assuming  the  line  A to  be 
1,200  ft.  long,  the  angle  A,  25°,  and  the  angle 
D B C,  40°,  we  have  the  following:  As  the 
angle  DB  C is  40°,  the  angle  ABC=  90°  — 
40°,  or  50°. 

Then,  having  the  side  B C,  and  the  angle 
D B C = 40°,  and  the  angle  B D C = 90°,  we 
find  the  side  CD  by  the  same  method  as  in 
Case  1. 

Second  Method.— li  it  is  not  convenient  to 
measure  a horizontal  base  line  toward  the 
object,  measure  any  line  AD,  Fig.  (6a),  and 
also  measure  the  horizontal  angles  BAD, 
A BD,  and  the  angle  of  elevation  D B C. 
Then,  by  means  of  the  two  triangles  ABD 
and  CBD,  the  height  CD  can  be  found. 

Then,  with  the  line  AB  and  the  angles 
BAD  and  ABD  known,  we  have  two 
angles  and  the  included  side  known.  The 
third  angle  is  readily  found,  and  the  side 
BD  can  be  found.  Then,  in  the  triangle 
B DC,  we  have  the  angle  D;  by  measure- 
ment, D = 90°,  and  we  have  the  side  B D. 

Then,  the  side  CD,  or  the  vertical  height, 
can  be  found  by  Case  1. 

Case  7.  To  Find  the  Distance  Between  Two 
Inaccessible  Objects  When  Points  Can  Be  Found 
From  Which  Both  Objects  Can  Be  Seen.— Wish- 
ing to  know  the  horizontal  distance  between 
a tree  and  a house  on  the  opposite  side  of  a river,  measure  the  line  A B,  and, 
at  point  A,  take  the  angles  DAC,  and  DAB,  and, 
at  the  point  B,  take  the  angles  CB A and  CBD. 
Assume  the  length  of  A D = 400  ft. 

Angle  DAC  = 56° 30'. 

Angle  DAB  = 42° 24'. 

Angle  CD  A = 44° 36'. 

Angle  CDD  = 68°50'. 


88 


SVnVEYING, 


In  the  triangle  ABD,  we  have  AB  = 40^  ft.,  the  angle  DAB  = 42^24', 
the  angle  ABB  = (44°  36'  + 68°  50')  = 113°  26',  and  the  angle  AD  B = 180° 
— (42°  24'  + 113°  26')  = 24°  10'.  Then,  according  to  Case  1,  lind  the  side  D B. 
We  then  have  three  angles  and  two  sides  of  the  triangle  J.  D .B.  We  find 
the  third  side  ADhy  Case  1. 

Then  in  the  triangle  AB  C,  we  have  the  angles  ABC  and  B A C\  and  the 
distance  A B.  From  these  we  find  the  side  A C.  Then,  in  the  triangle  ADC, 
we  have  the  sides  A D and  A C,  and  the  angle  D A C,  and  we  then  find  the 
side  CDhy  Case  4.  


SURVEYING. 


Surveying  is  an  extension  of  mensuration,  and,  as  ordinarily  practiced, 
may  be  divided  into  surface  work,  or  ordinary  surveying,  and  underground 
work,  or  mine  surveying.  With  slight  modifications,  the  instruments 
employed  in  both  are  the  same,  and  consist  of  a compass— if  the  work  is  of  little 
importance,  and  accuracy  is  not  required— a transit,  level,  transit  and  level 
rods,  steel  tape  or  chain,  and  measuring  pins,  and  sometimes  certain  acces- 
sory instruments,  as  clinometers  or  slope  levels,  dipping  needles,  etc.,  as  will 
be  described  later. 

As  the  instrumental  work  is  generally  the  same  in  both  kinds  of  survey- 
ing, a description  of  the  instruments  and  the  usual  practice  on  the  surface 
will  be  first  given,  and  afterwards  an  account  of  the  methods  of  mine  survey- 
ing as  practiced  in  the  anthracite  regions  of  Pennsylvania,  with  the 
deviations  from  the  practice  of  the  former. 


THE  COMPASS. 

The  compass  may  be  either  a pocket  compass,  or  a surveyor’s  compass, 
and  may  be  used  by  holding  in  the  hand,  or  with  a tripod.  The  Jacob’s 
staff,  convenient  for  use  on  the  surface,  is  frequently  useless  in  the  mine. 
The  compass  is  not  accurate  enough  for  the  construction  of  a general  map  of 
the  mine.  It  is  useful  inasmuch  as  it  enables  the  mine  foreman  to  readily 
secure  an  approximate  idea  of  the  shape  of  the  workings,  and,  from  a plan 
constructed  by  its  use,  he  can  get  an  approximate  course  on  which  to  drive  an 
opening  designed  to  connect  two  or  more  given  points.  If  the  opening  is  one 
that  will  be  expensive  to  drive,  and  should  be  straight,  the  compass  survey 
should  never  be  relied  on. 


TO  ADJUST  THE  COMPASS. 

The  Levels.— First  bri  \g  the  bubbles  into  the  center  by  the  pressure  of  the 
hand  on  different  partt  of  the  plate,  and  then  turn  the  compass  half  way 
around;  should  the  bubbles  run  to  the  ends  of  the  tubes,  it  would  indicate 
that  those  ends  were  tJie  higher;  lower  them  by  tightening  the  screws 
immediately  under,  and  loosening  those  under  the  lower  ends  until,  by 
estimation,  the  error  is  half  removed;  level  the  plate  again,  and  repeat  the 
first  operation  until  the  bubbles  will  remain  in  the  center  during  an  entire 
revolution  of  the  compass. 

The  sights  may  next  be  tested  by  observing  through  the  slits  a fine  hair  or 
thread,  made  exactly  vertical  by  a plumb.  Should  the  hair  appear  on  one 
side  of  the  slit,  the  sight  must  be  adjusted  by  filing  off  its  under  surface  on 
the  side  that  seems  the  higher. 

The  needle  is  adjusted  in  the  following  manner:  Having  the  eye  nearly  in 
the  same  plane  with  the  graduated  rim  of  the  compass  circle,  with  a small 
splinter  of  wood,  or  a slender  iron  wire,  bring  one  end  of  the  needle  in  line 
with  any  prominent  division  of  the  circle,  as  the  zero  or  90°  mark,  and  notice 
if  the  other  end  corresponds  with  the  degree  on  the  opposite  side;  if  it  does, 
the  needle  is  said  to  cut  opposite  degrees;  if  not,  bend  the  center  pin  by 
applying  a small  brass  wrench,  furnished  with  most  compasses,  about  one- 
eighth  of  an  inch  below  the  point  of  the  pin,  until  the  ends  of  the  needle 
are  brought  into  line  with  the  opposite  degrees. 

Then,  holding  the  needle  in  the  same  position,  turn  the  compass  half  way 
around,  and  note  whether  it  now  cuts  opposite  degrees;  if  not,  correct  half 
the  error  by  bending  the  needle,  and  the  remainder  by  bending  the  center  pin. 

The  operation  must  be  repeated  until  perfect  reversion  is  secured  in  the 
first  position.  This  being  obtained,  it  may  be  tried  on  another  quarter  of  the 


MAGNETIC  VARIATION. 


39 


circle;  if  any  error  is  there  manifested,  the  correction  must  be  made  in 
the  center  pin  only,  the  needle  being  already  straightened  by  the  previous 
operation. 

When  again  made  to  cut,  it  should  be  tried  on  the  other  quarters  of  the 
circle,  and  corrections  made  in  the  same  manner  until  the  error  is  entirely 
removed,  and  the  needle  will  reverse  in  every  point  of  the  divided  circle. 


TO  USE  THE  COMPASS. 

In  using  the  compass,  the  surveyor  should  keep  the  south  end  toward  his 
person,  and  read  the  bearings  from  the  north  end  of  the  needle.  In  the  sur- 
veyor’s compass,  he  will  observe  that  the  position  of  the  E and  W letters  on 
the  face  of  the  compass  are  reversed  from  their  natural  position,  in  order 
that  the  direction  of  the  sight  may  be  correctly  read. 

The  compass  circle  being  graduated  to  half  degrees,  a little  practice  will 
enable  the  surveyor  to  read  the  bearings  to  quarters— estimating  with  his 
eye  the  space  bisected  by  the  point  of  the  needle. 

The  compass  is  usually  divided  into  quadrants,  and  zero  is  placed  at  the 
north  and  south  ends.  90°  is  placed  at  the  E and  W marks,  and  the  gradua- 
tions run  right  and  left  from  the  zero  marks  to  90°.  In  reading  the  bearing, 
the  surveyor  will  notice  that  if  the  sights  are  pointed  in  a N W direction,  the 
north  end  of  the  needle,  which  always  points  approximately  north,  is  to  the 
right  of  the  front  sight  or  front  end  of  the  telescope,  and,  as  the  number  of 
degrees  is  read  from  it,  the  letters  marking  the  cardinal  points  of  the  compass 
read  correctly.  If  the  E,  or  east,  mark  were  on  the  right  side  of  the  circle,  a 
N W course  would  read  N E.  This  same  remark  applies  to  all  four  quadrants. 
The  compass  should  always  be  in  a level  position. 


MAGNETIC  VARIATION. 

Magnetic  declination  or  variation  of  the  needle  is  the  angle  made  by  the 
magnetic  meridian  with  the  true  meridian  or  true  north  and  south  line.  It 
is  east  or  west  according  as  the  north  end  of  the  needle  lies  east  or  west  of 
the  true  meridian.  It  is  not  constant,  but  changes  from  year  to  year,  and, 
for  this  reason,  in  rerunning  the  lines  of  a tract  of  land,  from  field  notes  of 
some  years’  standing,  the  surveyor  makes  an  allowance  in  the  bearing  of 
every  line  by  means  of  a ver- 
nier that  is  so  graduated  that 
30  spaces  on  it  equal  31  on  the 
limb  of  the  instrument,  as' 
shown  in  the  figure. 

To  Read  the  Vernier.— As  the 
compass  vernier  is  usually  so 
made  that  there  are  but  15 
spaces  on  each  side  of  the  zero 
mark,  it  is  read  as  follows: 

Note  the  degrees  and  half 

degrees  on  the  limb  of  the  instrument.  If  the  space  passed  beyond  the 
degree  or  half-degree  mark  by  the  zero  mark  on  the  vernier  is  less  than 
one-half  the  space  of  half  a degree  on  the  limb,  the  number  of  minutes  is, 
of  course,  less  than  15,  and  must  be  read  from  the  lower  row  of  figures.  If  the 
space  passed  is  greater  than  one-half  the  spacing  on  the  limb,  read  the  upper 
row  of  figures.  The  line  on  the  vernier  that  exactly  coincides  with  a line  on 
the  limb  is  the  mark  that  denotes  the  number  of  minutes.  If  the  index  is 
moved  to  the  right,  read  the  minutes  from  the  left  half  of  the  vernier;  if  moved 
to  the  left,  read  the  right  side  of  the  vernier. 

To  Turn  Off  the  Variation.— Moving  the  vernier  to  either  side,  and  with  it,  of 
course,  the  compass  circle  attached,  set  the  compass  to  any  variation  by 
placing  the  instrument  on  some  well-defined  line  of  the  old  survey,  and  by 
turning  the  tangent  screw  (slow-motion  screw)  until  the  needle  of  the  com- 
pass indicates  the  same  bearing  as  that  given  in  the  old  field  notes  of  the 
original  survey.  Then  screw  up  the  clamping  nut  underneath  the  vernier 
and  run  all  the  other  lines  from  the  old  field  notes  without  further  alteration. 

The  reading  of  the  vernier  on  the  limb  gives  the  amount  of  variation  since 
the  original  survey  was  made. 

The  accompanying  map  shows  the  general  course  and  direction  of  isogonic 
lines  (those  passing  through  points  where  the  magnetic  needle  has  the  same 


40 


SURVEYING, 


declination),  in  all  parts  of  the  United  States  and  Mexico  for  the  year  1900. 
These  lines  are  drawn  full  when  compiled  from  reliable  records,  but  dotted 
in  other  places.  The  declination  is  marked  in  degrees  at  each  end  of  every 
alternate  line,  the  sign  + indicating  a west  declination,  and  the  sign  — an 
east  declination.  The  yearly  variation,  or  change  of  declination,  for  the 
period  1895-1900  is  marked  in  numerous  places  on  the  map.  The  annual 
change  in  declination  is  given  in  minutes;  a + sign  signifies  increasing  west 
or  decreasing  east  declination,  a — sign  the  reverse  motion.  Stations  to  the 
right  of  the  agonic  curve,  or  curve  of  no  declination,  have  west  declination, 
and  those  to  the  left,  east  declination.  The  large  black  circles  or  dots 
indicate  the  capitals  of  the  several  states. 

The  use  of  this  chart  is  quite  simple.  The  declination  for  any  place 
within  its  borders  is  either  found  by  inspection  or  by  simple  interpolation 
between  the  two  adjacent  curves;  the  value  found  is  for  1900.  For  any 
other  year  (and  fraction),  a reduction  for  secular  change  between  the  epoch 
and  given  date  must  be  applied.  The  annual  change  of  the  declination 
during  the  period  1895-1900,  expressed  in  minutes  of  arc,  is  indicated  in 
the  chart  ( + for  increasing  west  or  decreasing  east  declination  and  for 
the  reverse  motion).  The  amount  varies  in  timej  but  not  sufficiently  during 
a brief  interval  of  years  to  cause  any  serious  inaccuracy,  and  the  values  given 
on  the  chart  can  be  used  for  a number  of  years  to  come  for  all  practical 
purposes;  its  variation  with  geographical  position  must  be  estimated  from 
the  map. 


THE  TRANSIT. 

The  tra  nsit  is  the  only  instrument  that  should  be  used  for  measuring  angles 
in  any  survey  where  great  accuracy  is  desired.  The  advantages  of  a transit 
over  a vernier  compass  are  mainly  due  to  the  use  of  a telescope.  By  its  use 
angles  can  be  measured  either  vertically  or  horizontally,  and,  as  the  vernier 
is  used  throughout,  extreme  accuracy  is  secured. 

The  illustration  shows  the  interior  construction  of  the  sockets  of  a transit 
having  two  verniers  to  the  limb,  the  manner  in  which  it  is  detached  from  its 

spindle,  and  how  it 
can  be  taken  apart 
when  desired.  The 
limb  h is  attached  to 
the  main  socket  c, 
which  is  carefully 
fitted  to  the  conical 
spindle  h,  and  held 
in  place  by  the  spring 
catch  s. 

The  upper  plate  a, 
carrying  the  compass 
circle,  standards, 
etc.,  is  fastened  to  the 
flanges  of  the  socket 
k,  which  is  fitted  to 
the  upper  conical 
surface  of  the  main 
socket  c.  The  weight 
of  all  the  parts  is  sup- 
ported on  the  small 
bearings  of  the  end 
of  the  socket,  as 
shown,  so  as  to  make  as  little  friction  as  possible  where  such  parts  are 
being  turned  as  a whole. 

A small  conical  center,  in  which  a strong  screw  is  inserted  from  below,  is 
brought  down  firmly  on  the  upper  end  of  the  main  socket  c,  thus  holding  the 
two  plates  of  the  instrument  securely  together,  and,  at  the  same  time,  allow- 
ing them  to  move  freely  around  each  other.  The  steel  center  pin  on  which 
the  needle  rests  is  held  by  the  small  disk  fastened  to  the  upper  plate  by 
two  small  screws  above  the  conical  center.  The  clamp  to  limb  dj,  with 
clamp  screw,  is  attached  to  the  main  socket.  The  instrument  is  leveled  by 
means  of  the  leveling  screws  I and  placed  exactly  over  a point  by  means  of 
the  shifting  center.  The  plummet  is  attached  to  the  loop  p. 

The  verniers  on  a transit  differ  from  those  on  a compass  in  detail  only. 


m-- 

te' 


ADJUSTING  THE  TRANSIT. 


41 


The  principle  is  the  same.  The  transit  vernier  is  so  divided  that  30  spaces  on 
it  equal  in  length  29  on  the  limb  of  the  instrument.  The  method  of  reading 
it  is  practically  the  same  as  reading  a compass  verniei,  except  that  on 
the  transit  the  vernier  is  made  with  all  of  the  30  divisions  on  one  side  of  the 
zero  mark. 

Each  division  of  the  vernier  is  therefore  or,  in  other  words,  1 minute 
shorter  than  the  half-degree  graduations  on  the  limb. 

In  the  figure  the  reading  is  20°  10'.  If  the  zero  on  the  vernier  should  be 
beyond  20i°  on  the  limb  of 
the  transit,  and  the  line 
marked  10  should  coincide 
with  a line  on  the  limb,  the 
reading  would  be  20°  40'. 

In  case  the  12th  line  from 
zero  should  coincide  with  a 
line  on  the  limb,  the  read- 
ing would  be  20°  42',  etc. 

In  some  transits,  the 
graduated  limb  has  two 
sets  of  concentric  gradua- 
tions, the  zero  in  both  being 
the  same,  and,  while  the  outside  set  is  marked  from  0°  each  way  to  90°,  and 
thence  to  0°  on  the  opposite  side  of  the  circle,  the  other  set  is  marked  from 
0°  to  360°  to  the  right,  as  a clock  face.  The  inside  set  has  the  N,  S,  E,  and  W 
points  marked,  the  0°  of  the  inside  set  being  taken  as  north. 

The  interior  of  the  telescope  is  fitted  up  with  a diaphragm  or  cross- wire 
ring  to  which  cross-wires  are  attached.  These  cross-wires  are  either  of 
platinum  or  are  strands  of  spider  web.  For  inside  work,  platinum  should 
be  used,  as  spider  web  is  translucent  and  cannot  readily  be  seen.  They  are 
set  at  right  angles  to  each  other  and  are  so  arranged  that  one  can  be 
adjusted  so  as  to  be  vertical  and  the  other  horizontal.  This  diaphragm  is 
suspended  in  the  telescope  by  four  capstan-headed  screws,  and  can  be  moved 
in  either  direction  by  working  the  screws  with  an  ordinary  adjusting  pin. 
The  transit  should  not  be  subjected  to  sudden  changes  in  temperature  that 
may  break  the  cross-hairs.  In  case  of  a break,  remove  the  cross-hair 
diaphragm  and  replace  the  broken  wire. 

The  intersection  of  the  wires  forms  a very  minute  point,  which,  when 
they  are  adjusted,  determines  the  optical  axis  of  the  telescope,  and  enables 
the  surveyor  to  fix  it  upon  an  object  with  the  greatest  precision. 

The  imaginary  line  passing  through  the  optical  axis  of  the  telescope  is 
termed  the  line  of  collimation,  and  the  operation  of  bringing  the  intersection  of 
the  wires  into  the  optical  axis  is  called  the  adjustment  of  the  line  of  collimation. 

All  screws  and  movable  parts  should  be  covered,  so  as  to  keep  out  acid 
water  or  dust.  If  this  is  not  done,  the  mine  work  will  soon  use  up  a transit. 
The  vertical  circle  on  the  transit  may  be  a full  circle  or  a segment.  The 
former  is  to  be  preferred,  as  it  is  always  ready  without  intermediate  clamp 
screws.  If  the  dip  of  a sight  is  to  be  taken,  the  tape  must  be  held  at  the 
transit  head,  and  stretched  in  the  line  of  sight.  If  the,  pitch  of  the  ground  is 
to  be  taken,  the  point  of  foresight  must  be  at  the  same  height  as  the  axis  of 
the  transit,  and  the  sight  will  then  be  parallel  to  the  surface.  The  angle  of 
dip  is  read  “ plus  ” or  “ minus,”  as  it  is  above  or  below  the  horizontal  plane. 
If  we  have  the  dip  of  a sight,  and  the  distance  between  the  transit  head  and 
the  point  of  sight,  we  can  get  the  vertical  and  horizontal  components  of  that 
distance  from  the  table  of  sines  and  cosines. 


ADJUSTMENTS  OF  THE  TRANSIT. 

The  use  of  a transit  tends  to  disarrange  some  of  its  parts,  which  detracts 
from  the  accuracy  of  its  work,  but  in  no  way  injures  the  instrument  itself. 
Correcting  this  disarrangement  of  parts  is  called  adjusting  the  transit. 

First  Adjustment. — To  make  the  level  tubes  parallel  to  the  vernier  plate. 

Plant  tne  feet  of  the  tripod  firmly  in  the  ground.  Turn  the  instrument 
until  one  of  the  levels  is  parallel  to  a pair  of  opposite  leveling  screws;  the 
other  level  will  be  parallel  to  the  other  pair.  Bring  the  bubble  in  each  tube 
to  the  middle  with  the  pair  of  leveling  screws  to  which  the  tube  is  parallel. 
Next  turn  the  vernier  plate  half  way  around;  that  is,  revolve  it  through  an 
angle  of  180°.  If  the  bubbles  have  remained  in  the  middle  of  the  tubes,  the 
levels  are  in  proper  adjustment.  If  they  have  not  remained  so,  but  have 


42 


SURVEYING. 


moved  toward  either  end,  bring  them  half  way  back  to  the  middle  of  the 
tubes  by  means  of  the  capstan-headed  screws  attached  to  the  tubes,  and  the 
rest  of  the  way  back  by  the  leveling  screws.  Again  turn  the  vernier  plate 
through  180°,  and  if  the  bubbles  do  not  remain  at  the  middle  of  the  tubes, 
repeat  the  correction.  Sometimes  the  adjustment  is  made  by  one  trial,  but 
usually  it  is  necessary  to  repeat  the  operation.  Each  level  must  be  adjusted 
separately. 

Second  Adjustment.— To  make  the  line  of  collimation  perpendicular  to  the 
horizontal  axis  that  supports  the  telescope. 

With  the  instrument  firmly  set  at  A,  and  carefully  leveled,  sight  to  a pin 
or  tack  set  at  a point  B,  about  400  ft.  distant,  and  on  level  or  nearly  level 

ground.  Reverse  the  tele- 

Q - 2>  scope;  that  is,  turn  it  over  on 

f its  axis  until  it  points  in  the 

" jIqq'  opposite  direction,  and  set  a 

*UO  point  at  about  the  same  dis- 

tance, which  will  be  at  D, 
for  example,  if  this  adjustment  needs  correction.  Unclamp  the  vernier 
plate,  and,  without  touching  the  telescope,  revolve  the  instrument  about 
its  vertical  axis  sufficiently  far  to  take  another  sight  upon  the  point  B. 
Then  turn  the  telescope  on  its  axis  and  locate  a third  point,  as  at  C. 
Measure  the  distance  CD,  and  at  E,  one-fourth  of  the  distance  from  Cto  D, 
set  the  pin  or  tack.  Move  the  cross-hairs,  by  means  of  the  capstan-headed 
screws,  until  the  vertical  hair  exactly  covers  the  pin  at  E,  being  careful 
to  move  it  in  the  opposite  direction  from  that  in  which  it  appears  it  should 
be  moved.  Having  done  this,  and  then  having  reversed  the  telescope,  the 
line  of  sight  will  not  be  at  the  point  B,  but  at  G,  a distance  from  B equal 
to  CE.  Again  sight  to  B,  then  reverse,  and  the  pin  will  be  at  F in  the 
same  straight  line  with  A B.  It  may  be  necessary  to  repeat  the  operation 
to  secure  an  exact  adjustment. 

Third  Adjustment.— To  make  the  horizontal  axis  of  the  telescope  parallel  to  the 
vernier  plate,  so  that  the  line  of  collimation  will  revolve  in  a vertical  plane. 

Sight  to  some  point  A at  the  top  of  a building,  so  that  the  tele- 
scope will  be  elevated  at  a large  angle.  Depress  the  telescope, 
and  set  a pin  on  the  ground  below  at  a point  B.  Loosen  the 
clamp,  turn  over  the  telescope,  and  turn  the  plate  around  suffi- 
ciently far  to  take  an  approximately  accurate  sight  upon  the 
point  A.  Then  clamp  the  instrument  and  again  take  an  exact 
sight  to  the  point  A.  Next  depress  the  telescope,  and  set  another 

Sin  on  the  ground,  which  will  come  at  C.  The  distance  R (7  is 
ouble  the  error  of  adjustment.  Correct  the  error  by  raising 
or  lowering  one  end  of  the  telescope  axis  by  means  of  a small 
screw  placed  in  the  standard  for  that  purpose.  The  amount 
the  screw  must  be  turned  is  determined  only  by  repeated  trials. 

Fourth  Adjustment.— To  make  the  axis  of  the  attached  level  of  the 
telescope  parallel  to  the  line  of  collimation. 

Drive  two  stakes  at  equal  distances  from  the  instrument  and 
in  exactly  opposite  directions.  Level  the  plate  carefully,  and 
clamp  the  telescope  in  a horizontal  position,  or  as  nearlv  so  as 
possible.  Sight  to  a rod  placed  alternately  upon  each  stake,  and  have 
the  stakes  driven  down  until  the  rod  reading  is  the  same  on  both  stakes. 
When  this  condition  is  reached,  the  heads  of  the  stakes  are  at  the  same 
level.  Then  move  the  instrument  beyond  one  stake  and  set  it  up  so  that 
it  will  be  in  line  with  both  stakes.  Level  the  plate  again  and  elevate  or 
depress  the  telescope  so  that,  when  a sight  is  taken  to  the  rod  held  on  first 
one  stake  and  then  on  the  other,  the  reading  will  be  alike  on  both.  In 
this  position,  the  line  of  collimation  is  level,  and  the  bubble  in  the  level 
attached  to  the  telescope  should  stand  in  the  center  of  the  bubble  tube.  If 
it  does  not,  bring  it  to  the  center  by  turning  the  nuts  at  the  ends  of  the  tube, 
being  careful  at  the  same  time  to  keep  the  telescope  in  the  position  that 
gives  equal  rod  readings  on  both  stakes. 


THE  CHAIN  OR  STEEL  TAPE  AND  PINS. 

The  chain,  which  is  generally  50  or  100  ft.  long,  should  be  made  of  annealed 
steel  wire,  each  link  exactly  1 ft.  in  length.  The  links  should  be  so  made  as 
to  reduce  the  liability  to  kink  to  a minimum.  All  joints  should  be  brazed, 
and  handles  at  each  end  of  D shape,  or  modifications  of  D shape,  should  be 


CHAIN  AND  PINS. 


43 


provided.  These  handles  should  he  attached  to  short  links  at  each  end,  and 
the  combined  length  of  each  of  these  short  links  and  one  handle  should  be 
exactly  1 ft.  The  handles  should  be  attached  to  the  short  link  in  such  a 
manner  that  the  chain  may  be  slightly  lengthened  or  shortened  by  screwing 
up  a nut  at  the  handle.  It  should  be  divided  every  10  ft.  with  a brass  tag,  on 
which  either  the  number  of  points  represents  the  number  of  tens  from  the 
front  end,  or  the  number  of  tens  may  be  designated  by  figures  stamped  on 
the  tags. 

When  a chain  is  purchased,  one  that  has  been  warranted  as  “ Correct,!!.  S. 
Standard,”  should  be  selected,  and,  before  using  it,  it  should  be  stretched  on 
a level  surface,  care  being  taken  that  it  is  straight,  and  no  kinks  in  it,  and 
the  extremities  marked  by  some  permanent  mark.  These  marks  can  be 
used  in  the  future  to  test  the  chain.  It  should  be  tested  frequently,  and  the 
length  kept  to  the  standard  as  marked  when  it  was  new. 

In  chaining,  the  chainmen  should  always  remember  the  axiom  that  a 
straight  line  is  the  shortest  distance  between  two  points.  Ordinarily,  the  chain 
should  be  held  horizontally,  and  if  either  end  is  held  above  the  ground,  a 
plumb-bob  and  line  should  be  used  to  mark  the  end  of  the  chain  on  the 
ground.  If  used  on  a regular  incline,  the  chain  may  be  stretched  along  the 
incline,  and,  by  having  the  amount  of  declination,  the  horizontal  and 
vertical  distances  may  either  be  calculated  or  found  in  the  Traverse  Table. 

For  accuracy,  steel  tapes  are  now  almost  exclusively  used  by  the  leading 
mining  engineers,  on  account  of  their  greater  accuracy  as  compared  with 
chains. 

The  steel  tape  is  simply  a ribbon  of  steel,  on  which  are  marked,  by  etching, 
or  other  means,  the  different  graduations,  which  may  be  down  to  inches  or 
tenths  of  a foot,  or  may  be  only  every  foot.  It  is  wound  on  a reel,  and  may 
be  any  desired  length  up  to  500  ft. 

A well-made  tape  should  not  vary  ft.  in  100  ft.,  at  any  given  standard 
of  temperature.  The  steel  of  the  tape  should  not  be  too  high  in  carbon,  or  it 
will  be  brittle  and  liable  to  snap  on  a short  bend,  nor  should  it  be  of  too  soft 
steel,  or  it  will  stretch  when  strongly  pulled. 

Careful  gunsmiths  can  make  and  repair  steel  tapes  v/ith  a high  degree  of 
accuracy,  and  fully  as  reasonably  as  the  instrument  makers.  For  outside 
work,  tapes  1,000  ft.  long  have  been  made,  but  500  ft.  will  be  found  as  long  as 
can  well  be  used  in  a mine,  owing  to  the  lack  of  long  sights,  and  to  the 
increased  weight  of  so  long  a tape.  The  average  length  is  300  ft.  The  300  ft. 
are  divided  into  10-ft.,  5-ft.,  2-ft.,  or  1-ft.  lengths,  as  desired,  and  the  tenths 
and  hundredths  of  a foot  are  read  by  means  of  a pocket  tape  or  measuring 
pin.  Sometimes  there  is  an  extra  division  before  the  zero  mark,  which  is 
divided  into  feet  and  the  first  foot  into  tenths.  With  such  a tape,  a distance 
can  be  accurately  measured  to  tenths,  or  even  quite  approximately  to 
hundredths  of  a foot. 

The  ends  are  fitted  with  eyes  on  swivel-joints,  to  prevent  straining  by 
twisting.  Handles  of  various  forms  have  been  devised  to  enable  the  tape  to 
be  stretched,  or  to  clamp  a broken  end.  Some  parties  use  ordinary  springs 
to  prevent  overstraining,  and,  in  certain  cases,  spring  scales  are  used,  and 
the  same  degree  of  tension  can  be  readily  produced,  and,  in  this  way,  the 
exact  amount  of  sag  can  be  calculated  for  any  length,  and  the  necessary 
correction  made.  To  keep  a mark  on  the  tape  for  frequent  reference,  a clip 
(made  by  bending  sharply  on  itself  a piece  of  steel  i in.  X 3 in.)  is  slipped 
upon  the  tape,  where  it  will  remain  unless  subjected  to  considerable  force. 
Reels  for  winding  the  tape  are  made  of  iron  or  wood,  and  vary  greatly  in 
size  and  shape. 

When  distances  do  not  come  at  even  feet,  the  fractional  part  of  the  foot 
should  always  be  noted  in  tenths.  Thus,  53  ft.  and  6 in.  should  always 
be  noted  as  53.5  ft. 

Pins.— Pins  should  be  from  15  to  18  in.  long,  made  of  tempered-steel  wire, 
and  should  be  pointed  at  one  end,  and  turned  with  a ring  for  a handle. 
When  using  a 50-ft.  chain,  a set  of  pins  should  consist  of  eleven,  one  of  which 
should  be  distinguished  by  some  peculiar  mark.  This  should  be  the  last  pin 
stuck  by  the  front  chainman.  When  all  eleven  pins  have  been  stuck,  the 
front  chainman  calls  “Out!”  and  the  back  chainman  comes  forward  and 
delivers  him  the  ten  pins  that  he  has  picked  up,  and  he  notes  the  “out.” 
When  giving  the  distance  to  the  transitman,  he  counts  his  “outs,”  each  of 
which  consists  of  500  ft.,  and  adds  to  their  sum  the  number  of  fifties  as  denoted 
by  the  pins  in  his  possession,  and  the  odd  number  of  feet  and  fractional  parts 
of  a foot  from  the  last  pin  to  the  front  end  of  the  chain. 


44 


SURVEYING, 


The  accuracy  and  value  of  a survey  depend  as  much  on  the  careful  work 
of  the  chainmen  as  on  anything  else,  and  no  one  should  be  allowed  to 
either  drag  or  read  the  chain  that  is  not  intelligent  enough  to  appreciate  the 
importance  of  extreme  accuracy. 

Pins  are  generally  used  in  outside  work,  where  they  can  be  easily  stuck 
into  the  ^ound,  readily  seen,  and  avoided,  and  the  chances  of  their  being 
disturbed  are  slight.  Inside  work  generally  contains  so  many  chances  of 
error  in  their  use  that  they  are  usually  abandoned  in  favor  of  other 
methods.  If  the  sight  be  longer  than  the  length  of  the  tape,  it  is  usual  to 
drive  a tack  in  a sill  or  a collar  at  a point  intermediate  between  the  stations, 
and  take  a measurement  to  the  tack  from  each  station,  with  the  dip  of  the 
sights;  or  a tripod  is  set  up  in  the  line  of  sight,  and  the  horizontal  distance 
is  measured  from  each  station  to  the  string  of  the  plumb-bob  under  the 
tripod.  The  first  method  is  the  more  accurate, 

Plumb-Bob.— The  plumb-bob  takes  the  place  of  the  transit  rod  in  under- 
ground work,  as  the  stations  are  usually  in  the  roof,  and  strings  are  hung  from 
them  to  furnish  foresights  and  backsights.  Plumb-bobs  vary  in  weight  and 
shape.  At  various  times  and  in  various  countries  where  mine  surveys  have 
been  made,  the  idea  of  sighting  at  a flame  has  been  considered,  and,  from 
rough  methods  of  setting  a lamp  on  the  floor  on  foresight  and  backsight, 
there  have  arisen  various  forms  of  plummet  lamps.  The  idea  is  to  continue 
the  practice  of  sighting  to  a flame,  but  to  make  that  flame  exactly  under  the 
station,  and  to  avoid  the  difficulty  in  sighting  to  the  string  of  the  plummet. 
The  idea  is  good,  but  there  has  never  been  devised  a plummet  lamp  that 
would  be  as  free  from  error  under  all  circumstances  as  the  old-ffishioned 
plummet,  so  that  the  majority  of  the  best  engineers  have  gone  bac  ^ to  the 
plummet.  The  best  plummet  is  the  one  that  combines  the  least  surface  with 
the  greatest  weight,  and  the  ordinary  shapes  used  for  outside  work  are  the 
best  for  inside  also.  In  a “ windy  ” place,  a hole  can  be  dug  in  the  ballast 
of  the  track  and  the  “ bob  ” let  into  this  shelter  where  it  will  be  unaffected 
by  the  air.  The  cord  is  best  illuminated  by  placing  a white  paper  or  card- 
board behind  it  and  holding  the  lamp  in  front  and  to  one  side.  The  string 
shows  as  a dark  line  against  a white  ground,  and  there  is  less  difficulty  in 
finding  it  than  when  the  light  is  placed  exactly  behind  it,  and  in  this  way  a 
careless  man  cannot  burn  the  string  by  poking  the  flame  against  it.  The 
white  background  will  also  illuminate  the  cross-hairs  of  the  transit.  The 
backsight  “ bob  ” can  be  made  of  lead,  as  there  are  no  “ centers  ” to  be  set  by 
this  man.  A number  of  varieties  have  been  made  for  the  foresight,  to  aid  him 
in  “ center  setting  but  all  get  out  of  order  easily.  A quick  man  will  do  as 
good  work  with  the  old-style  bob,  and  have  none  of  the  accidents  common 
to  the  others.  In  general,  it  may  be  said  that  the  instruments  used  for  outside 
work  will  be  sufficient  for  mine  work  also. 

The  clinometer,  or  slope  level,  is  a valuable  instrument  for  side-note  work; 
but  it  is  not  accurate  enough  for  a survey,  and  its  place  is  taken  by  the 
vertical  circle  on  the  transit.  There  are  two  styles  of  clinometer,  with  a 
bubble  and  with  a pendulum.  The  latter  is  the  old-fashioned  and  more 
accurate  German  “ Gradbogen”  that  is  found  on  some  old  corps.  The  bubble 
variety  is  much  more  easily  rendered  worthless  by  the  breaking  of  the  bubble 
tube,  and  in  general  is  not  so  accurate  as  the  other  style,  which  consists  of  a 
semicircular  protractor  cut  out  of  thin  brass  and  furnished  with  hooks  at 
each  end,  that  it  can  be  hung  on  a stretched  string  so  that  the  string  will 
pass  through  the  0°  and  180°  points.  The  dip  is  read  by  a pendulum  swung 
from  the  center  of  the  circle.  If  made  sufficiently  large  it  will  readily  read 
to  quarter  degrees.  By  inclining  the  string  parallel  to  the  surface  and 
hanging  the  clinometer,  the  dip  will  be  obtained.  A pocket  instrument 
combining  a compass  and  clinometer  can  be  obtained  from  any  dealer  in 
surveying  instruments.  

FIELD  NOTES  FOR  AN  OUTSIDE  COMPASS  SURVEY. 

Call  place  of  beginning  Station  1. 

Stations.  Bearings.  Distances. 

1-2  N 35°  E 270.0 

At  1 -f  37  ft.  crossed  small  stream  3 ft.  wide. 

At  1 -f- 116  ft.  = first  side  of  road. 

At  1 -h  131  ft.  = second  side  of  road. 

At  1 -f  137  ft.  = blazed  and  painted  pine  tree,  3 ft.  left,  marked  for  a 
“go  by.” 


TRANSIT  SUE  VEYTNG. 


45 


Station  2 is  a stake  at  foot  of  white-oak  tree,  blazed  and  painted  on  four 
sides  for  corner. 

2- 3  N 831°  E 129.0 

Station  3 is  a stake-and-stones  corner. 

3- 4  S 57°  E 222.0 

3  -f  64  ft.  = center  of  small  stream  2 ft.  wide. 

3 + 196  ft.  = white  oak  “ go  by,”  2 ft.  right. 

Station  4 = cut  stone  corner. 

4- 5  S 34i°  W 355.0 

4 + 174  ft.  = ledge  of  sandstone  10  ft.  thick,  dipping  27°  south. 

5- 1  N 56i°  W 323.0 

5 + 274  ft.  = ledge  of  sandstone  10  ft.  thick,  dipping  25°  south  (evidently 

continuation  of  same  ledge  as  at  4 + 174). 

Station  1 = place  of  beginning. 


TRANSIT  SURVEYING. 

To  Read  an  Angle.— The  angle  read  may  be  included  or  deflected.  If  we 
set  up  at  0 with  backsight  at  B and  foresight  at  C,  we  shall  find  that  there 
are  two  angles  made  by  the  line  C 0 with  the  line  BOA,  namely  the  included 
angle  B 0 (7,  and  the  deflected  angle  CO  A. 

To  Read  the  Included  Angle.— Set  the  zeros  of  vernier  and  graduated  limb 
together  accurately,  and  clamp  the  plates.  Turn  the 
telescope  on  the  backsight,  with  the  level  bubble  down, 
and,  when  set,  fasten  lower  clamp  so  as  to  fix  both 
clamped  plates  to  the  tripod  head.  Loosen  the  upper 
clamp  and  turn  the  telescope  to  C and  set  accurately. 

The  vernier  will  read,  for  example,  “45°  left  angle.” 

To  Read  the  Deflected  Angle.— Arrange  verniers  as  above, 
and  be  sure  and  turn  the  telescope  over  on  its  axis  till 
the  bubble  tube  is  up,  and  then  take  the  backsight  and 
fix  lower  clamp.  Turn  the  telescope  back  (this  is 
called  “ plunging”  the  telescope)  and  sight  to  foresight 
and  fix  as  before.  The  vernier  will  read  a “right  angle  of  135°.”  The  sum 
of  included  and  deflected  angles  must  always  be  180°. 

Note. — In  making  a survey  by  included  angles,  we  must  add  or  subtract 
180°  at  each  reading  to  have  the  vernier  and  compass  agree;  by  deflected 
angles,  they  will  agree  without  the  above  addition  or  subtraction,  and  the 
latter  method  is  generally  used.  


TO  MAKE  A SURVEY  WITH  A TRANSIT. 

By  Individual  Angles.— Set  vernier  at  zero  of  limb,  plunge  telescope,  and, 
when  set  on  backsight,  loosen  needle  and  read  bearing  of  the  line  from  back- 
sight to  set-up.  Plunge  telescope  back  and  set  on  foresight  and  read  both 
needle  and  vernier.  The  difference  in  needle  readings  should  agree  with  the 
vernier  reading  within  15',  as  local  attraction  will  affect  the  needle  equally 
on  both  sights. 

Note. — Any  mass  of  iron  or  steel  that  may  and  will  be  moved  during  the 
readings  of  the  needle,  will  affect  the  same  and  destroy  the  value  of  the 
needle  as  a check.  The  tape  and  other  iron  materials  should  not  be  moved 
during  the  taking  of  angles. 

By  Continuous  Vernier. — Set  vernier  at  zero,  unclamp  compass  needle,  and, 
when  stationary,  turn  the  north  point  of  compass  limb  so  as  to  coincide  with 
the  north  point  of  the  needle.  Fix  lower  clamp,  plunge  telescope,  and  take 
backsight  by  loosening  upper  clamp.  The  vernier  and  needle  should  agree 
in  giving  the  magnetic  bearing  of  the  line  from  backsight  to  set-up.  Record 
this  in  note  book;  plunge  telescope,  and  take  foresight.  Needle  and  vernier 
should  agree  as  before.  After  making  record,  set  up  over  foresight  and  take 
sight  to  station  just  left  with  telescope  plunged,  having  first  seen  that  the 
vernier  reads  exactly  as  it  did  on  the  last  foresight,  as  a slip  in  carrying  the 
transit  from  one  station  to  another,  which  is  not  detected  at  the  time,  can 
never  be  checked  afterwards  when  the  final  work  is  found  to  be  in  error. 
The  foresight  is  taken  as  before.  On  every  sight  the  needle  and  vernier 
should  agree  if  there  is  no  local  attraction  of  the  needle. 

If  we  can  see  all  the  corners  of  a field  that  is  to  be  surveyed  from  a central 
point,  we  can  make  the  survey  by  setting  up  at  that  point,  and,  with  one 


46 


TRANSIT  SVRVEYING. 


corner  as  a backsight,  take  all  the  other  corners  as  foresights  with  but  one 
set-up,  and  by  measuring  from  this  point  to  all  of  the  corners;  or  we  can 
set  up  at  any  corner  and  run  a line  of  survey  around  the  field.  This  latter 
method  is  called  meandering.  Both  methods  will  give  the  same  result  when 
plotted;  but  the  former  is  much  quicker,  as  the  boundaries  of  a tract  are 
frequently  overgrown  with  bushes  that  must  be  cleared  to  allow  a sight; 
while  a central  point  can  frequently  be  found  that  will  allow  a free  sight  to 
all  the  corners,  and  the  distance  can  be  measured  by  tape,  or  stadia.  As  the 
central  point  is  nearer  the  corners  than  they  are  to  one  another,  it  follows 
that  a shorter  distance  must  be  chained  or  cut  in  the  case  of  a central  set-up. 

Outside  surveys  maybe  made  for  many  purposes.  It  matters  not  what 
the  purpose  is,  the  work  should  be  fully  and  accurately  done,  and  the  map 
should  contain  everything  that  will  throw  light  upon  the  subject.  If  the 
outside  work  is  to  be  connected  with  inside  surveys,  there  are  a number  of 
points  to  be  observed,  and  they  will  be  given  under  the  head  of  underground 
work. 

Meridians,  or  Base  Lines. — The  surveys  must  be  based  on  some  meridian, 
and  started  from  some  fixed  point.  There  are  four  kinds  of  meridians,  or 
“base  lines.” 

First.— A line  already  on  the  ground,  as  one  of  the  sides  of  the  tract,  is 
taken  as  a base.  The  subsequent  work  is  referred  to  one  or  both  ends  of  this 
line,  and  all  angles  measured  are  taken  as  deviations  from  it. 

Second.— A stone  post  is  sunk  in  the  ground,  or,  better,  an  iron  plug  is  put 
into  rock  “in  place”— that  is,  not  loose  rock,  even  if  a large  boulder— at  such 
a distance  from  the  works  as  to  be  beyond  the  influence  of  moving  machinery, 
and  a line  of  sight  is  taken  to  sonue  permanent  natural  object,  as  far  distant  as 
can  be  clearly  seen  under  adverse  circumstances,  as  cloudy  or  dark  weather. 
This  line  of  sight  is  the  base  line,  and  the  plug  is  the  origin.  No  measurements 
of  distance  are  needed.  If  no  natural  objects  exist,  a station  is  set  up  at 
a distance,  so  as  to  be  as  permanent  as  possible,  and  angles  are  turned  from 
this  to  other  points,  so  as  to  check  any  movement  in  it.  Generally  there  are 
a number  of  tall  chimneys,  church  spires,  etc.  to  be  found.  While  this  is 
preferable  to  the  first,  it  gives  no  method  of  check  in  underground  work, 
and  is  seldom  used. 

Third.— The  magnetic  meridian  is  taken  as  the  base  line.  The  transit  is 
set  up  over  a plug,  as  just  noted,  and  the  subsequent  work  is  as  described 
under  running  continuous  vernier.  As  the  needle  is  subject  to  constant 
variation,  this  base  line  will  afford  a check  underground  only  for  a short 
time  after  the  meridian  is  established,  and  all  subsequent  work  can  be 
checked  only  by  applying  the  difference  between  the  variation  at  the  time 
of  establishment,  and  at  the  time  of  making  the  survey.  If  the  time  of 
establishing  the  survey  should  be  lost,  the  base  line  would  become  no  better 
than  that  noted  in  Case  2. 

Fourth.— The  true  meridian  is  taken  as  a base.  The  true  north  and  south 
line  may  be  determined  by  observing  the  North  Star,  Polaris,  or  by  observing 
the  sun.  The  North  Star  does  not  lie  exactly  at  the  North  Pole,  but  revolves 
about  it  in  a small  circle.  There  are  two  times  in  a day  when  it  is  exactly 
above  or  below  the  pole,  and  we  take  our  sight  at  one  of  these  times,  when 
our  transits  do  not  have  their  graduated  limbs  made  accurately  enough  to 
apply  the  proper  angle  for  a sight  at  any  other  time.  If  we  do  not  know  the 
time  when  the  star  is  crossing  the  meridian,  we  can  find  it  by  remembering 
that  the  fourth  star  in  the  handle  of  the  “dipper”  is  in  the  same  vertictd 
plane  with  the  north  star  17  minutes  before  the  latter 
crosses  the  meridian. 

The  true  meridian  will  give  us  an  invariable  base 
line.  At  any  date  after  the  establishment  of  the  same, 
we  can  check  the  work  above  or  below  ground  by 
applying  the  variation  of  the  needle. 

To  Find  the  True  North  by  an  Observation  of  the  North 
Star,  Polaris,  at  Elongation. — This  star  has  a motion 
around  a small  circle,  the  azimuth  angle  of  which 
from  the  north  is  known  for  different  latitudes.  The 
star  may  be  readily  found  by  following  the  line  of  the 
so-called  pointers  in  the  Big  Bear,  or  Dipper.  The 
time  of  the  greatest  eastern  or  western  elongation  is 
found  from  a table.  Some  10  minutes  before  this  time 
the  transit  is  carefully  set  up  and  leveled  over  a peg. 
The  cross-wires  are  made  to  bisect  the  star;  they  are 


JPolaris 


\ I 
\i 

\tt9erver 


THE  SOLAR  ATTACHMENT. 


47 


illuminated  by  a light  held  under  the  reflector  fastened  on  the  object 
end  of  the  telescope.  The  star  is  followed  with  the  cross-wires  until  its 
motion  toward  the  point  of  its  greatest  elongation  ceases.  The  telescope  is 
lowered  vertically,  care  being  taken,  of  course,  not  to  move  it  horizontally, 
arid  a peg  is  set  up  on  the  line,  say  300  ft.  or  400  ft.  distant.  The  next  morn- 
ing the  correction  is  made  for  the  star’s  azimuth.  These  corrections  are 
different  for  different  latitudes  and  different  years.  They  are  to  be  found  in 
the  nautical  almanac. 

The  method  “by  equal  shadows”  may  be  used  with  considerable  accu- 
racy, if  we  take  a sufficiently  long  staff,  or  can  obtain  the  shadows  of  a 
tall  spire  on  a level  surface.  A vertical  staff  casts  equal  shadows  at  the 
same  time  before  and  after  noon.  If  we  drive  a stake  at  any  time  before 
noon,  in  the  extremity  of  the  shadow  cast  by  such  a staff,  and  measure 
its  distance  from  the  staff,  we  have 
one  leg  of  an  angle.  After  noon  we 
wait  till  the  shadow  becomes  exactly 
as  long  as  the  distance  measured,  and 
drive  a stake  at  the  extremity  of  the 
shadow.  A line  bisecting  the  angle 
made  by  lines  drawn  from  these  two 
stakes  to  the  staff  will  be  in  the 
meridian. 

Establishing  a Meridian  Line  With  the 
Solar  Attachment.— The  angle  from 
the  equator  to  the  horizon  of  a place 
is  its  latitude;  consequently,  from  the 
zenith  to  the  pole  is  the  colatitude, 
or  90°  — latitude.  The  angular  dis- 
tance from  the  equator  to  the  sun  is 
the  declination;  consequently,  from 
the  sun  to  the  pole  is  the  polar  dis- 
tance. The  angular  distance  from 
the  horizon  to  the  sun  is  the  sun’s 
altitude;  consequently,  the  zenith  distance  is  the  angular  distance  between 
the  sun  and  the  zenith. 

Adjustments  of  Burt’s  Solar  Attachment.— After  the  instrument  has  been 
carefully  leveled,  the  zero  of  the  vernier  of  the  solar  is  placed  opposite  the 
zero  of  the  arc.  The  horizontal  plates  of  the  instrument  are  clamped,  and 
the  sun’s  image  brought  between  the  horizontal  lines  of  either  silver  plate 
by  any  manipulation  of  the  instrument  and  attachment  possible,  keeping 
the  plates  horizontal  and  the  zero  of  the  vernier  opposite  the  zero  on  the  arc. 
When  the  image  is  accurately  between  the  horizontal  lines,  the  arc  is 
revolved  so  that  the  image  falls  on  the  other  plate;  this  must  be  done 
rapidly,  as  the  sun’s  image  moves.  If  it  does  not  fall  between  the  lines,  half 
the  error  is  corrected  by  the  tangent  screw  of  the  solar  and  half  by  the 
tangent  screw  of  the  telescope.  The  operation  is  repeated  until  the  sun’s 
image  falls  between  the  lines  of  the  second  plate,  after  a revolution  of  the 
arc,  it  having  been  made  to  fall  between  the  lines  of  the  first,  as  described. 
Near  noon  is  a good  time  to  make  this  adjustment,  as  the  sun’s  apparent 
motion  is  not  so  rapid.  The  zero  of  the  vernier  is  now  brought  opposite  to 
the  zero  of  the  arc  by  loosening  the  screws  that  fasten  the  vernier,  and 
sliding  it  as  may  be  necessary.  It  is  often  difficult  to  make  the  zeros  come 
exactly  opposite  each  other,  as  the  vernier  plate  is  apt  to  move  slightly 
when  the  screws  are  tightened  again.  The  second  adjustment  is  to  make 
the  tops  of  the  rectangular  blocks  of  the  solar  attachment  level,  when  the 
telescope  is  level  and  the  arc  of  the  solar  is  set  at  zero.  Level  the  transit 
carefully,  as  before  described,  set  the  solar  at  zero  and  place  the  level, 
furnished  with  the  solar,  across  the  tops  of  the  blocks.  If  the  bubble  comes 
to  the  center  of  the  tube,  no  correction  is  needed;  if  it  does  not,  correct  the 
error  by  turning  the  screws  under  the  hour  circle,  care  being  taken  in  this 
as  in  all  other  movements  of  these  adjusting  screws,  to  leave  them  tight  after 
the  correction.  Revolve  180°  and  correct  again  if  necessary.  Placing  the 
blocks  90°  horizontally  from  their  first  position,  go  through  the  same 
operation  as  described  until  in  all  positions  the  bubble  remains  centered. 

To  Use  the  Solar.— Before  this  instrument  can  be  used  at  any  given  place, 
it  is  necessary  to  set  off  upon  its  arcs  both  the  declination  of  the  sun,  as 
affected  by  its  refraction  for  the  given  day  and  hour,  and  the  latitude  of  the 
place  where  the  observation  is  made. 


A 


48 


TRANSIT  S UR  VE  YINO. 


The  declination  of  the  sun  as  given  in  the  ephemeris  of  the  nautical 
almanac  from  year  to  year,  is  calculated  for  apparent  noon  at  Greenwich, 
England.  To  determine  it  for  any  other  hour  at  a place  in  the  United 
States,  reference  must  be  had,  not  only  to  the  difference  of  time  arising 
from  the  difference  of  longitude,  but  also  to  the  change  of  declination 
during  that  time. 

The  longitude  of  the  place,  and  therefore  its  difference  in  time,  if  not  given 
directly  in  the  tables  of  the  almanac,  can  be  ascertained  very  nearly  by 
reference  to  that  of  other  places  given  which  are  situated  on,  or  very  nearly 
on,  the  same  meridian. 

It  is  the  practice  of  surveyors  in  states  east  of  the  Mississippi  to  allow  a 
difference  of  6 hours  for  the  difference  in  longitude,  calling  the  declination 
given  in  the  almanac  for  12  m.  that  of  6 a.m.  at  the  place  of  observation. 
Beyond  the  meridian  of  Santa  Fe,  the  allowance  would  be  about  7 hours; 
and  in  California,  Oregon,  and  Washington,  about  8 hours.  Having  thus 
the  difference  of  time,  we  very  readily  obtain  the  declination  for  a certain 
hour  in  the  morning,  which  would  be  earlier  or  later  as  the  longitude  was 
greater  or  less,  and  the  same  as  that  of  apparent  noon  at  Greenwich  on  the 
given  day.  Thus,  suppose  the  observation  made  at  a place  5 hours  later  than 
Greenwich,  then  the  declination  given  in  the  almanac  for  the  given  day  at 
noon,  affected  by  the  refraction,  would  be  the  declination  at  the  place  of 
observation  for  7 a.m.  This  give  us  the  starting  point. 

To  obtain  the  declination  for  the  other  hours  of  the  day,  take  from  the 
almanac  the  declination  for  apparent  noon  of- the  given  day,  and,  as  the 
declination  is  increasing  or  decreasing,  add  to,  or  subtract  from,  the  decli- 
nation of  the  first  hour  the  difference  of  one  hour  as  given  in  the  ephemeris, 
that  will  give,  when  affected  by  the  refraction,  the  declination  of  the 
succeeding  hour.  Proceed  in  like  manner  to  make  a table  of  the  declinations 
for  every  hour  of  the  day. 

To  Find  the  True  North  With  the  Burt  Solar. — Find  from  an  ephemeris  or 
nautical  almanac  the  sun  declination  for  noon  of  the  day  of  observation  at 
Greenwich.  Find  the  declination  for  the  hour  of  observation  at  the  place 
of  observation  by  first  figuring  what  time  it  is  at  the  place  of  observation 
when  it  is  noon  at  Greenwich.  If  the  place  of  observation  is  west  of  Green- 
wich, it  will  be  earlier  there;  if  east,  later,  and  in  either  case  the  difference 
will  be  one  hour  for  every  15°  of  longitude.  If  the  place  is  west,  subtract  the 
hour  just  found  as  described  from  the  hour  of  the  observation,  and  multiply 
the  hourly  difference,  also  taken  from  the  ephemeris,  by  the  remainder.  If 
the  declination  is  increasing  from  the  equator  either  north  or  south,  add 
this  product  to  it;  if  decreasing,  subtract  it.  A table  of  refractions  is  given 
in  the  ei^hemeris  for  the  different  latitudes  and  the  different  hours  of  the 
day.  This  refraction  is  to  be  added  if  the  declination  is  north,  and 
subtracted  if  the  declination  is  south.  Having  thus  ascertained  the  declina- 
tion, lay  it  off  on  the  declination  arc.  Set  the  colatitude  of  the  place  off  on 
the  vertical  arc  after  having  leveled  the  instrument  carefully  with  clamped 
horizontal  plates  at  zero.  Always  in  solar  observations  it  is  well  to  level  by 
means  of  the  upper  telescope  bubble.  Now,  revolve  the  horizontal  plates  still 
clamped,  and  also  the  declination  arc,  around  its  polar  axis  until  the  sun’s 
image  is  exactly  between  the  horizontal  lines  of  the  silver  plates.  When  the 
sun’s  image  is  between  these  lines,  the  object  end  of  the  telescope  will  be 
pointing  north. 

To  Take  the  Latitude  With  Burt’s  Solar.— A few  minutes  before  apparent 
noon  clamp  the  plates  at  zero,  level  the  instrument  carefully,  and  set  the 
zero  of  the  vernier  opposite  the  zero  of  the  vertical  arc.  Lay  off  the  declina- 
tion, corrected  for  noon  at  the  place  of  observation  and  for  refraction,  on 
the  declination  arc,  and  set  the  time  mark  on  the  declination  arc  opposite 
XII  on  the  hour  dial.  Bring  the  sun’s  image  between  the  horizontal  lines 
of  the  silver  plate  by  moving  the  plates  horizontally  and  the  telescope 
vertically,  clamp  both  plates  and  telescope  and  follow  with  the  tangent 
movements  the  rising  sun.  Be  careful  to  stop  when  the  sun  ceases  to  mount. 
For  a moment  before  apparent  noon  there  is  no  perceptible  motion  of  the 
image.  The  reading  on  the  vertical  arc  is  the  colatitude  of  the  place. 

The  colatitude  should  never  be  taken  this  way  for  direct-sight  calcula- 
tions, for  while  it  satisfies  the  automatic  solution  of  the  true  north,  it  may 
not  be  accurate,  and  the  latitude  needed  for  direct-sight  calculation  should 
be  true  to  within  a minute.  With  the  Burt  solar  there  is  at  times  what  is 
calle<l  a false  image  to  guard  against,  an  image  that  comes  between  the  lines 
of  the  silver  plates  when  the  object  end  of  the  telescope  is  not  pointing 


TRANSIT  S UR  VE  YINO. 


49 


north.  If  the  time  be  observed  on  the  hour  dial,  or  the  magnetic  north  be 
noticed,  no  error  need  ever  occur  on  this  score,  for  with  the  false  image  the 
time  will  be  out  considerably  and  also  the  magnetic  variation. 

General  Remarks.— -With  the  base  line  located  and  the  survey  made,  we  see, 
by  coming  back  to  the  point  from  which  we  started  or  “ closing”  the  work, 
whether  it  be  correct  in  distance  or  angle.  If  it  be  in  error,  see  if  the  error 
can  be  located  (as  will  be  shown  under  plotting),  and  if  it  can  be  found,  run 
those  parts  over  again;  if  not,  repeat  the  whole  survey.  Shoving  the  work, 
as  it  is  called,  or  “ doctoring”  it  so  that  it  will  close,  is  the  poorest  practice 
that  an  engineer  can  engage  in,  as  all  subsequent  work  that  depends  on  a 
doctored  survey  must  be  doctored  to  fit  the  faulty  work— even  if  it  be  right 
in  itself.  Every  engineer  should  be  able  to  swear— not  that  he  “ thinks  the 
survey  is  accurate,”  but  “ that  he  knows  it  to  be  so,”  if  he  should  be  called 
as  a witness  in  court.  One  of  the  causes  of  inaccuracy  is  haste. 

To  make  a complete  map,  the  engineer  should  first  make  a survey  around 
the  tract  to  be  worked,  locating  all  the  prominent  physical  features  and 
improvements.  If  he  can  do  so,  he  should  make  a topographical  map  of  the 
tract  at  once;  but,  if  time  is  limited,  by  running  the  vertical  as  well  as  the 
horizontal  angle,  he  can  carry  the  tidal  elevation  or  the  elevation  above 
some  assumed  datum,  to  every  station,  and  m,ark  it  on  the  map  at  that  point. 
Then  as  he  makes  subsequent  surveys,  he  can  gradually  get  data  enough  to 
make  a fairly  complete  topographical  map  in  course  of  time.  Every  ledge 
of  rock  in  place  should  be  located,  and  the  amount  and  direction  of  its  dip, 
as  well  as  the  character  of  the  rock,  should  be  marked  neatly  on  the  map. 
The  streams  of  water  on  the  tract  should  be  regarded  as  of  primary  impor- 
tance, and  should  be  located  with  exactness. 

With  a true  meridian  base  line  we  can  connect  maps  made  at  different 
places  with  little  trouble.  This  is  especially  useful  with  adjoining  mines 
connected  at  but  one  point.  Having  made  the  survey  and  come  home,  we 
must  examine  all  the  apparatus  and  see  if  the  instruments  are  out  of  adjust- 
ment, as  such  a fact  will  prevent  our  bothering  over  work  that  will  not 
close.  It  will  assure  us,  also,  that  we  can  start  out  at  a moment’s  notice 
with  no  thought  of  the  adjustment  of  our  tools.  A famous  wit  said  that  the 
proper  time  to  strop  a razor  was  just  after  you  had  used  it,  as  you  then  knew 
how  much  it  needed  it.  The  same  will  apply  to  surveying  instruments  and 
tools— especially  for  underground  work.  Here  the  lamp  smoke,  powder 
gases,  mine  dust,  paint  smears,  acid  water  from  “droppers,”  and  the  other 
abominations  incident  to  underground  surveying,  especially  in  a coal  mine, 
will  so  cover  the  tools  that  they  would  be  useless  if  left  uncleaned  half  a 
dozen  times.  As  soon  as  the  corps  comes  back  from  the  mine,  and  before 
the  clothes  are  Changed,  the  tape  must  be  stretched,  tested,  wiped,  and  oiled. 
It  can  be  inspected  to  see  if  marks  are  too  much  worn,  or  it  stands  in  need  of 
mending,  the  marking  pot  is  cleared  of  “muck,”  and  fresh  white  paint  is 
mixed,  if  the  corps  is  going  out  in  24  hours;  the  plummets  will  have  their 
strings  overhauled  and  freed  from  knots;  hatchets  will  be  sharpened,  and 
axes  ground,  pouches  overhauled,  and  a supply  of  tacks  or  “ spads  ” taken. 
Then  the  transitman  changes  his  clothes  and  sets  up  the  transit,  wipes  it 
with  a cloth  wet  with  alcohol,  so  as  to  remove  dirt,  oil,  and  paint.  If  water 
has  gotten  between  the  graduated  limb  and  compass  box,  the  verniers  must 
be  uncovered  and  the  whole  wiped  dry.  If  the  sulphureted  hydrogen  from 
the  ix)wder  smoke  has  tarnished  the  silver  surfaces  of  any  of  the  graduated 
circles,  it  must  be  removed  with  whiting.  Alcohol  should  be  always  used 
instead  of  water,  as  it  will  quickly  evaporate  and  leave  the  parts  dry.  The 
telescope  glasses  are  then  wiped  with  soft  chamois  leather,  and  the  instru- 
ment is  tested  for  want  of  adjustment  before  putting  it  away  in  its  box. 
When  going  to  and  from  work,  the  transit  should  not  be  carried  on  the 
transit  head,  or  the  spindle  will  become  sprung.  Nor  should  it  be  carried 
with  the  arm  crooked  under  the  telescope,  as  the  weight  comes  on  the  axis, 
and  that  soon  gets  sprung  so  that  all  the  adjusting  in  the  world  will  not 
make  it  work  right.  When  carried  in  the  hand,  it  should  be  reversed  and 
the  hand  slipped  under  the  compass  plate  and  brought  over  so  as  to  clamp 
both  plates.  In  this  way  there  will  be  no  strain  on  any  part.  In  case  of  a 
“fall”  in  the  mine,  remember  that  the  transit  is  the  baby  to  be  protected, 
and  stand  a few  bumps  to  save  a strained  or  broken  instrument,  that  will 
end  the  work  for  some  time. 

Plotting.— A “plot”  is  not  only  a piece  of  ground  with  bodies  of  water, 
roads,  vegetation,  etc.  upon  it,  but  refers  also  to  the  map  of  the  same  drawn 
to  a given  scale,  and  showing  all  of  the  above  natural  features.  Plotting  is 


50 


TRANSIT  S UR  VE  YINO. 


the  making  of  such  a map  from  notes  of  a survey,  and  may  or  may  not 
require  the  permanent  placing  of  the  stations  on  the  map,  by  which  the 
survey  is  made.  In  underground  work,  the  exact  location  and  the  retention 
of  those  stations  is  a matter  of  the  first  importance,  and  is  secondary  only  to 
the  exact  plotting  of  the  side  notes.  The  scale  of  the  plot  is  generally 
as  large  as  will  show  the  points  of  interest  in  the  property;  but  in 
Pennsylvania,  the  maps  for  coal  mines  must  be  drawn  to  a scale  of  100  ft.  to 
an  inch.  There  are  two  methods  of  plotting:  by  protractor,  and  by 
coordinates.  When  the  scale  is  sufficiently  large,  it  is  a matter  of  little  choice 
which  method  is  used,  if  the  work  be  carefully  done  with  exact  instruments; 
but  with  small  scales— 100  ft.  or  above,  to  the  inch— we  should  use  the 
method  by  coordinates.  With  the  latter  scale,  the  prick  of  a pin  on  the 
paper  will  represent  a foot  square,  or  a circle  slightly  larger  than  a foot 
in  diameter.  If  the  next  station  is  to  be  located  from  the  pin  prick  of  the 
first,  and  that  is  exactly  located,  we  may  not  hit  the  exact  center  of  that 
small  indentation.  In  fact,  the  chances  are  greatly  against  our  doing  so, 
and  the  location  of  the  second  station  will  probably  be  in  error.  If  we  have 
a bad  habit  of  placing  the  protractor  or  the  straightedge  against  one  side  of 
the  pin  pricks,  or  pencil  marks,  when  the  scale  is  large,  we  shall  constantly 
be  introducing  a “personal  error,”  as  it  is  called,  and  the  sum  of  all  the 
errors  made  at  each  of  100  stations  will  bring  our  final  point  very  much  out 
of  the  way.  On  this  account,  and  from  the  fact  that  no  protractor  that  is 
movable  can  be  used  without  the  chances  of  slipping  while  the  angle  is  read 
or  marked,  has  led  all  careful  enmneers  to  abandon  its  use  in  favor  of  the 
method  by  coordinates.  When  the  scale  is  from  1 to  25  ft.  to  an  inch,  the 
errors  are  small  enough  to  make  little  chances  of  variation  in  a close  of  ten 
or  twelve  stations;  when  the  survey  is  of  short  sights  from  a main  line  to 
points  where  no  further  work  is  to  be  done,  the  protractor  will  afford  a quick 
method  of  plotting. 

There  is  a chance  of  error  in  both  methods  that  must  be  noted  here,  where 
the  survey  is  not  completed  at  one  time.  If  the  map  be  made  in  a day  or 
two,  and  will  never  be  extended  by  subsequent  work,  there  will  be  no 
chance  of  error  from  a change  in  the  paper  on  which  it  is  made,  due  to 
moisture  or  dryness;  but  if  the  map  be  made  on  a series  of  very  damp  days, 
or  a series  of  very  dry  ones,  a change  in  the  weather  to  the  other  extreme 
will  swell  or  shrink  the  map.  The  general  tendency  in  a large  mine  map 
that  is  frequently  used,  and  is  rolled  and  unrolled  every  day  for  five  or  six 
years,  is  to  stretching,  so  that  there  will  be  a variation  of  from  1 to  5 ft.  in 
1,000.  If  we  extend  a recent  survey  on  such  a map,  we  are  plotting  it  to  a 
different  scale  to  that  assumed  by  the  map  under  the  conditions  above 
noted.  The  paper  on  which  the  map  is  to  be  drawn  should  be  tacked  down 
to  the  table  or  board,  and  should  be  covered  with  squares  each  exactly  10  in. 
square.  The  sides  of  these  squares  should  be  the  meridians,  or  north  or  south 
lines,  and  the  tops  and  bottoms  should  run  due  east  and  west.  Mark  the  first 
station  on  the  paper,  set  your  parallel  ruler  or  T square  on  the  meridian  nearest 
it,  and  with  the  protractor  produce  the  course  to  tne  next  station.  Measure  the 
distance  with  a scale,  and  proceed  in  this  manner  to  plot  all  the  courses,  using 
each  time  the  meridian  nearest  the  station  the  course  is  taken  from.  After  all 
the  stations  have  been  plotted,  fill  in  the  side  notes,  marking  everything  on 
the  map  with  great  care  and  neatness.  Always  use  the  horizontal  distances. 
All  surveys  should  be  traversed,  and  all  plotting  should  be  either  checked 
by  the  traversing,  or  the  principal  stations  should  be  plotted  by  use  of  the 
traverse.  For  a large  mine  map  that  will  be  in  use  many  years,  muslin- 
backed  egg-shell  paper  must  be  used.  It  comes  in  a long  roll,  and  any 
reasonable  length,  and  a width  up  to  6 ft.  can  be  obtained. 

To  Calculate  the  Vertical  Distances.— When  making  the  survey,  read  the 
vertical  angles  to  all  stations.  If  the  angle  is  one  of  depression,  note  it  with 
a minus  sign  (— ) preceding  it.  If  it  is  an  angle  of  elevation,  precede  it  with 
a plus  sign  ( + ).  These  will  show  whether  the  vertical  distance  is  to  be 
added  to,  or  subtracted  from,  the  height  of  the  preceding  station. 

Having  the  horizontal  distance  and  the  vertical  angle: 

Distance  X tangent  of  vertical  angle  = vertical  distance. 

Having  the  pitch  distance  and  vertical  angle: 

Distance  X sine  of  vertical  angle  = vertic^  distance. 

To  Calculate  the  Horizontal  Distance,  or  Latitude.— Pitch  distance  X cosine 
of  vertical  angle  = horizontal  distance. 

Vertical  height,or  departure  tang.of  vertical  angle  = horizontal  distance. 


TRANSIT  SURVEYING. 


61 


To  Calculate  the  Pitch  Distance.— Horizontal  distance  cosine  of  bearing, 
or  multiplied  by  secant  of  bearing  ==  pitch  distance. 

Vertical  distance  -4-  sine  of  vertical  angle,  or  multiplied  by  cosecant  of 
bearing  = pitch  distance. 

To  Calculate  the  Vertical  Angle.— The  horizontal  distance  the  pitch 
distance  = cosine  of  vertical  angle. 

Vertical  distance  pitch  distance  = sine  of  vertical  angle. 

Vertical  distance  ^ horizontal  distance  = tangent  of  vertical  angle. 

Note. — Whenever  sines,  cosines,  tangents,  etc.  are  here  named,  they  mean 
the  natural  sines,  etc.  of  the  angle. 

Plotting  by  Coordinates.- In  describing  the  establishment  of  a meridian 
and  a fixed  point,  we  made  the  latter  a stone  post,  or  iron  plug  sunk  in  solid 
rock.  This  point  is  called  the  on^m  0/ coordmates.  We  have  the  principal 
meridian  passing  through  this  point  in  an  exact  north  and  south  direction, 
and  a secondary  meridian  or  base  line  passing  through  this  point  at  right 
angles  to  the  first,  or  in  an  exact  east  and  west  line.  Any  point  we  may 
select  on  the  map  will  be  a certain  distance  north  or  south,  and  east  or  west  of 
the  origin.  The  lines  drawn  from  this  point  at  right  angles  to  the  two  base 
lines  just  given  are  called  the  coordinates  of  that  point,  and  we  can  plot  the 
point  when  they  are  given.  For  example,  the  coordinates  of  Station  24  are 
North  345.67,  and  East  890.12.  We  measure  890.12  ft.  east  of  the  origin  on  the 
secondary  meridian  and,  from  this  point,  measure  345.67  ft.  north  to  the  point 
desired;  or  we  can  measure  first  on  the  primary  meridian  to  the  north  and 
then  turn  off  a right  angle  to  the  east  and  reach  the  same  point.  In  any 
event  we  plot  the  position  of  each  station  independently  of  all  the  others, 
and  any  error  in  locating  one  is  not  carried  to  the  next.  When  two  stations 
are  plotted,  the  distance  between  them  on  the  map  should  be  exactly  what 
we  found  for  their  horizontal  distance  on  the  ground.  This  check  shows 
whether  our  plotting  is  correct.  This  is  also  called  traversing  a survey  if  the 
meridian  be  north  and  south,  and  in  books  on  surveying  there  are  printed 
tra, verse  tables,  which  are  accurate  within  certain  limits,  but  not  so  accurate 
as  the  tables  of  coordinates  published  separately,  as  the  latter  are  carried  to  a 
greater  number  of  decimals.  Gordon’s  Traverse  Tables  will  enable  you  to 
find,  without  calculation,  the  coordinates  for  a distance  of  12  miles  with  a 
chance  of  error  of  only  half  an  inch,  which  is  much  more  accurate  than  the 
graduation  of  the  instruments  with  which  the  work  was  done. 

With  a north  and  south  meridian,  the  point  from  which  we  begin  to 
measure  angles — the  zero  point — is  the  north  point,  and  the  angles  are  read 
for  continuous  vernier  in  the  direction  of  the  hands  of  a watch.  The  sines 
of  angles  are  eastings  and  westings,  and  the  cosines  are  northings  and 
southings. 

To  Traverse  a Survey. — To  traverse  a survey,  means  to  determine  by  calcu- 
lation how  far  north  or  south  and  east  or  west  any  station  may  be  from 
another,  the  location  of  which  is  fixed.  To  do  this,  all  distances  must  be 
either  measured  horizontally,  or  calculated  to  horizontal  distances.  The 
horizontal  angles,  or  courses,  must  be  either  read  as  quadrant  courses,  or 
reduced  from  azimuth  to  quadrant  courses.  An  azimuth  course  is  one  that 
is  read  on  the  transit  which  is  graduated  from  0°  to  360°.  A quadrant  course 
is  one  read  in  the  quadrant  of  the  circle,  as  S 67°  W,  N 43°  E,  etc. 

Latitude  means  distance  north  or  south,  and  is  determined  by  the  first 
initial  of  the  recorded  course.  Thus,  if  a course  is  S 67°  W,  the  latitude  is 
south;  if  N 43°  E,  the  latitude  is  north. 

Departure  means  distance  east  or  west,  and  is  determined  by  the  last 
initial  of  the  recorded  course.  Thus,  if  a course  is  S 67°  W,  the  departure  is 
west;  if  N 43°  E,  the  departure  is  east. 

The  latitude  = distance  X cosine  of  bearing. 

The  departure  = distance  X sine  of  bearing. 

If  the  survey  is  a continuous  one  around  a tract,  and  ending  at  the 
place  of  beginning,  the  sum  of  the  northings  should  equal  the  sum  of 
the  southings,  and  the  sum  of  the  eastings  should  e^ual  the  sum  of  the 
westings.  Or,  in  other  words,  the  sum  of  all  the  latitudes  north,  should 
equal  the  sum  of  all  the  latitudes  south;  and  the  sum  of  all  the  departures 
east,  should  equal  the  sum  of  all  the  departures  west.  It  is  evident  that  by 
coming  back  to  the  place  of  beginning  the  surveyor  has  traveled  the  same 
distance  north  as  he  has  south,  and  the  same  distance  east  as  he  has  west. 

The  most  accurate  way  to  construct  a map  is  to  traverse  the  survey  and 
place  all  stations  on  it  by  the  traversed  distances,  or  to  at  least  put  a 
number  of  the  principal  stations  on  the  map  by  the  traversed  distances,  and 


52 


TRANSIT  S UR  VE  YINO. 


use  the  protractor  to  plot  only  the  intermediate  stations.  As  the  origin  of 
the  survey  is  at  the  fixed  point  just  mentioned,  we  must  make  a rough 
pencil  sketch  to  find  the  approximate  location  of  this  point  from  the 
boundaries  of  the  property,  and  the  general  trend  of  the  property  itself. 
This  will  show  us  the  place  to  put  the  origin  upon  the  paper  so  that  all  of 
the  property  can  be  placed  on  the  map,  and  leave  about  the  same  amount  of 
margin  on  all  sides.  It  will  also  show  us  the  direction  the  north  and  south 
line  must  take  on  the  paper.  When  this  is  settled,  mark  the  origin  by  a needle 
point,  and  lay  the  straightedge  across  it  in  the  direction  to  be  taken  by  the 
principal  meridian,  and  draw  the  meridian  with  a quite  hard  pencil 
brought  to  a very  fine  point.  Then  lay  off  on  both  sides  of  the  origin 
distances  of  5 in.,  and  mark  them  with  needle  points.  These  must  be  so 
accurately  located  that  there  will  not  be  an  error  of  one  hundredth  of  an 
inch  in  them,  or  one  foot  in  five  hundred.  At  the  point  where  we  can  get 
the  longest  line  on  the  paper  at  right  angles  to  the  principal  meridian,  lay 
off  points  for  a right  angle  accurately  on  each  side  of  the  meridian,  and 
draw  through  the  three  points,  by  means  of  the  straightedge,  a line  parallel 
to  the  secondary  meridian  and  divide  this  accurately  into  5"  distances  as 
before.  Through  each  of  the  points  thus  marked,  draw  lines  at  right  angles 
to  the  lines  already  drawn,  until  the  paper  is  accurately  divided  into  squares 
5 in.  on  a side,  and  none  of  them  with  an  error  of  one  five-hundredth. 
Beginning  with  the  origin,  mark  the  extremities  of  the  lines  passing  through 
it  zero.  All  distances  to  the  east  or  upon  the  right  side  of  the  north  and 
south  zero  fine  are  marked  -f  with  respect  to  that  line;  those  to  the  left  are 
marked  — . All  distances  above  the  east  and  west  zero  line  are  marked  + 
with  respect  to  that  line,  and  all  distances  below  it  — . If  the  coordinates  of 
a point  are  N 234,  and  E 2,468.78,  we  need  not  measure  the  whole  east 
distance  from  the  origin,  but  start  from  the  north  and  south  line  marked 
+ 20.  With  5"  squares,  a 6"  scale  will  be  sufficiently  long  for  plotting.  To 
illustrate  plotting  by  use  of  the  traversed  distances,  we  will  use  the  following 
example: 


Stations. 

Quadrant 

Courses. 

Distances. 

Latitudes. 

Departures. 

Totals. 

N 

S 

E 

W 

N 

S 

E 

W 

1-2 

N350E 

270 

221 

155 

221 

155 

2-3 

N 83°  30'  E 

129 

15 

128 

236 

283 

3-4 

S570E 

222 

121 

186 

115 

469 

4-5 

S 34°  15'  W 

355 

293 

200 

178 

269 

236 

414 

469 

200 

The  foregoing  table,  calculated  according  to  formula  for  latitudes  and 
departures,  shows  that  Station  2 is  221  ft.  north  and  155  ft.  east  of  Station  1 ; 
and  that  Station  5 is  178  ft.  south  and  269  ft.  east  of  Station  1. 

These  stations,  or  Stations  3 and  4,  or  all,  may  be  placed  on  the  map  by 
simply  making  the  two  measurements  for  each  station. 

To  Find  the  Area  of  a Tract  of  Land.— If  a regular  polygon,  find  the  area 
by  the  rule  given  under  the  head  of  “Mensuration”  for  polygons  of  the 
same  number  of  sides.  If  an  irregular  polygon,  divide  it  into  triangles  and 
calculate  the  area  of  each  triangle;  the  sum  of  these  areas  will  be  the  area  of 
the  tract.  If  the  tract  is  an  irregular  polygon  in  shape,  the  map  should  be 
made  on  as  large  a scale  as  possible,  and  the  distances  should  be  measured 
with  the  greatest  care,  owing  to  liability  to  error  through  very  slight  inac- 
curacies of  measurement. 

To  Find  the  Contents  of  a Seam  of  Coal  Under  a Tract.— If  the  seam  lies  fiat, 
multiply  the  area  of  the  tract  in  square  feet  by  the  thickness  of  the  seam  in 
feet.  The  product  will  be  the  cubical  contents  of  the  seam  in  feet.  If  the 
seam  is  an  inclined  one,  find  its  area  by  measuring  the  width  of  the  tract  on 
its  line  of  pitch,  and  find  the  distance  on  the  pitch  of  the  seam  by  dividing 
the  horizontal  distance  measured  by  the  cosine  of  the  angle  of  inclination. 
This  will  give  you  the  pitch  distance.  Multiply  the  pitch  distance  by  the 
length  of  the  tract,  and  you  will  have  the  area  of  the  seam.  This  multiplied 
by  its  thickness  will  give  the  contents. 

cubic  contents  in  feet  X Sp.  Gr.  X 62.5 
2,240 


Tons  of  coal  = 


LEVELING. 


53 


LEVELING. 

instruments. — But  two  instruments  are  used— the  level  and  a leveling  rod. 
The  level  consists  of  a telescope  to  which  is  fitted,  on  the  under  side,  a long 
l^vel  tube.  The  telescope  rests  in  a Y at  each  end  of  a revolving  bar,  which  is 
attached  to  a tripod  head  very  similar  to  that  used  for  a transit.  The 
telescope  is  similar  to  the  telescope  of  a transit.  The  leveling  rod  is 
merely  a straight  bar  of  wood,  6 ft.  or  more  in  length,  divided  into  feet  and 
tenths  of  a foot.  A target  divided  into  four  equal  parts  by  two  lines,  one 
parallel  with  the  staff,  and  the  other  at  right  angles  to  it,  and  painted  red 
and  white,  so  as  to  make  it  prominent  at  a distance,  slides  on  the  rod  and  is 
provided  with  a clamp  screw.  The  center  of  the  target  is  cut  out  and  a 
vernier,  graduated  decimally,  is  set  in,  which  enables  the  rodman  to  read  as 
close  as  of  a foot. 

If  a long  rod  is  required,  it  is  made  of  two  sliding  bars,  which,  wheii 
closed,  are  similar  to  a single  rod,  as  described  above.  When  used  at  points 
where  it  is  necessary  to  shove  the  target  to  a greater  height  than  6 or  6^  ft., 
the  target  is  clamped  at  the  highest  graduation  on  the  front  of  the  rod,  and 
•the  rod  is  extended  by  pushing  up  the  back  part,  which  carries  the  target 
with  it.  The  readings,  in  this  case,  are  made  either  from  the  vernier  on  a 
graduated  side,  or  a vernier  on  the  back.  The  rodman  must  always  hold  his 
rod  perfectly  plumb  or  perpendicular. 

To  Adjust  the  Level.— The  proper  care  and  adjustment  of  the  level  is  of  great 
importance.  A very  slight  error  in  adjustment  will  completely  destroy  the 
utility  of  any  work  done. 

To  Adjust  the  Line  of  Collimation.— Set  the  tripod  firmly,  remove  the  Y pins 
from  the  clips,  so  as  to  allow  the  telescope  to  turn  freely,  clamp  the  instru- 
ment to  the  tripod  head,  and,  by  the  leveling  and  tangent  screws,  bring 
either  of  the  wires  upon  a clearly  marked  edge  of  some  object,  distant  from 
100  ft.  to  500  ft. 

Then  with  the  hand,  carefully  turn  the  telescope  half  way  around,  so  that 
the  same  wire  is  compared  with  the  object  assumed. 

Should  it  be  found  above  or  below,  bring  it  half  way  back  by  moving  the 
capstan-headed  screws  at  right  angles  to  it,  remembering  always  the  invert- 
ing property  of  the  eyepiece;  now  bring  the  wire  again  upon  the  object,  and 
repeat  the  first  operation  until  it  will  reverse  correctly.  Proceed  in  the 
same  manner  with  the  other  wire  until  the  adjustment  is  completed. 
Should  both  wires  be  much  out,  it  will  be  well  to  bring  them  nearly  correct 
before  either  is  entirely  adjusted. 

To  Adjust  the  Level  Bubble.— Clamp  the  instrument  over  either  pair  of 
leveling  screws,  and  bring  the  bubble  into  the  center  of  the  tube. 

Now  turn  the  telescope  in  the  wyes,  so  as  to  bring  the  level  tube  on  either 
side  of  the  center  of  the  bar.  Should  the  bubble  run  to  the  end,  it  would 
show  that  the  vertical  plane,  passing  through  the  center  of  the  bubble,  was 
not  parallel  to  that  drawn  through  the  axis  of  the  telescope  rings.  To 
rectify  the  error,  bring  it  by  estimation  half  way  back,  with  the  capstan- 
headed screws,  which  are  set  in  either  side  of  the  level  holder,  placed 
usually  at  the  object  end  of  the  tube.  Again  bring  the  level  tube  over  the 
center  of  the  bar,  and  adjust  the  bubble  in  the  center,  turn  the  level  to 
either  side,  and,  if  necessary,  repeat  the  correction  until  the  bubble  will 
keep  its  position,  when  the  tube  is  turned  half  an  inch  or  more  to  either  side 
of  the  center  of  the  bar.  The  necessity  for  this  operation  arises  from  the 
fact  that  when  the  telescope  is  reversed,  end  for  end,  in  the  wyes  in  the 
other  and  principal  adjustment  of  the  bubble,  we  are  not  certain  of  placing 
the  level  tube  in  the  same  vertical  plane,  and,  therefore,  it  would  be  almost 
impossible  to  effect  the  adjustment  without  a lateral  correction. 

Having  now,  in  a great  measure,  removed  the  preparatory  difficulties,  we 
proceed  to  make  the  level  tube  parallel  with  the  bearings  of  the  Y rings.  To 
do  this,  bring  the  bubble  into  the  center  with  the  leveling  screws,  and  then, 
without  jarring  the  instrument,  take  the  telescope  out  of  the  wyes  and 
reverse  it  end  for  end.  Should  the  bubble  run  to  either  end,  lower  that  end, 
or,  what  is  equivalent,  raise  the  other  by  turning  the  small  adjusting  nuts, 
on  one  end  of  the  level,  until,  by  estimation,  half  the  correction  is  made; 
again  bring  the  bubble  into  the  center  and  repeat  the  whole  operation,  until 
the  reversion  can  be  made  without  causing  any  change  in  the  bubble.  It 
would  be  well  to  test  the  lateral  adjustment,  and  make  such  correction  as 
may  be  necessary  in  that,  before  the  horizontal  adjustment  is  entirely 
completed. 


54 


TRANSIT  S UR  VEYING, 


To  Adjust  the  Wyes.— Having  effected  the  previous  adjustments,  it  remains 
now  to  describe  that  of  the  wyes,  or,  more  precisely,  that  which  brings  the 
level  into  a position  at  right  angles  to  the  vertical  axis,  so  that  the  bubble 
will  remain  in  the  center  during  an  entire  revolution  of  the  instrument. 
To  do  this,  bring  the  level  tube  directly  over  the  center  of  the  bar,  and  clamp 
the  telescope  firmly  in  the  wyes,  placing  it  as  before,  over  two  of  the  leveling- 
screws,  unclamp  the  socket,  level  the  bubble,  and  turn  the  instrument  half 
way  around,  so  that  the  level  bar  may  occupy  the  same  position  with  respect 
to  the  leveling  screws  beneath.  Should  the  bubble  run  to  either  end,  bring 
it  half  way  back  by  the  Y nuts  on  either  end  of  the  bar;  now  move  the 
telescope  over  the  other  set  of  leveling  screws,  bring  the  bubble  again  into 
the  center,  and  proceed  precisely  as  above  described,  changing  to  each  pair 
of  screws,  successively,  until  the  adjustment  is  very  nearly  perfected,  when 
it  may  be  completed  over  a single  pair. 

The  object  of  this  approximate  adjustment  is  to  bring  the  upper  parallel 
plate  of  the  tripod  head  into  a position  as  nearly  horizontal  as  possible,  in 
order  that  no  essential  error  may  arise,  in  case  the  level,  when  reversed,  is  not 
brought  precisely  to  its  former  situation.  When  the  level  has  been  thus 
completely  adjusted,  if  the  instrument  is  properly  made,  and  the  sockets  well 
fitted  to  each  other  and  the  tripod  head,  the  bubble  will  reverse  over  each 
pair  of  screws  in  any  position.  Should  the  engineer  be  unable  to  make  it 
perform  correctly,  he  should  examine  the  outside  socket  carefully  to  see 
that  it  sets  securely  in  the  main  socket,  and  also  notice  that  the  clamp  does 
not  bear  upon  the  ring  that  it  encircles.  When  these  are  correct,  and  the 
error  is  still  manifested,  it  will  probably  be  in  the  imperfection  of  the 
interior  spindle. 

After  the  adjustments  of  the  level  have  been  effected,  and  the  bubble 
remains  in  the  center  in  any  position  of  the  socket,  the  engineer  should 
carefully  turn  the  telescope  ,in  the  wyes,  and  sighting  upon  the  end  of  the 
level,  which  has  the  horizontal  adjustments  along  each  side  of  the  wye, 
make  the  tube  as  nearly  vertical  as  possible.  When  this  has  been  secured, 
he  may  observe,  through  the  telescope,  the  vertical  edge  of  a building, 
noticing  if  the  vertical  hair  is  parallel  to  it;  if  not,  he  should  loosen  two  of 
the  cross-wire  screws  at  right  angles  to  each  other,  and  with  the  hand  on 
these,  turn  the  ring  inside,  until  the  hair  is  made  vertical;  the  line  of  colli- 
mation  must  then  be  corrected  again,  and  the  adjustments  of  the  level  will 
be  complete. 

To  Use  the  Level.— When  using  the  instrument,  the  legs  must  be  set  firmly 
into  the  ground,  and  neither  the  hands  nor  person  of  the  operator  be 
allowed  to  touch  them;  the  bubble  should  then  be  brought  over  each  pair  of 
leveling  screws  successively,  and  leveled  in  each  position,  any  correction 
being  made  in  the  adjustments  that  may  appear  necessary.  Care  should  be 
taken  to  bring  the  wires  precisely  in  focus,  and  the  object  distinctly  in  view, 
so  that  all  errors  of  parallax  may  be  avoided. 

This  error  is  seen  when  the  eye  of  an  observer  is  moved  to  either  side  of 
the  center  of  the  eyepiece  of  a telescope,  in  which  the  foci  of  the  object  and 
eyeglasses  are  not  brought  precisely  upon  the  cross-wires  and  object;  in  such 
a case  the  wires  will  appear  to  move  over  the  surface,  and  the  observation 
will  be  liable  to  inaccuracy.  In  all  instances  the  wires  and  object  should  be 
brought  into  view  so  perfectly  that  the  spider  lines  will  appear  to  be  fastened 
to  the  surface,  and  will  remain  in  that  position  however  the  eye  is  moved. 

If  the  socket  of  the  instrument  becomes  so  firmly  set  in  the  tripod  head  as 
to  be  difficult  of  removal  in  the  ordinary  way,  the  engineer  should  place  the 
palm  of  his  hand  under  the  wye  nuts  at  each  end  of  the  bar,  and  give  a 
sudden  upward  shock  to  the  bar,  taking  care  also  to  hold  his  hands  so  as  to 
grasp  it  the  moment  it  is  free. 

Field  Work.— If  the  survey  has  been  carefully  made  and  vertical  angles 
taken  at  every  sight,  leveling  will  be  necessary  only  in  cases  where  extreme 
accuracy  in  regard  to  vertical  heights  is  necessary.  In  most  cases  of 
practical  work  at  collieries,  particularly  in  determining  thickness  of  strata, 
general  rise  or  fall  of  an  inside  road,  etc.,  the  elevations  calculated  by  the 
use  of  the  vertical  angle  will  be  close  enough,  but  there  are  frequently 
instances  when  leveling  must  be  done  to  insure  success  in  certain  work.  In 
this  connection  it  is  well  to  state  that  if  the  transit  telescope  is  supplied 
with  a long  level  tube,  and  it  is,  as  a whole,  in  first-class  adjustment,  levels 
can  be  successfully  run  with  it,  if  the  transitman  uses  due  car®.  Having  his 
instrument  in  proper  adjustment  and  his  note  book  ruled,  the  levelmau  is 
ready  to  proceed  with  the  work. 


FIELD  WORK. 


55 


The  rodman  holds  the  rod  on  the  starting  point,  the  elevation  of  which  is 
either  known  or  assumed.  The  levelman  sets  up  his  instrument  somewhere 
in  the  direction  in  which  he  is  going,  hut  not  necessarily,  or  usually,  in  the 
precise  line.  He  then  sights  to  the  rod  and  notes  the  reading  as  a backsight 
or  + (plus)  sight,  entering  it  in  the  proper  column  of  his  note  book,  and 
adding  it  to  the  elevation  of  the  starting  point  as  the  “height  of  instrument.” 
The  rodman  then  goes  ahead  about  the  same  distance,  sets  his  rod  on  some 
well  defined  and  solid  point,  and  the  levelman  sights  again  to  the  target, 
which  the  rodman  moves  up  or  down  the  rod  till  it  is  exactly  bisected  by  the 
horizontal  cross-hair  in  the  telescope,  as  he  did  when  giving  the  backsight. 
This  reading  is  noted  as  a foresight  or  — (minus)  sight.  The  foresight 
subtracted  from  the  height  of  instrument  gives  the  elevation  of  the  second 
station.  The  rodman  holds  this  latter  point,  and  the  levelman  goes  ahead 
any  convenient  distance,  backsights  to  the  rod,  and  proceeds  as  before.  In 
this  case  we  have  assumed  that  levels  are  only  being  taken  between  regular 
stations  or  two  extreme  points. 

If  a number  of  points  in  close  proximity  to  each  other  are  to  be  taken, 
the  rodman,  after  giving  the  backsight,  holds  his  rod  at  each  point  desired. 
The  readings  of  any  number  in  convenient  sighting  distance  are  taken  and 
recorded  as  foresights,  and  any  descriptive  notes  are  made  in  the  column  of 
remarks.  These  are  each  subtracted  from  the  height  of  instrument,  and  the 
elevation  found  is  noted  in  column  headed  elevation.  After  all  the  inter- 
mediate points  are  taken,  the  rodman  goes  ahead  to  some  well-defined  point, 
which  is  called  a “turning  point”  (T.  P.)  in  the  notes.  The  elevation  of 
this  is  found  and  recorded.  The  rodman  remains  at  this  point  until  the 
levelman  goes  ahead,  sets  up  and  takes  a backsight.  This  backsight  reading, 
added  to  the  elevation  of  the  turning  point,  gives  a new  height  of  instrument 
from  which  to  subtract  new  foresights,  and  thus  obtain  the  elevation  of  the 
next  set  of  points  sighted  to. 

When  running  levels  over  a long  line,  the  levelman  should  set  frequent 
“bench  marks.”  These  are  any  permanent  well-defined  marks  that  can  be 
readily  found  and  identified  at  any  future  time.  By  leveling  to  them  he  has 
secured  the  elevation  of  points  from  which  to  start  any  subsequent  levels 
that  may  be  necessary.  A good  bench  mark  can  always  be  made  on  the  side 
or  root  of  a large  tree  or  stump  by  chopping  it  away  so  as  to  leave  a wedge- 
shaped  projection  with  the  point  up.  Drive  a nail  in  the  highest  point  of 
this,  to  mark  where  the  rod  was  held,  and  blaze  the  tree  or  stump  above  the 
bench  mark.  In  this  blaze,  either  cut  or  paint  the  number  of  the  bench 
mark,  which  should,  of  course,  correspond  with  the  number  in  the  note 
book.  In  the  mines,  prominent  frogs  or  castings  in  the  main  roads,  if 
permanent,  make  good  bench  marks. 


Level  Notes. 


Station. 

B.  S. 

F.  S. 

H.  Inst. 

Elev. 

Remarks. 

1 

3.412 

103.412 

100. 

Assumed  elevation  of  Station  1. 

2 

4.082 

99.33 

Station  2 of  survey.  See  page 

Vol 

6.791 

96.621 

Sight  taken  to  ground  at  N.  E.  cor. 

John  Smith’s  house. 

3 = T.  P. 

11.698 

4.862 

110.248 

98.55 

Station  3 of  survey  noted  above. 

4 

9.817 

100.431 

Station  4 of  survey  noted  above. 

B.  M.l 

6.311 

103.937 

B.  M.  1 is  on  north  side  of  large 

white  oak. 

5 

6.427 

103.821 

Station  5 of  survey  noted  above.  • 

In  underground  leveling,  extreme  care  must  be  observed  to  record  the 
algebraic  signs  of  the  readings,  which  show  whether  the  level  rod  was  held 
in  its  usual  position,  indicated  by  a -f  sign  or  the  absence  of  any  sign,  or 
upside  down,  indicated  by  the  — sign. 

Proof  of  Calculations.— The  calculations  are  proven  by  adding  together 
the  backsights  and  also  the  foresights  taken  to  turning  points  and  last 


56 


UNDERGROUND  SURVEYING, 


station.  Their  difference  equals  the  difference  of  level  between  the  starting 
point  and  last  station.  Thus: 

Backsights. 

3.412 
11.698 
15.110 
11.289 

3.821  = 103.821  — 100.0  or  3.821. 


TRIGONOMETRIC  LEVELING, 

This  method  determines  the  difference  in  elevation  between  two  points 
from  the  measurement  of  the  distance  between  the  points,  and  from  the 
vertical  angle  between  them.  Although  generally  less  accurate  than  level- 
ing with  a Y level,  it  is  much  more  rapid  and  is  especially  adapted  for  pre- 
liminary work  in  a hilly  country,  or 
for  the  leveling  of  mine  slopes  and 
pitching  rooms  where  the  Y level  can- 
not be  used  with  any  advantage  or 
accuracy.  By  reading  the  angles  and 
by  checking  the  measurements  a very 
high  degree  of  accuracy  can  be  ob- 
tained in  trigonometric  leveling. 

Case  1.  Assume  the  elevation  of  A 
to  be  100  ft.  A.  T.  With  the  transit  set 
up  over  A and  properly  leveled,  sight 
to  a point  (7  on  a rod  so  that  B C 
equals  A D.  Measure  the  vertical  angle 
Z and  the  inclined  distance  D C,  then  the  difference  in  the  elevation 
between  A and  B equals  B C = CD  X sin  Z,  and  the  elevation  of  B equals 
100  + B a 

Case  2.  Assume  the  elevation  of 
station  A in  the  roof  of  a mine  to  be 
100  ft.  A.  T.  Then  with  the  transit 
set  up  directly  under  A and  properly 
leveled  sight  to  a point  C upon  the 
plumb-line  suspended  from  the  station 
B,  measure  the  vertical  angle  X,  in- 
clined distance  D C,  and  roof  distance 
B C.  From  this,  the  distance  C Y ^ 

D C X sin  X.  The  elevation  of  B is 
then  found  as  follows:  The  elevation 
of  B = the  elevation  of  A — AD  -\- 
(DCX  sin  X)  + BC. 

There  are  many  modifications  of 
this  simple  method,  but  from  the  above  diagrams  the  most  complex  modifi- 
cations can  be  worked  out. 

Trigonometric  Level  Notes. 


Station. 

Vertical 

Angle. 

Inclined 

Distance. 

Vertical 

Distance. 

Height  of 
Instrument. 

Roof 

Distance. 

Eleva- 

tion. 

A 

A - B 

-f5° 

100 

4-8.72 

2' 

3' 

4-100 

109.72 

B ~ C 

-f2o 

100 

-f3.49 

3' 

2' 

114.21 

C — D 

-3° 

100 

—5.23 

4' 

3' 

107.99 

D-  E 

_40 

100 

—6.98 

2' 

V 

100.01 

UNDERGROUND  SURVEYING. 

There  are  a number  of  variations  in  the  foregoing  practice  that  are  caused 
by  the  entirely  different  set  of  conditions  in  underground  work.  These  have 
been  grouped  together  for  convenience  of  reference. 


STATIONS. 


57 


The  Establishment  of  Stations. — As  this  is  the  most  important  duty  of  an 
engineer  in  surface  work,  so  it  takes  the  first  place  in  work  underground,  as 
the  accuracy  of  the  work  depends  on  the  location  of  the  stations,  while  its 
rapidity  depends  on  using  the  fewest  number  consistent  with  completeness. 
It  also  stands  to  reason  that  the  fewer  the  number  of  stations,  the  fewer  the 
chances  of  error.  In  underground  work,  stations  should  be  located  under 
the  conditions  of  permanence,  freedom  from  destroying  agencies,  and  ease  of 
access.  Temporary  stations  for  a single  sight  need  not  fill  all  these  require- 
ments. We  establish  them  generally  in  the  roof  of  the  mine— less  frequently 
in  the  floor.  In  the  former  case  we  must  establish  a “ center”  before  each 
set-up  of  the  transit,  and  thus  underground  differs  from  surface  work.  The 
first  surveys  were  made  with  lamps  set  on  the  floor,  sighted  to,  and  then  set 
over.  Permanence  was  secured  by  driving  iron  nails  or  tacks  in  the  sills  of 
the  track  or  sets  of  timber.  As  acid  water  soon  destroyed  these,  they  were 
followed  by  copper  tacks  or  brads,  and  all  were  witnessed  by  notches  cut  on 
both  sides  of  the  sill,  as  in  outside  work,  and  by  a vertical  paint  mark  on  the 
solid  wall,  with  the  number  of  the  station.  This  method  is  faulty,  as  the 
tracks  in  crooked  gangways  are  seldom  placed  where  one  can  get  the  longest 
sig:ht,  and,  as  they  are  the  traveling  ways,  the  stations  run  the  chance  of 
being  knocked  out  by  passing  men  or  mules,  and  the  whole  track,  on  a curved 
incline,  is  generally  sprung  by  every  loaded  trip.  As  the  sights  must  be  as 
long  as  carefulness  of  work  will  allow,  we  put  them  generally  in  the  roof,  as 
that  offers  the  greatest  area  for  a choice,  and  is  not  under  foot.  Any  settling 
of  the  roof  so  as  to  affect  the  accuracy  of  the  station  would  be  equally  effect- 
ive in  destroying  the  accuracy  of  a station  in  the  floor.  We  therefore  choose 
places  that  will  be  least  affected  by  subsequent  work,  and  put  the  stations  in 
collars,  lids  or  wedges  of  props,  in  the  props  themselves,  when  they  have 
incline  sufficient  to  allow  the  transit  to  be  set  under  them,  or  in  the  roof 
itself.  Wherever  set,  they  should  not  project  far  from  the  surface,  and  thus 
be  liable  to  be  brushed  away  in  a low  gangway  by  cars  with  topping  higher 
than  usual,  or  knocked  away  by  flying  fragments  from  a shot,  if  near  the 
working  faces.  Top  stations  have  a mark  about  them  to  call  attention  to 
their  location.  It  is  generally  a circle,  unless  there  are  other  corps  at  work 
in  the  same  mine  that  use  the  circle,  and  the  stations  of  the  two  surveys 
would  be  confused  if  marked  alike.  In  this  case  a corps  selects  some  easily 
made  flgure,  as  a triangle,  square,  etc.  If  two  surveys  use  the  same  statioii, 
the  mark  of  the  second  survey  is  placed  around  that  of  the  first,  and  the 
“ Remarks  ” give  “ Station  No.  234  of  L.  & S.  corps,”  etc. 

Kinds  of  Stations.— The  simplest  top  station  is  a shallow  conical  hole,  made 
with  the  point  of  the  foresight  man’s  hatchet,  which  is  dug  into  the  top  rock 
and  rotated,  and  is  called  by  some  a jigger  station.  Corps  using  these  entirely 
have  a jigger  consisting  of  a steel-pointed  extension  rod,  with  an  offset  hold- 
ing a paint  brush.  The  rod  is  long  enough  to  allow  the  point  to  be  driven 
into  the  roof  at  any  height,  and  its  rotation  marks  a circle  with  the  brush, 
which  is  also  used  to  mark  the  number  beside  it.  Centers  are  set  under  such 
stations  and  sights  are  given  by  another  tool— also  called  a jigger.  This  is  an 
extension  rod,  beyond  the  upper  end  of  which  projects  a piece  of  sheet  iron 
shaped  like  an  isosceles  triangle,  with  the  upper  and  smaller  angle  cut  off  so 
as  to  form  an  end  one-quarter  of  an  inch  broad,  and  in  this  end  is  cut  a 
U-shaped  groove. 

The  sights  are  given  and  the  “ centers  ” set  by  putting  the  plummet  cord 
in  this  groove,  and  placing  the  end  in  the  “jigger  hole”  in  the  roof.  The 
cord  must  be  more  than  twice  the  length  of  the  section  of  the  place,  as  it 
must  be  held  in  the  hand,  run  over  the  jigger  notch,  and  hang  vertically  to 
the  plummet,  which  must  come  to  the  floor  when  the  stations  are  set.  The 
rod  and  cord  are  held  in  the  left  hand,  and  the  right  is  free  to  steady  the 
“bob,”  give  sight,’  or  set  the  center.  The  advantage  of  this  method  lies  in 
the  quickness  with  which  the  centers  are  set  and  the  sights  given,  and  the 
ease  with  which  the  highest  stations  are  reached.  The  disadvantages  are 
the  impossibility  of  making  the  jigger  hole  perfectly  conical,  so  that  the  jig- 
ger can  be  set  in  the  same  place  on  two  successive  sights,  and  the  plummet 
cord  will  hang  exactly  in  the  same  place. 

Second— Common  shingle  nails  are  driven  into  collars,  or  cracks  in  the 
roof.  The  end  of  the  plummet  line  is  noosed  and  put  over  the  head.  This 
causes  an  eccentric  hanging  of  the  plummet  that  may  cause  an  error  in  back- 
sight and  foresight  of  the  width  of  the  nail  head,  which  will  be  quite  appreci- 
able in  a short  sight.  To  do  away  with  this  error,  a variety  of  nails  ( called  spads, 
spuds,  etc.)  are  made  of  iron  or  copper.  Iron  will  not  corrode  in  dry  mines, 


58 


UNDERGROUND  SURVEYING. 


and  is  much  cheaper.  The  simplest  is  made  by  hammering  out  the  head  of  a 
horseshoe  or  mule-shoe  nail,  punching  a hole  in  the  flattened  head  for  insert- 
ing the  cord,  and  cutting  off  the  point,  so  as  to  make  the  flnished  spad  an 
inch  long.  This  will  bring  the  head  near  the  surface  without  having  to  drill 
too  deep  a hole,  and  will  make  them  unfit  for  lamp  picks,  as  they  are  very 
handy  for  such  purposes,  and  thousands  have  been  pulled  out  to  this  end. 
Any  blacksmith  can  furnish  them  for  less  than  1 cent  each.  They  are 
driven  broadside  to  the  line  of  sight,  or  they  will  be  liable  to  the  same  objec- 
tion as  the  shingle  nail.  To  remove  all  chance  of  eccentricity,  a form  is 
made  with  a shoulder  in  which  a hole  is  drilled  parallel  to  the  length  of  the 
nail.  The  practice  of  using  staples  for  stations  is  antiquated— though  given 
in  the  last  editions  of  some  modern  textbooks— and  should  never  be  used 
where  accuracy  is  required. 

Third. — All  these  varieties  of  spads  are  driven  into  a crack  of  the  roof;  but 
such  stations  cannot  be  called  permanent,  as  the  same  force  that  made  the 
crack  will  tend  to  open  it  and  let  the  nail  drop.  Even  if  this  does  not  hap- 
pen, we  shall  have  the  water  in  a wet  mine  coming  in  by  these  cracks,  and 
rotting  the  nails,  or  the  rock  at  the  sides  of  the  crack,  and  in  a month  after 
the  placing  of  the  station,  it  will  be  unfit  for  use. 

Fourth.— Into  a hole  drilled  in  the  roof,  a wooden  plug  is  driven,  and  into 
this  we  drive  the  spad.  The  swelling  wood  clamps  the  same  and  prevents 
its  coming  out  as  readily  as  it  was  put  in.  The  plugs  are  made  of  well-dried 
wood  outside,  and  are  carried  by  the  man  that  sets  the  stations.  The  flrst 
holes  were  made  by  a jumper,  and  the  plugs  were  2 in.  square  and  6 in.  long. 
The  modern  holes  are  usually  made  by  a twist  drill  of  as  small  a diameter  as 
will  do  the  work  without  bending  at  the  shank.  Such  drills  can  be  used  in 
slates  or  clays;  but  an  ordinary  drill  and  hammer  must  be  used  in  harder 
rocks.  The  average  modern  holes  are  i in.  to  | in.  in  diameter,  while 
the  plugs  are  i in.  to  1 in.  long  at  the  maximum.  The  smaller  the  hole,  the 
quicker  the  work.  All  stations  should  be  put  in  the  roof  in  preference  to  the 
under  side  of  a collar,  or  in  any  ordinary  timbering.  The  only  exception  is 
where  the  roof  is  too  poor  to  hold  them.  Such  stations  should  be  checked  in 
extending  a survey  before  they  are  used,  if  we  wish  to  swear  to  the  accuracy 
of  our  work.  The  engineer  that  believes  in  using  collars  may  And  himself 
in  the  quandary  of  the  man  whose  company  worked  across  their  line  because 
he  started  from  a collar  station.  Since  its  location,  the  place  was  working 
and  the  collar  was  taken  down  and  shifted  end  for  end  when  replaced. 
Good  side  notes,  if  consulted,  would  have  shown  him  the  change. 

Fifth. — A twist  drill  in.  in  diameter  is  used  to  make  a hole  in  the  roof; 
a piece  of  cord— or,  better,  a copper  mre— is  placed  across  this,  and  a hard- 
wood shoe  peg  is  driven  into  the  hole  and  binds  the  cord  tight.  The 
plummet  is  tied  to  the  lower  end.  A cord  will  soon  rot,  and,  if  in  the 
gangway,  is  pulled  out  by  the  drivers  for  whip  lashes,  while  the  wire  is 
more  permanent;  but  even  this  will  be  pulled  out  by  catching  in  the  topping 
of  a car  in  a low  place. 

Lastly.— use  of  spads  is  dispensed  with,  and  all  the  stations  put  in  rock 
roof  where  possible.  A i"  twist  drill  makes  a vertical  hole  1 in.  deep. 
Into  this,  when  a sight  is  to  be  taken,  the  foresight  man  puts  a steel  clip  with 
serrated  edges.  This  is  made  by  bending  upon  itself  a thin  piece  of  steel 
A in.  wide.  When  the  ends  are  pressed  together  it  will  go  into  the  hole,  and 
the  spring  of  the  sides  and  the  serrated  edges  hold  the  clip  in  the  hole  so  that 
it  is  hard  to  pull  out.  The  cord  passes  through  a hole  in  the  center  of  the 
bend  and  is,  therefore,  in  the  center  of  the  hole— no  matter  how  the  clip 
is  inserted.  It  is  removed  by  pressing  together  the  ends  of  the  clip.  This  is 
the  easiest  and  quickest  way  of  working,  as  there  is  no  eyehole  to  be  freed 
from  dirt  and  no  knot  to  be  tied  and  untied.  The  hanging  of  the  plummet 
takes  a fraction  of  a second,  and  the  station  will  remain  as  long  as  the  roof 
keeps  up.  The  disadvantages  are  the  putting  of  the  holes  inclined  to  the 
vertical  by  a careless  man,  and  the  many  roofs  that  are  unfit  for  piercing 
Mith  a twist  drill.  , ,,  , , ^ • 

Marking  Stations.—We  should  have  some  regular  way  of  witnessing  our 
stations.  In  general,  a vertical  line  on  the  nh  calls  attention  to  a station  in 
the  floor  near  the  side  marked.  A roof  station  has  the  mark  around  it,  as  has 
been  described,  and  it  is  some  geometric  figure.  If  three  regular  corps  are 
engaged  in  the  same  field  and  meet  in  the  same  mines,  as  the  company 
corps,  the  corps  of  the  individual  operator,  and  the  private  corps  that  is 
looking  after  the  interest  of  one  or  more  of  the  land  owners,  they  must  use 
different  signs  for  stations.  The  most  common  are  the  circle,  square,  and 


STATIONS. 


59 


triangle.  If  the  “circle”  corps  puts  in  the  station,  it  has  a circle  about  it. 
The  next  corps  uses  it  and  puts  a square  about  it  and  notes  “ Sta.  472  = to 
Sta.  742  of  ( ) Corps.”  The  third  corps  uses  it  and  puts  a triangle  about 
the  square,  and  notes  “ Sta.  617  = to  Sta.  472  of  ( ) Corps,  and  Sta.  742  of  ( ) 
Corps’.”  If  the  first  corps  uses  the  station  again,  it  notes  the  numbers  given 
by  the  two  other  corps,  and  these  three  numbers  will  aid  in  identifying  it  if 
one  or  two  of  the  numbers  are  lost. 

Distinguishing  Stations.— Each  station  must  be  lettered  or  numbered  so  that 
it  can  be  readily  recognized  when  the  subsequent  surveys  are  made.  When 
set  it  may  have  been  at  the  end  of  a gangway,  while  six  months  later 
the  gangway  has  been  driven  hundreds  of  feet  from  that  place,  chambers 
have  been  turned  offin  what  was  solid,  and  the  place  be  so  utterly  unlike 
its  former  state  that  nothing  but  a fixed  mark  belonging  to  that  station 
alone  will  enable  us  to  recognize  it.  The  methods  of  distinguishing  stations 
vary  widely.  In  one  place  the  writer  found  that  each  gangway  and  room 
had  a Station  1 at  its  beginning,  and'The  various  stations  numbered  1 were 
designated  “ Grog  Run  1,  2,  3,  etc.”;  “ Pat  James  Gangway  1,  2,  etc.”;  and  so 
on  through  the  map,  that  showed  between  fifty  and  one  hundred  stations 
numbered  1,  so  that  a new  engineer  would  have  had  to  learn  the  mine 
thoroughly  before  he  could  extend  a survey.  Another  way  is  to  use  Al, 
A2,  etc.,  up  to  AlOO,  and  so  through  the  alphabet  to  avoid  running  up  too  high 
in  numbers.  A third  was  lettering  the  various  sections  of  the  mine  A,  B, 
C,  etc.,  and  the  numbers  begin  with  1 in  each  and  run  up  indefinitely. 

All  of  the  above  have  disadvantages,  as  powder  or  lamp  smoke,  mud, 
mold,  or  the  misplaced  ingenuity  of  small  boys  may  so  obliterate  or  obscure 
a mark  that  it  will  be  recognized  only  by  association  with  its  immediate 
neighbors,  and  these  may  have  shared  the  same  fate.  You  may  have  only  a 
part  of  the  mine  map  with  you,  and  because  the  system  of  marking  strives  to 
get  along  with  as  few  symbols  as  possible,  you  have  to  go  to  the  office,  when 
there  would  have  been  a chance  of  deciphering  the  mark  if  there  had  been 
a number  of  figures  to  it.  The  best  practice,  therefore,  courts  large  numbers, 
begins  with  Station  0 at  the  mouth  of  the  slope  or  drift,  or  the  foot  of  the 
shaft,  and  numbers  consecutively  in  each  bed.  In  a short  time  three  figures 
are  reached,  while  in  old  mines  the  numbers  require  four  digits.  The 
chances  of  obscuring  such  a mark  are  lessened,  while  the  chances  of  our 
deciphering  it  are  increased. 

Centers.— When  the  station  is  in  the  roof,  there  must  be  something  for  the 
transit  to  set  over,  as  it  is  easier  to  do  so  than  to  set  under  a station,  and  much 
more  accurate  as  instruments  are  now  made.  The  set-up  is  made  over  a 
“ center.”  At  first,  a cross  scratched  on  the  floor  or  on  a loose  piece  of  slate, 
a daub  of  white  lead  on  the  same  with  a small  piece  of  coal  placed  under 
the  point  of  the  plummet — when  that  had  been  steadied — or  finally,  a nail 
driven  into  a block  and  afterwards  pointed,  were  used.  All  of  these,  except 
where  the  mark  was  on  the  solid  fioor— if  they  were  large  enough  to  be 
stable — were  in  the  way  of  the  observer’s  feet,  while,  if  small,  they  were  so 
light  as  to  be  readily  displaced.  It  must  be  noted  here  that  it  is  not  so  much 
the  errors  that  we  can  foresee  and  detect  that  influence  the  accuracy  of  the 
work  in  our  own  eyes,  but  the  chances  of  error  from  accidents  that  we 
cannot  control  and  that  cannot  be  readily  detected.  To  avoid  the  above 
chances,  we  make  the  centers  as  small  and  as  heavy  as  we  can — in  other 
words,  we  make  them  of  lead.  A hole  li  in.  in  diameter  and  i in.  deep  is 
bored  in  a thick  plank,  a brad  is  set  in  its  center  with  the  head  down;  the 
hole  is  filled  Avith  melted  lead  and  the  brad  is  slightly  raised  to  surround  the 
head  with  lead,  and  held  with  pincers  in  a vertical  position  till  the  lead  has 
set.  The  brad  is  cut  off  i in.  above  the  lead  and  pointed.  This  “center” 
combines  weight  and  small  size,  and  is  generally  used. 

Paint. — White  lead,  or  Dutch  white,  thinned  with  linseed  oil,  is  ordinarily 
used.  It  is  carried  in  a covered  tin  pail  holding  a pint.  The  cover  has  a 
hole  large  enough  to  admit  the  brush.  The  pail  generally  has  to  be  cleaned 
out  after  each  day’s  work,  as  the  brush  gathers  dirt  every  time  it  is  used.  In 
case  the  paint  is  to  be  kept  for  a number  of  days,  it  must  be  covered  with 
water,  which  can  be  poured  off  before  using.  If  the  ordinary  paint  brush 
has  too  long  bristles,  it  can  be  shortened  and  kept  from  wearing  by  winding 
with  fine  wire  to  the  proper  length.  The  top  should  be  wiped  clean  and 
dry  with  a piece  of  cotton  waste  before  the  paint  is  applied,  or  the  white 
will  be  so  discolored  as  to  be  scarcely  visible,  or  if  the  top  is  dirty  it  will 
fiake  off,  and  the  numbers  be  lost. 


60 


SVRVEY  NOTES. 


KEEPING  NOTES. 

Taking  Notes.— Complete  notes  should  be  taken  and  recorded  neatly  and 
systematically,  so  that  a stranger  can  easily  follow  them.  Every  physical 
characteristic,  and  all  surface  improvements  should  be  noted  and  located. 
Every  ledge  of  rock  should  be  noted,  its  character,  dip,  and  course  of  strike 
should  be  taken.  In  a large  company  there  should  be  a separate  book  for 
transit  notes  and  for  side  notes,  and  where  many  collieries  are  operated,  a 
separate  set  of  books  should  be  used  for  eaph  colliery. 

However  the  notes  are  kept,  we  must  note  the  following  things:  The 
numbers  of  the  stations;  the  needle  readings  to  check  the  vernier;  the 
vernier  reading;  the  dip  of  the  sight;  the  distance  measured,  either  flat  or  on 
the  dip;  the  height  of  the  axis  of  the  transit  from  the  ground;  the  height  of 
the  point  sighted  at  from  the  ground;  and  all  other  necessary  remarks  to 
make  the  work  plain.  It  is  customary  to  have  series  of  vertical  columns 
headed  (to  suit  the  above)  Sta.,  Needle  F.  S.,  Needle  B.  S.,  Vernier,  Pitch, 
Dist.,  H.  I.  (height  of  instrument),  H.  R.  (height  of  rod,  or  point  to  which 
sight  was  taken),  and  Remarks. 

At  the  top  of  the  page  in  starting  a survey,  there  should  be  entered  the 
name  of  the  mine  and  of  the  bed  where  the  work  is  to  be  done;  the  names  of 
the  regular  corps  employed  for  the  work,  and  those  that  were  taken  from  the 
mine  to  point  out  work  or  assist;  the  instruments  used;  the  date  of  the  work, 
and,  in  case  it  be  the  continuation  of  a previous  survey,  the  pages  where  such 
work  was  noted  must  be  set  down.  Such  books  are  complete  records,  and 
can  be  used  as  time  books  in  paying  the  men,  or  as  proofs  of  the  kind  of 
work  done  in  case  a lawsuit  requires  such  testimony,  by  showing  the  number 
of  men,  the  instruments  used,  and  the  time  employed. 

Transit  and  Side  Notes. — There  are  about  as  many  methods  of  keeping  these 
notes  as  there  are  engineers.  These  methods  arrange  themselves  into  groups, 
and  specimens  of  four  groups  will  be  shown,  as  the  most  common  in  use  in 
the  mines: 

The  side  notes  of  each  sight  follow  the  transit  notes  of  that  sight, 
and  on  the  same  page. 

/Second.— They  are  entered  in  the  same  book  on  opposite  pages. 

T/iird.— The  transit  notes  of  the  whole  survey  come  first,  and  are  followed 
by  the  side  notes  in  the  same  book. 

Fourth.— set  of  notes  has  a separate  book. 

The  last  method  is  the  best— even  if  the  same  man  takes  both  sets  of 
notes,  and  where  two  men  do  the  work  at  the  same  time,  such  a method  is 
imperative.  Each  mine  should  have  a separate  set  of  books  for  ordinary 
work  and  special  work,  and  such  a practice  gives  the  engineer  reference 
notes  in  a portable  form.  Unless  this  is  done,  and  if  the  party  makes  surveys 
in  twenty  different  mines,  the  notes  of  two  succeeding  surveys  in  any 
locality  are  generally  in  separate  books,  and  both  must  be  carried.  This 
applies  to  side  notes,  and  four  books  must  be  carried.  With  a special  book 
for  each  mine,  no  index  is  needed  to  find  a certain  survey,  and  no  set  of 
books  must  be  overhauled.  The  book  for  that  mine  is  taken,  the  date 
looked  up,  and  the  notes  found. 

The  taking  of  side  notes  in  an  ordinary  outside  survey  is  secondary  to  the 
instrumental  work;  while  in  underground  work,  of  ordinary  character,  the 
lines  of  the  survey  are  skeletons  upon  which  are  built  the  side  notes.  The 
side  notes  are  therefore  of  the  highest  value,  and  the  forms  for  taking  them 
should  embrace  the  salient  features  of  the  underground  work,  so  that 
the  mapper  can  reproduce  them  faithfully  even  if  he  may  never  have  been 
inside. 

Forms  for  Transit  Notes.— Suppose  we  are  setting  up  at  5;  with  backsight  at 
a;  foresight  to  c;  deflected  angle  abc  = 85° 27'  left;  and  that  the  distance  be 
is  421.76  ft.  measured  on  a pitch  of  + 4°  35'. 

First  Form: 


Sta. 

Needle. 

Vernier. 

Needle. 

Pitch. 

Dist.  ! Sta. 

B.  S. 

A 

B 

F.  S. 

—a 

b 

S 25°  30'  W 

L 85°  27' 

L 85°  26' 

S 60°  0'  E 

+ 4°  35' 

421.76  c 

FORMS  FOR  NOTES. 


61 


This  is  read:  “Set-up  at  6;  backsight  at  a;  foresight  to  c;  Liat  reading  of 
vernier  under  A;  second  (check)  reading  under  B;  check  reading  by  needle 
computed  from  foresight  and  backsight  needle,  etc.”  Some  note  the 
readings  of  one  vernier  at  A,  and  the  opposite  one  at  B,  and  take  only 
one  sight.  The  last  column  for  stations  is  sometimes  omitted,  and  the  first 
widened,  so  that  the  three  can  be  entered  as  fol- 
lows: “a-6-c.”  — 

Second  Form. — This  differs  from  the  first  in  <*» 

having  but  one  column  for  the  venier  reading,  6 zsa 

which  is  not  noted  until  two  readings  agree, 
and  also  in  omitting  the  last  column  for  sta- 
tions, as  noted  above.  In  some  cases  the  line 
is  indicated  by  but  two  stations,  the  one  set  up 
at,  and  the  foresight,  as  in  the  angle  given 
a bove,  h-c.  To  note  the  backsight,  the  previous 
line  is  always  taken,  and  under  “Sta.”  we  put 
“ 0^-6,”  and  the  needle  reading. 

Third  Form. — In  this  case  a continuous  ver- 
nier is  carried  and  the  readings  are  put  in 
the  second  column,  with  the  needle  course  on 
foresights  as  a check  in  the  third.  In  the  column 
for  stations  only  the  station  at  which  the  set-up 
is  made  is  noted  on  the  line  with  the  readings 
tor  that  set-up— the  backsight  going  on  the  pre- 
vious, and  the  foresight  on  the  following,  lines. 

Fourth  Form. — This  is  also  a form  for  record-  Fig.  1. 

ing  a continuous  vernier,  as  well  as  the  deflected 

angle.  The  right-hand  page  is  for  noting  differences  of  level  as  measured 
by  level  or  transit.  Certain  columns  are  filled  in  at  the  office,  to  make  the 
book  complete  as  a reference  in  mapping,  or  in  the  mine.  This  form  is 
advocated  for  its  compactness^ f but  there  is  such  a thing  as  too  much  of 
that  article,  as  there  is  no  room  on  either  page  for  remarks,  while  in  all  the 
other  systems,  the  right-hand  page  is  set  aside  for  this  purpose. 

Fifth  Form. — Where  the  leveling  is  performed  by  the  transit,  and  each 
sight  is  taken  with  that  end  in  view,  the  level  notes  are  added  to  any  form 
of  transit  notes  chosen  and  they  are  recorded  as  shown  in  table  on  page  56. 
These  figures  are  used  to  calculate  the  differences  in  elevation,  as  shown  by 
the  pit6h  of  the  sight.  The  minus  signs  show  that  the  points  noted  are 
. below  the  stations.  If  the  station  were  in  the 

floor,  the  sight  would  have  a plus  sign.  A contin- 
uous vernier  can  be  used  with  this  form. 

Forms  for  Side  Notes.— In  every  case  the  notes 
should  convey  to  the  man  that  plots  some  idea  of 
the  form  of  the  place  surveyed.  An  accurate  sketch 
cannot  be  made  unless  the  whole  locality  can  be 
seen  at  a glance— which  is  seldom,  if  ever,  the  case— 
and  yet  we  must  not  go  to  the  other  extreme  and 
write  down  the  notes  without  a sketch;  yet  that  is 
what  is  frequently  done,  and  may  be  simply  noted 
as  the  first  form,  and  put  aside  as  a faulty  method 
with  no  good  points. 

Second  Form.— In  this,  see  Fig.  1,  as  in  a sketch 
made  as  a person  advances  with  no  definite  idea  of 
the  arrangement  of  the  work,  there  is  too  frequently 
a running  of  the  sketch  off  the  page— on  one  side  or 
the  other,  and  a cramping  of  certain  parts.  Insert- 
ing the  figures  on  the  line  of  survey  confuses  the 
one  that  plots  if  the  sketch  is  distorted  or  cramped. 
As  the  hands  of  the  note  man  are  dirty  from  rub- 
bing along  the  tape,  to  find  the  numbers,it  generally 
happens  that  the  sketches  are  smeared  and  blurred 
so  that  they  are  hard  to  decipher  when  the  notes 
Fig.  2.  are  most  clearly  kept,  and  a method  that  encourages 

cramping,  confusion,  or  obscurity  must  be  rejected. 

Third  Form. — There  is  no  attempt  made  at  sketching  in  this  form,  Fig.  2, 
but  the  red  line  in  the  center  of  the  page  of  the  note  book  is  taken  as  the  line 
of  survey,  and  the  next  parallel  lines  on  either  side  are  taken  as  the  boundaries 
pf  the  solid  on  either  side.  The  only  figures  on  each  side  of  the  red  line  are 


023S  (/(?7.g2)(  ' 


+ //0 


+ 5/  — 4 


+ 20 


8 f3 

in" 


62 


SURVEY  NOTES. 


the  distances  from  the  line  to  the  solid,  while  the  “ pluses”  at  which  they 
were  taken  are  noted  at  the  side  of  the  page,  and  the  exact  distance  between 
the  two  stations  is  enclosed  in  the  parallelogram.  This  method  at  the 
pluses  155  and  157  calls  attention  to  a point  where  practice  varies  greatly; 
namely.  How  shall  we  note  the  “ corner  of  pillar  ” ? and  Where  is  the  corner? 
One  method  calls  the  corner  that  point  where  the  pillar  begins  to  diverge 
from  the  gangway  line,  as  noted  in  Fig.  2,  at  a,  where  a chamber,  cross- 
cut, or  counter  starts  from  the  gangway;  a second  method  designates  the 
corner  as  the  first  or  last  solid  part  met  with  in  the  line  of  survey,  as  at  b, 
Fig.  2.  The  first  is  faulty,  as  there  is  no  record  of  the  gradual  divergence  of 
the  pillar  from  the  gangway  line,  and  the  words  “ corner  of  pillar”  usually 
mean  the  end  of  the  same.  We  should  therefore  call  the  pillar  solid  till  the 
line  at  right  angles  to  the  line  of  survey  is  tangent  to  the  ends,  no  matter 
whether  that  end  be  10  or  100  ft.  distant.  Any  one  can  plot  side  notes  if 
accurately  taken,  and  two  persons  accurately  plotting  such  notes  will  reach 
the  same  result. 

Level  Notes.— These  are  kept  as  in  outside  work,  as  has  been  before  stated, 
with  the  exception  that,  as  the  rod  is  reversed  in  getting  the  elevation  of  a 
station  in  the  roof,  the  record  of  the  reading  is  prefixed  with  a minus  sign. 
A record  of  such  a reversed  rod, when  the  target  is  3.78  ft.  below  the  station, 
is  recorded  —3.78. 

The  shaft  is  measured  (if  deep)  by  a fine  steel  wire  running  about  an 
accurately  graduated  wheel  (a  sufficient  number  of  turns  being  laid  to 
prevent  slipping)  and  noting  the  number  of  turns  before  the  bottom  is 
reached.  The  wire  may  be  measured  before  and  after  the  operation,  to 
insure  against  stretching.  An  aneroid  mining  barometer,  if  in  good  condi- 
tion, will  give  quite  accurate  results  if  a number  of  trips  are  made  between 
top  and  bottom,  to  give  an  average.  In  this  case  the  barometer  must  be  left 
quiet  10  or  15  minutes,  to  be  sure  that  it  has  expanded  or  contracted  to  the 
proper  degree.  For  rough  measurements,  the  length  of  the  winding  rope 
between  top  and  bottom  is  taken. 

By  one  of  these  methods  we  locate  a bench  mark  below,  that  is  connected 
with  the  outside  work  and  referred  to  tide  w^ater.  As  has  been  stated,  the 
rod  must  be  reversed  to  get  the  elevation  of  all  stations  in  the  roof,  and  all 
such  readings  are  noted  with  the  minus  sign,  as  —4.32'  (read  4.32  ft.  below 
station-).  We  must  bear  in  mind  that  roof  stations  are  almost  certain  to 
settle,  from  the  pressure  of  the  superincumbent  rocks.  To  check  such 
settling,  we  must  measure  the  distance  from  roof  to  fioor  accurately.  Some 
measure  from  floor  to  rail  of  track.  This  is  inaccurate,  as  the  track  may  be 
shifted  or  the  grade  changed  in  making  repairs,  or  to  take  out  a “ sag.”  A 
noted  expert  once  swore  that  the  roof  had  settled  in  a mine,  as  his  measure- 
ments were  from  roof  to  track,  and  the  latter  had  been  raised  without  his 
knowledge. 

Whenever  we  begin  a level  survey,  we  must  measure  the  distance  between 
roof  and  floor  and  see  if  it  agrees  with  the  notes.  If  it  differs,  we  must  note 
the  fact  under  the  original  notes,  as  a check  for  future  work. 


STORE  BOOKS. 

By  Joseph  Barrell.* 

In  large  metal  mines,  where  the  veins  are  more  or  less  vertical  and  great 
volumes  of  ore  are  extracted  from  between  the  levels,  it  becomes  important 
to  adopt  such  a system  for  recording  the  shape  and  location  of  the  stopes  that 
at  any  future  time  the  engineers  may  be  able  to  give  precise  information 
concerning  them,  without  entering  the  mine  for  the  purpose. 

Preparation  of  the  Stope  Book. — Although  the  timbering  furnishes  meapsfor 
sketching  and  locating  the  stopes,  some  regular  system  must  be  followed  or 
inextricable  confusion  will  result.  The  book  must  connect  the  stope 
sketches  with  the  transit  work  of  the  drifts  and  also  the  various  floors  with 
one  another. 

Fig.  1 is  a hypothetical  map  of  a portion  of  two  levels.  Figs.  2,  3,  and  4 
follow  from  it.  Fig.  2 being  one  leaf  from  the  stope  book.  The  paper  should 
be  of  the  quality  of  that  used  in  field  books,  ruled  by  the  printer  vertically 
and  horizontally,  with  waterproof  lines  in  a colored'  ink— preferably  green. 
A convenient  scale  has  been  found  to  be  4 lines  to  the  inch,  every  fourth  or 

♦See  “Mines  and  Minerals,”  October,  1899,  page  97. 


STOPE  BOOKS. 


63 


fifth  line  to  be  heavier.  Each  square  will  represent  a square  set,  giving  an 
actual  scale  of  about  20  ft.  to  the  inch.  A smaller  scale  does  not  show  enough 
detail, *and  a larger  one  is  not  necessary  for  this  class  of  work. 

The  most  convenient  size  for  the  bound  books  is  11  in.  long  by  in.  wide. 
Only  the  right-hand  leaves  are 
numbered,  so  that  when  open 
a page  extends  entirely  across 
the  book,  20  in.,  showing  400  ft. 
of  the  length  of  the  vein  and 
wide  enough  for  two  floors  on 
one  page.  The  floors  imme- 
diately above  each  other  must 
follow  on  consecutive  pages; 
thus,  on  the  first  double  page 
will  be  400  ft.  of  the  sill  floor 
and  first  floor,  on  the  second 
page  the  second  and  third 
floors,  and  on  the  seventh  page 
the  twelfth  and  thirteenth 
floors.  The  eighth  page  is 
reserved  for  cross-sections  of 
the  vein,  and  the  ninth  for  the 
long  upright  section,  these  two 
being  shown  by  Figs.  3 and  4. 

The  next  400  ft.  of  the  same 
drift  will  be  shown  on  page  10, 

so  that  it  joins  on  to  page  1 on  one  side  and  to  page  19  on  the  other,  and 
in  this  way  the  work  of  one  level  is  kept  together.  For  convenience,  the 
book  should  be  indexed  by  placing  a projecting  tag  with  the  number  of  the 
level  on  each  page  of  the  drift  floor. 

Having  now  a general  idea  of  the  arrangement  of  the  work  in  the  book,  it 
remains  for  us  to  determine,  precisely,  how  to 
place  it  and  how  to  show  the  relation  to  the 
transit  surveys.  First,  it  is  necessary  to  have 
some  reference  line  on  the  vein.  For  this 
purpose  draw  on  the  map,  through  the  center 
of  the  shaft,  a line  perpendicular  to  the  strike 
of  the  vein,  as  shown  in  Fig.  1.  Scale  off  from 
the  map  the  distance  at  which  it  cuts  the 
transit  course  from  the  nearest  station.  Then, 
by  adding  the  known  distances  between  sta- 
tions to  this,  we  obtain  the  surveyed  distance 
of  any  point  on  the  drift  from  our  reference 
line.  Select  the  middle  or  end  of  a page  in 
the  stope  book  for  the  zero  or  reference  line, 
such  that  the  drift  will  go  most  conveniently 
in  the  book,  and  on  the  upper  line  locate  the 
survey  points  at  their  proper  distances  from  it, 
as  in  Fig.  2.  The  vertical  location  of  any  part 
can  be  told  when  the  dimensions  of  the  tim- 
bering are  known.  In  this  instance  the  drift 
is  7 ft.  10  in.  high,  and  each  of  the  following 
12  floors  are  7 ft.  2 in.  If  the  levels  are  exactly 
100  ft.  apart,  the  thirteenth  floor  will  conse- 
quently be  6 ft.  2 in.  in  height. 

The  Stope  Book  in  the  Mine. — Having  indi- 
cated in  the  office,  by  a regiriar  system,  the 
place  for  everything  that  will  be  found  in  the 
mine,  the  next  step  is  to  proceed  to  the  details 
of  sketching.  The  location  of  the  stations  on 
the  top  line  of  the  drift-floor  pages  shows  on 
what  vertical  line  they  should  lie  in  the 
sketch;  but  the  fact  that  each  square  must 
be  kept  as  representing  a square  set,  and  that 
any  or  all  of  them  may  not  be  exactly  to  our 
scale,  will  cause  the  location  made  in  the  mine  to  vary  slightly  from  that 
made  in  the  office.  Any  such  discrepancy  must  be  taken  upon  the  edge 
of  the  page.  Therefore,  proceed  to  the  station  nearest  the  center  of  the  page 


64 


UNDERGROUND  SURVEYING. 


and  locate  it  as  nearly  as  possible  under  its  position  at  the  top,  remembering 
that  the  sets  of  timber,  no  matter  how  irregular,  must  be  represented  as 
squares.  Now  walk  along  the  drift,  watching  the  character  of  one  side  at  the 
line  of  the  floor,  sketching  while  walking,  counting  the  sets,  and  indicating 
the  posts  by  dots  of  the  pencil.  Check  up  the  number  of  sets  on  each  station 
and  continue  to  the  end  of  the  drift.  Sketch  the  other  side  in  coming  back, 
and  by  counting  the  sets  a second  time,  from  station  to  .station,  a further 
check  is  placed  upon  the  work.  On  the  correctness  of  the  sketches  of  the 
drift  floor  that  of  the  overlying  stopes  depends. 

Having  finished  the  drift,  climb  to  the  first  floor  and  locate  the  set  climbed 
through  the  same  distance  east  or  west  of  the  reference  line  as  on  the  drift 
below,  see  Fig.  2.  Since  the  chutes  and  manways  will  ordinarily  not  step  off 
sideways,  but  only  along  the  dip,  a chute  will  be  represented  the  same 
distance  from  the  side  edge  of  a page  on  all  those  floors  where  it  occurs.  In 
this  way  each  floor  is  located  in  longitude.  To  do  the  same  in  latitude  it 
will  be  necessary  to  give  an  arbitrary  number  to  that  row  of  timbers  on  the 
ground  floor  against  the  hanging  wall.  It  is  well  to  start  with  10,  since  then, 
on  a wider  working  of  the  hanging  wall,  there  will  be  no  danger  of  running 
down  into  negative  numbers.  The  rows  are  numbered  consecutively  as  they 
step  off  toward  the  foot-wall.  Thus,  in  Fig.  2,  on  the  drift  floor,  the  manway 
to  chute  No.  102  is  in  row  14,  and  that  determines  the  numbering  on  the  first 
floor.  On  the  thirteenth  floor,  in  this  instance,  as  shown  in  Fig.  3,  the  man- 
way is  in  row  19.  In  such  a manner  each  floor  is  completely  located  with 
reference  to  the  drift  below  and  ultimately  with  the  transit  survey. 

The  ease  and  rapidity  of  the  work  will  depend  on  the  character  of  the 
mine.  Much  is  gained  by  practice,  the  work  not  being  sketched  set  by  set, 
but  a pause  for  sketching  being  made  every  fifth  or  tenth  set,  or  wherever 
there  is  a change  in  the  character  of  the  wall.  In  drifts  such  as  are  usually 
found,  from  3,000  to  8,000  ft.  of  sketching  is  a good  da3’'’s  work.  The  sketch 
should  be  taken  at  some  definite  horizon,  and  that  of  the  floor  level  is  best. 
Features  of  constant  recurrence  must  be  represented  by  conventional  signs. 

Thus,  in  Fig.  2,  c enclosed  by  a square  indicates  a 
chute  passing  through  the  floor;  up  means  a ladder 
up;  M,  a manway  down.  A full  line  indicates  a 
rock  wall,  a broken  line,  lagging;  cross-hatching 
represents  filling;  a dashed-and-dotted  line,  the 
presumed  limit  of  filled  workings,  etc.  It  is  of 
importance  to  indicate  irregularities  in  the  tim- 
bers. If  it  is  a short  set,  write  5 within  the  square; 
if  a long  set,  L,  giving  the  length  if  necessary.  If 
there  should  be  an  angle  in  the  timbering  so  that 
there  may  be  a set  more  on  one  side  of  the  drift 
than  on  the  other,  represent  it  by  a wedge-shaped 
opening,  as  shown,  being  the  appearance  of  the 
drift  if  it  were  straightened  out.  In  sketching,  it  is 
essential  to  accuracy  that  the  attention  be  held 
to  a few  things  at  a time.  On  reaching  the  top  of 
the  raise  the  plan  views  are  completed,  each  floor 
having  been  sketched  on  the  way  up.  On  descend- 
ing, turn  to  page  8 and  sketch  the  cross-section  of 
the  manway,  as  shown  in  Fig.  3.  Each  set  is  still  represented  by  a square, 
although  the  sets  are  higher  than  wide,  but  since  that  fact  is  known  it  can 
lead  to  no  error. 

The  stope  book  is  taken  through  the  mine  and  brought  up  to  date  at  the 
first  of  each  month,  and  it  is  necessary  for  the  foreman  or  shift  boss  to 
accompany  the  engineer  and  point  out  each  place  where  work  has  been 
done.  To  pick  up  the  work  readily,  and  identify  the  last  set  of  the  previous 
month,  the  last  cap  should  have  a notch  cut  in  it  and  the  same  indicated  in 
the  book. 

The  Long  Section.— The  view  of  the  vein  that  will  be  of  most  general  use, 
and  show  at  a glance  the  progress  of  the  work  of  ore  extraction,  is  the  long 
section.  It  is  a modified  vertical  projection  of  the  vein,  such  as  would  be 
obtained  if  the  rock  on  the  hanging-wall  side  should  be  removed  and  the 
vein  viewed  from  a distant  standi)oint  at  the  same  level.  Fig.  4 shows  the 
final  section  made  in  the  office  to  the  same  scale  as  the  map,  but  each  part  of 
it  for  the  corresponding  400  ft.  of  a level  will  be  placed  on  pages  10,  19,  etc. 
of  the  stope  book,  and  is  compiled  from  the  sketches  of  each  floor.  The 
long  sections  can  be  drawn  from  the  plan  views  of  the  floors  either  iji  the 


THE  LONG  SECTION. 


65 


mine  or  the  office,  but  it  is  a little  better  to  determine  the  limiting  points  in 
the  mine.  The  transit  stations,  chutes,  and  raises  should,  of  course,  be 
located  upon  it  as  common  points  with  the  map,  connecting  the  two.  The 
final  long  section  is  drawn  by  merely  piecing  together  the  several  parts 
from  the  stope  book  and  drawing  them  horizontally  and  vertically  to  the 
same  scale. 

Since  a vein  is  quite  an  irregular  surface,  the  question  arises  as  to  what 
modification  of  a vertical  projection  will  give  the  most  accurate  and  con- 
venient representation  of  it.  That  devised  by  Mr.  A.  A.  Abbott,  of  which 
the  essential  feature  is  the  horizontal  adjustment  space  left  between  the 
levels,  is  shown  in  Fig.  4.  At  our  reference  line,  in  this  case  the  projection 
of  the  shaft  upon  the  vein,  the  zero  points  of  the  levels  are  placed  over  each 
other.  But  owing  to  the  warpings  in  the  vein,  a raise,  such  as  No.  201, 
started,  in  this  case,  40  ft.  east,  will  not  break  through  on  the  similar  point 
of  the  level  above.  The  simplest  way  in  which  to  allow  for  these  discrep- 
ancies is  to  draw  the 
levels  more  than  their 
true  distance  apart  by 
the  width  of  an  adjust- 
ment space,  lay  out 
each  level  at  its  true 
length,  and  drkw  the 
raises  perpendicular  to 
them,  provided,  of 
course,  that  the  raises 
only  step  off  along  the 
dip  and  not  along  the 
strike.  All  these  fea- 
tures can  be  appreci- 
ated by  studying  Figs. 

1,  2,  3,  and  4 in  con- 
uection  with  each 
other.  Lines  corre- 
sponding to  the  height 
are  ruled  on  the  sides 
of  the  drawing,  and 
the  floor  on  which  the 
work  is  being  done  is 
ascertained  by  means 
of  a parallel  ruler. 

Such  a view  approxi- 
mates to  a development 
of  the  vein  horizon- 
tally, but  vertically  to 
a projection,  since  the 
vein  is  projected  on  a 
series  of  vertical  planes  passing  through  the  transit  courses.  The  drifts  are 
shown  at  their  true  lengths,  but  the  heights  are  the  vertical  distances  and 
not  the  lengths  up  the  dip. 

The  long  section  will  be  brought  up  to  date  every  3 or  6 months,  and  the 
ortions  of  the  veins  extracted  during  the  interval  indicated  by  cross- 
atching  or  tinting.  In  the  illustration,  the  ore  bodies  are  cross-hatched  to 
bring  them  out  more  clearly,  but  to  do  this  on  the  regular  map  would 
involve  erasures  with  every  extension  in  the  workings.  In  the  mine,  a 
hard  and  sharp  drafting  pencil  will  be  used,  but  pencil  markings  in  a book 
constantly  in  use  soon  become  faint  and  blurred.  It  is  necessary  to  go 
through  the  book  at  intervals  and  ink  in  everything  with  waterproof  draw- 
ing ink.  Two  colors  can  be  used  with  advantage,  red  for  all  transit  lines 
and  survey  figures,  and  black  for  the  stopes  and  those  symbols  relating  to 
them.  If  there  are  several  splits  to  a vein,  sometimes  worked  together  and 
sometimes  not,  the  work  on  the  different  splits  can  be  readily  distinguished 
on  the  long  section  by  using  red  for  the  hanging-wall  split,  and  blue  for  that 
of  the  foot-wall.  If  old  filling  is  taken  out,  such  as  ore,  as  frequently  hap- 
pens, the  parts  extracted  can  be  cross-hatched  in  red,  and  thus  a record  of 
both  the  first  and  second  extractions  preserved. 

The  value  of  these  methods  over  mere  sketches  made  without  system  lies 
in  their  accuracy.  Where  the  timbering  is  irregular,  the  accuracy  of  thQ 
results  depends  largely  upon  the  time  and  care  taken  in  the  worl?. 


66 


UNDERGROUND  SURVEYING, 


MINE  CORPS. 

The  method  of  dividing  the  work  in  an  underground  survey  depends  on 
the  size  of  the  corps.  We  will  therefore  consider  the  work  of  each  man, 
in  order  to  get  the  right  number  for  the  corps.  The  chief  of  the  party 
should  be  where  he  can  do  the  most  good,  and  where  he  can  plan  the 
work  for  his  subordinates.  The  principal  point  of  the  survey  is  the 
setting  of  the  stations  so  as  to  do  the  work  thoroughly  with  the  fewest 
set-ups,  and  thus  diminish  the  chances  of  error  in  instrumerital  work. 
The  chief  should  locate  the  stations  and  add  all  the  necessary  signs 
to  show  how  the  work  is  to  be  done.  The  transitman  should  not 
have  his  attention  distracted  from  his  particular  work  by  questions  as  to- 
procedure.  He  should  work  untrammeled.  The  chief,  therefore,  should  not 
run  transit.  Upon  this  basis  the  ideal  mine  corps  works,  and  such  a corps 
consists  of  at  least  four,  and  better  five,  men  from  the  office,  and  three  from 
the  mine.  It  is  divided  into  two  sections.  The  chief  takes  the  men  supplied 
by  the  mine— one  or  more  of  whom  are  acquainted  with  the  work  done  since 
the  last  survey — and  locates  the  vStations;  the  transitman  follows  with  the 
second  section,  to  measure  angles  and  distances.  By  this  time  the  stations 
are  set  and  the  chief  takes  his  men  after  the  transit  party  and  gets  the  side 
notes,  with  a check  measurement  of  the  distances  between  stations. 

Such  a corps  goes  to  the  end  of  the  former  survey  and  identifies  the  last 
two  stations.  The  transitman  prepares  to  set  up  at  the  last,  while  the  chief 
and  party  goes  as  far  as  he  can  see  the  light  from  the  last  station,  or  to  some 
intermediate  point  from  which  one  or  more  sights  are  to  be  taken.  He  then 
stops  and  sends  a man  along  each  place  where  a sight  must  be  taken,  as  long 
as  their  lights  are  plainly  seen  from  top  to  bottom  where  he  is  standing,  and 
over  this  place  he  marks  a point  for  a station  to  be  inserted,  and  generally 
inserts  it  himself  unless  he  be  pushed  by  work,  and  must  leave  it  for  another 
to  do,  when  he  places  a circle  about  the  dot,  places  the  number  at  the  side, 
and  as  many  arrows  as  there  are  new  stations,  the  longer  arrow  generally 
pointing  to  the  sight  to  be  last  taken  and  where  the  transit  is  to 

Jbe  set  up  next.  Leaving  a backsight  at  the  point  just  set, 
I he  sets,  successively,  stations  at  the  points  where  the 
I foresight  men  have  stood,  in  the  manner  just  described, 
I until  he  has  covered  the  new  work— the  mine  boss  or  some 
. I intelligent  miner  going  with  him  to  give  him  an  idea  of 
7 I the  ‘‘lay  of  the  ground,”  so  that  the  work  can  be  covered 

/ I with  the  fewest  number  of  stations.  Sometimes  the  chief 

o I takes  the  side  notes  and  measures  the  distances  between 

473  I stations  as  fast  as  they  are  set.  In  a pitching  place,  a circu- 

I lar  brass  protractor  with  small  plummet  is  hung  at  the 
I center  of  a stretched  tape,  to  give  the  angle  at  which  the 
I tape  is  held;  this  serves  as  a check  to  the  measurements 
I of  the  transit  party,  which  are  taken  as  the  basis  of  the 
work,  and  the  other  measurements  are  solely  as  checks. 
In  flat  work,  both  measurements  should  coincide. 

In  a small  corps,  and  where  time  is  of  little  importance,  the  foresight 
man  puts  in  the  stations  ahead  of  the  transit,  and  while  he  is  so  doing  the 
transitman  takes  the  side  notes.  Sometimes  the  side  notes  are  taken  by  the 
same  man,  while  one  of  the  party  is  taking  the  transit  to  the  next  station 
and  setting  it  up  for  the  next  sight.  There  are  about  as  many  variations 
from  these  two  methods  as  there  are  corps. 

The.  foresight  man  should  be  intelligent  and  active,  as  the  amount  of  work 
done  in  a day  depends  on  his  ability  to  keep  ahead  of  the  transitman.  Some  of 
the  latter  are  fast  enough  to  keep  two  foresight  men  on  the  jump.  His  duty 
is  to  set  the  center  for  the  next  set-up  under  the  station,  and  also  place  the 
tripod  if  three  are  used  in  the  work,  to  give  the  sight,  and,  in  some  corps,  to 
carry  the  front  end  of  the  tape  and  assist  in  taking  the  distance.  In  some 
corps  he  also  carries  the  bag  with  tools  for  setting  stations,  so  that  he  gen- 
erally has  a load  that  makes  rapidity  of  movement  difiicult,  and  anything 
that  will  diminish  the  weight  carried  will  tend  to  quicken  the  work. 

The  rapidity  with  which  good  work  is  done  varies  considerably,  but  it 
depends  on  the  activity  of  transitman  and  foresightman,  and  a good  corps 
should  have  no  trouble  in  making  twelve  set-ups  an  hour,  and  taking 
two  or  three  sights  from  each  set-up.  It  varies  also  with  the  distances 
between  stations.  The  saving  of  time  should  never  be  sought  at  the  expense 
of  accuracy  in  the  work;  it  is  to  be  gained  by  rapidity  of  moving  about,  in 


S UR  VE  YING  ME  THODS. 


67 


setting  transit,  center,  etc.,  and  in  hanging  plummets  to  give  sight.  The 
foresight  man  and  backsight  man  should  be  in  position  to  give  sight  before 
the  transitman  is  ready,  so  that  he  can  turn  his  instrument  on  one  or  the 
other  and  find  them  in  position.  The  slowest  parties  were  those  that  carried 
empty  powder  kegs  (in  the  days  when  loose  powder  was  allowed  inside) 
for  seats,  and  spent  the  greater  part  of  the  time  sitting  on  them. 

The  backsight  man  has  little  to  do  inside,  and  to  compensate  for  this,  he 
is  the  one  that  cleans  and  oils  the  tape,  gets  out  new  plummet  strings,  and 
sees  that  the  tools  are  ready  for  the  next  work,  as  soon  as  the  corps  gets  to 
the  office. 

The  transitman  cleans  the  transit,  unless  the  corps  has  subordinates  that 
can  be  trusted  with  so  delicate  an  instrument.  The  blackening  from 
sulphureted  hydrogen  is  rubbed  from  the  silvered  surfaces  with  whiting, 
and  the  oil  or  paint  smears  are  removed  with  alcohol.  Alcohol  should  be 
used  instead  of  water  for  cleaning  the  instruments,  and  especially  the  lenses, 
which  are  wiped  with  jewelers’  cotton  or  soft  chamois  skin. 


SURVEYING  METHODS. 

Outside  Surveys. — We  have  spoken  of  the  points  necessary  to  include  in 
the  survey  outside,  and  how  the  base  line  is  established.  It  remains  to  call 
attention  to  several  points  that  must  be  known  before  the  surface  plant  can 
be  protected  from  settling,  from  the  removal  of  the  deposit  below.  The 
exact  location  of  all  buildings,  lakes,  ponds,  rivers,  railroads,  etc.  is  not 
only  necessary  for  the  making  of  a correct  map;  it  is  necessary  for  the 
determination  of  the  amounts  and  location  of  the  beds  that  must  be  left 
untouched  by  the  subsequent  mining.  Here  must  be  mentioned  an  error 
that  generally  governs  the  location  of  the  retaining  pillars  to  support  the 
above  and  prevent  damages  to  themselves  or  to  the  mine.  The  settling  of 
the  ground  would  make  all  bodies  of  water  leak  into  the  mine,  and  also 
destroy  to  a greater  or  less  degree  all  surface  plant,  as  well  as  throw  out  of 
plumb  all  shafts  or  other  openings  for  hoisting,  if  it  did  not  close  them 
entirely.  The  usual  custom  is  to  extend  vertical  planes  through  the  bound- 
ary lines  of  such  objects,  and  leave  untouched  all  parts  of  the  superincum- 
bent beds  embraced  by  those  planes.  This  is  accurate  only  when  the  strata 
are  horizontal  or  vertical,  as  beds  settle  normally  to  the  planes  of  the  strata 
and  not  in  a vertical  line  in  case  the  open  spaces  are  stowed.  If  the  spaces 
are  left  open,  they  are  first  filled  by  falls,  and  then  the  settling  goes  on 
according  to  the  above  rule.  No  cut  is  necessary  to  show  the  method  of 
settling,  and  the  place  where  the  bed  is  to  be  left  untouched  may  be  found 
as  follows:  Draw  a vertical  section  through  the  point  to  be  supported,  and  also 
the  underlying  bed  on  the  line  of  the  dip  of  the  bed — the  section  being  accurately 
drawn  to  any  scale.  Draw  through  the  extremities  of  the  object  to  be  supported, 
lines  to  the  bed,  which  will  make  right  angles  with  it.  The  space  included  will 
give  the  dimension  of  the  pillar  measured  along  the  dip  of  the  bed,  and  the 
dimensions  of  the  object  taken  at  right  angles  to  the  first  plane  will  give  the  other 
dimension  of  the  pillar. 

Inside  Surveys.— As  the  beds  of  anthracite  lie  at  all  angles  with  the  hori- 
zontal plane,  the  methods  of  surveying  them  vary  accordingly,  and  can  be 
divided  into  fiat  and  pitching  work.  Flat  work  is  where  the  beds  have  so 
slight  a dip  that  the  cars  can  be  drawn  to  the  face  of  the  room,  and  where 
there  is  nothing  to  prevent  a sight  to  that  face  from  the  gangway.  The 
variations  in  the  methods  of  work  in  this  case  depend  on  the  accuracy  with 
which  the  work  must  be  performed,  as,  in  some  cases,  the  workings  are 
approaching  the  boundary  line  of  the  property,  and  the  sides  of  the  rooms 
must  be  located  accurately.  In  general,  the  rooms  are  driven  at  right  angles 
to  the  gangway,  unless  the  dip  is  too  great  to  haul  a car  to  the  face  on  that 
line,  when  they  are  inclined  to  the  gangway  at  an  acute  angle.  The  width 
of  the  rooms  in  flat  work  is  generally  uniform  where  the  roof  is  good,  but 
where  the  roof  is  poor  the  entrance  is  narrowed  for  a short  distance  (to  better 
support  the  gangway)  and  then  widened  to  the  full  width,  or  the  whole  is 
driven  to  the  limit  narrow,  and  the  side  is  robbed  when  the  top  is  drawn, 
and  the  whole  room  caves  in.  This  last  must  be  surveyed  before  the  robbing 
begins. 

The  most  accurate  method  of  survey  is  to  run  a line  along  the  gangway 
and  put  a station  at  the  entrance  of  each  room,  whence  a sight  is  taken 
to  the  face.  This  may  be  varied  by  putting  the  stations  at  alternate  rooms 


68 


SVRVEYING. 


and  measuring  through  the  cross-cuts  to  get  the  thickness  of  the  pillars  of 
the  intermediate  rooms,  or  placing  stations  at  every  third  room  and  measur- 
ing the  thickness  of  pillars  and  width  of  rooms  that  intervene;  or,  finally,  by 
running  out  the  gangway  with  as  few  sights  as  possible  and  paying  no  atten- 
tion to  the  positions  of  the  rooms  in  setting  stations,  thence  up  to  the  last 
room  to  the  face,  and  back  through  the  cross-cuts  nearest  the  face  to  the 
former  work,  where  a tie  is  made.  When  opportunity  offers,  sights  are  made 
from  the  face  of  the  rooms  to  the  stations  in  the  gangway  for  immediate  ties. 
In  case  a gangway  and  airway  have  been  driven  considerably  ahead  of  the 
rooms,  it  is  always  necessary  to  run  lines  out  each  and  tie  at  the  last  cross- 
cut. This  must  be  done  in  everj^  case  where  the  gangway  is  approaching  the 
boundary  line,  or  old  workings  that  have  been  abandoned  and  are  full 
of  water.  In  addition  to  this  check  the  miners  must  keep  bore  holes  20  ft. 
ahead  in  the  line  of  the  gangway,  and  every  20  ft.  must  drive  others  from 
the  corners  of  the  heading  at  an  angle  of  30°  with  the  line  of  the  gangway. 
In  this  way  there  will  be  no  danger  of  running  into  “ a house  of  water,”  as 
the  Cornish  miners  call  it,  if  the  survey  be  inaccurate. 

Pitching  Work.— When  the  bed  pitches  so  that  a car  cannot  be  run  to  the 
face,  and  when  there  is  a good  deal  of  firedamp  in  the  mine,  it  is  generally 
difficult  to  see  from  the  gangway  to  the  face,  where  the  roof  is  good  and  the 
room  straight,  as  a buggy  track  or  chute,  or  both— when  the  pitch  is  slight- 
fill  up  the  room,  and,  where  the  pitch  is  great,  the  gangway  pillars  generally 
run  across  the  face,  or  there  is  a “ battery  ” shutting  off  the  bottom  of  the 
room,  so  that  the  face  can  be  reached  only  by  several  sights.  Where  the 
roof  is  poor,  the  obstructions  are  increased,  as  the  rooms  are  driven  narrower, 
or,  if  wide,  have  center  props  and  stowing  in  the  center.  If  the  coal  is  full  of 
slate,  or  if  the  partings  are  thick,  a large  part  of  the  room  is  taken  up  with 
piles  of  “ gob,”  and  with  a very  poor  roof  the  body  of  the  room  that  has  been 
worked  out  is  filled  with  the  fallen  roof,  and  the  coal  is  sent  out  through  the 
triangular  manways,  where  it  is  almost  impossible  to  take  a sight. 

Work  of  this  kind  is  surveyed  by  lines  out  gangway  and  back  through  the 
faces  of  the  rooms,  which  are  generally  clear,  even  if  the  bodies  of  the  rooms 
are  filled  with  the  fallen  top.  Where  chance  favors,  sights  are  taken  to.  the 
gangway;  but  this  very  seldom  happens,  as  the  two  lines  are  as  effectually 
separated  as  if  in  different  mines.  From  the  stations  in  the  faces,  lines  are 
run  down  the  rooms  as  far  as  possible  to  get  their  direction,  and  to  locate 
the  cross-cuts.  The  very  worst  case  of  all  is  where  two  beds  are  separated 
by  a thin  parting  of  rock  and  the  gangway  is  driven  in  the  lower  one  alone, 
the  rooms  in  the  upper  one  being  worked  by  rock  chutes  into  the  rooms 
below,  or  into  the  chutes  from  those  rooms.  This  class  of  work  is  hard  to 
ventilate,  and  to  survey  where  the  rooms  above  are  ventilated  by  the  air 
system  of  the  lower  beds;  but  is  readily  mapped  where  there  is  an  air  system 
for  each  bed. 

Closing  Surveys.— To  diminish  the  chance  of  error  and  to  furnish  a ready 
check,  the  survey  must  be  closed  upon  itself  or  some  part  of  a former  survey 
with  every  twelve  new  stations.  With  good  work  the  error  in  arc  in  a close 
should  not  exceed  1',  and  the  error  in  position  should  be  less  than  6 in. 
Errors  must  not  be  “balanced”;  they  must  be  detected  and  rectified  by 
running  the  line  again,  if  they  are  not  readily  seen  from  the  methods  to  be 
given.  If  an  incorrect  survey  be  balanced,  each  subsequent  one  must  be 
altered  to  fit  this  incorrect  work,  though  it  may  be  correct  in  itself,  and  we 
never  know  where  our  work  really  stands.  It  is  well,  therefore,  to  check 
the  work  in  arc  as  soon  as  we  make  a close  and  before  the  party  leaves  the 
place,  as  it  is  easy  to  rerun  the  work  then. 


CONNECTING  OUTSIDE  AND  INSIDE  WORK  THROUGH  SHAFTS  AND 
SLOPES. 

As  the  dip  of  the  bed  increases,  it  is  less  easy  to  make  a connection,  and 
the  chances  of  accuracy  diminish.  In  a survey,  R.  Cos.  Vert.  Angle  is  what 
locates  the  station  with  regard  to  former  work.  The  greatest  angular 
accuracy  for  a given  value  of  R is  where  Vert.  Angle  = 0°  and  R ==  Cos.  Vert. 
Angle.  As  the  pitch  or  vertical  angle  of  sight  increases,  the  above  cosine 
diminishes  until,  at  a vertical  sight.  R.  Cos.  Vert.  Ang.  — 0°. 

In  the  case  of  an  adit  level,  or  a slope  of  less  than  45°,  there  is  no  difficulty 
beyond  the  want  of  absolute  rigidity  in  setting  u])  the  transit,  and  the 
danger  of  moving  it  in  going  about  it.  The  difficulty  increases  more  rapidly 


SHAFTS  AND  SLOPES. 


69 


than  does  the  pitch,  and  as  R.  Cos.  Vert.  Ang.  diminishes,  though  R be  fixed, 
the  chances  of  error  increase.  When  the  slope  reaches  60°  there  is  an 
impracticability  in  running  a line  down  a slope,  as  the  line  of  collimation  of 
the  telescope  strikes  the  graduated  limb  of  the  instrument.  We  can  use 
a prismatic  eyepiece  and  see  up  the  slope;  but  cannot  look  down.  As  we 
have  assumed  that  it  is  unnecessary  to  use  an  additional  telescope,  we  shall 
have  to  run  the  line  hy  intermediates.  Set  up  at  the  bottom  of  the  slope 
where  the  longest  sight  up  the  same  can  be  secured  and  backsight  on  a 
station  of  the  underground  work;  or  set  a backsight  for  the  occasion  (both 
stations  will  afterward  be  connected  with  the  work  below).  With  the 
prismatic  eyepiece,  sight  up  the  slope  on  a line  that  will  give  the  longest 
sight  and,  at  the  same  time,  afford  a good  intermediate  place  to  set  up 
the  transit,  as,  on  a pitch  of  60°  or  more,  it  is  absolutely  necessary  that  the 
legs  of  the  transit  should  be  set  solidly  (in  holes  in  the  floor,  or  between  the 
sills  of  the  track)  so  that  they  will  not  be  moved  by  subsequent  walking 
about  it.  By  this  method,  all  the  sights  will  be  taken  from  one  side  alone, 
and  the  tripod  legs  can  be  shortened  to  make  the  sight  possible  without 
building  a standing  place— if  the  man  be  short-legged. 

Call  this  station  A;  at  the  foot  of  the  slope  locate  B,  where  the  transit  can 
be  readily  set  up,  and  as  far  up  the  slope  as  we  can  see  (this  distance  must  be 
at  least  100  ft. ),  and  in  a continuation  of  A B,  locate  C.  Set  up  at  B and  take 
foresight  to  C;  locate  D under  the  same  conditions  that  governed  the  placing 
of  B,  and,  in  a continuation  of  the  line  B D,  place  E.  Set  up  at  D with 
foresight  at  E,  and  locate  F and  G as  before.  The  survey  is  carried  by  the 
intermediates  B,  D,  F,  etc.,  to  the  top,  by  a series  of  foresights  to  C,  E,  G,  etc. 

Shafts. — The  term  shaft  in  American  coal-mining  practice  is  applied  only 
to  vertical  openings,  though  in  metal  mining,  both  in  this  country  and 
abroad,  it  is  also  applied  to  highly  inclined  slopes.  For  such  shafts,  most  of 
the  methods  given  in  the  textbooks  are  worthless,  as  they  are  for  transit 
work  and  R.  Cos.  Vert.  Ang.  in  rare  cases  may  be  as  great  as  20  ft.,  while  R 
varies  from  100  to  1,500  ft.  Again,  to  sight  down  a shaft  necessitates  the 
erection  of  a temporary  (and  therefore  more  or  less  unsteady)  support  for 
the  tripod  of  the  transit,  and  the  chances  of  variation  in  its  position  as  we 
stand  on  different  sides  of  it  are  so  great  that  we  cannot  feel  sure  that  a 
movement  has  not  taken  place  that  will  vitiate  the  work. 

In  sighting  up  a shaft  of  greater  depth  than  100  ft.,  there  is  annoyance— if 
not  danger— from  dripping  water  or  the  fall  of  more  solid  substances.  In  a 
wet  shaft  the  object  glass  is  instantly  covered  with  water,  and  a sight  is 
impossible.  We  must  also  have  a platform  to  stand  upon,  and  we  cannot 
feel  sure  that  this  will  be  perfectly  rigid.  From  all  these  considerations  the 
methods  with  a transit  are  never  used  by  engineers  in  the  anthracite  regions, 
and  the  connections  are  made  as  follows: 

When  the  bottom  of  the  shaft  can  be  reached  by  an  adit  or  slope  in  a 
roundabout  route  of  such  length  as  to  render  errors  in  measurement  of  dis- 
tance of  great  importance,  the  angles  are  carried  by  a transit  with  as  long 
sights  as  possible,  and  no  distances  are  measured,  from  a point  on  the  surface 
in  the  shaft  to  a point  vertically  below  it  in  the  mine.  Sometimes  the  guide 
of  the  cage  is  taken  when  it  has  been  recently  set,  as  the  guides  are  plumbed 
into  position;  but  the  better  way  is  to  suspend  an  iron  plummet  by  a copper 
wire:  sink  the  former  in  a barrel  of  water  so  as  to  lessen  the  tendency  to 
swing  on  account  of  the  pull  upon  the  “bob”  and  wires  from  the  air-cur- 
rents, or  falling  drops  in  a wet  shaft.  The  top  of  the  barrel  is  covered  with 
two  pieces  of  plank  with  a semicircular  groove  of  3 in.  radius  cut  out  of  the 
middle  for  the  passage  of  the  wire,  to  catch  the  substances  whose  fall  upon 
the  water  would  cause  waves.  The  heavier  the  plummet  and  the  lighter 
the  wire,  the  less  the  tendency  to  swing.  This  wire  can  be  sighted  at  by 
parties  above  and  below  at  the  same  time,  and  the  swing  can  be  bisected 
to  get  the  position  of  the  wire.  A number  of  sights  that  agree  can  be  taken 
as  accurate. 

When  the  shaft  is  the  only  way  to  get  below  from  above,  it  must  be 
plumbed  with  two  or  more  wires  suspended  as  just  described.  With  two 
wires,  they  are  so  hung  that  an  instrument  can  be  set  up  below  in  a line 
passing  through  them  produced,  and  at  a sufficient  distance  from  them  to 
insure  an  accurate  sight;  with  more  wires,  the  station  below  can  be  located 
at  any  point  whence  all  the  wires  can  be  seen. 

Case  1.— Two  wires  are  used,  which  are  located  as  far  apart  as  possible. 
Two  pieces  of  scantling  c d and  e /,  Fig.  1,  are  spiked  across  the  opposite  corners 
of  two  compartments  of  a shaft  to  allow  the  cages  to  pass  up  and  down 


70 


SURVEYING. 


Fig.  1. 


without  interference.  The  station  X is  (roughly)  located  in  a line  through 
the  corners  x,  x and  is  connected  with  the  outside  survey.  From  this  station 
locate  in  the  line  Xxx  two  spads  for  holding  the  wires  of  the  plumb-bobs. 
These  are  driven  up  to  the  head  in  the  scantlings  in  such  a way  that  the  line 
of  sight  passes  through  the  center  of  the  holes  in  their  heads.  Measure  the 
distances  X a and  a b.  This  completes  the  work  of  the  survey  above  ground. 

The  light  copper  wire  is  rolled  upon  a 
reel,  and  one  end  is  fastened  to  a light 
plumb-bob  to  keep  it  free  from  coils  or 
kinks  in  descending.  It  can  thus  be 
readily  lowered  without  accident. 
When  at  the  bottom,  the  upper  end 
is  fastened  in  the  spad  and  the  heavy 
“bob”  applied  to  the  bottom  and 
placed  in  the  empty  barrel.  The  cages 
are  then  run  slowly  up  and  down, 
with  an  observer  on  each,  to  see  that  the  wires  hang  free  from  top  to  bot- 
tom. By  this  time  the  wire  will  have  stretched  so  that  it  will  be  straight, 
and  if  there  be  any  slack,  it  is  taken  up,  the  barrel  is  filled  with  water,  and 
the  top  boards  put  in  place.  As  a last  check,  measure  the  distance  between 
the  wires  below  and  see  if  it  agrees  with  the  distance  above. 

Lining  in  below  a point  Y on  the  line  a 6,  make  a hole  in  the  roof  two 
inches  in  diameter,  and  drive  in  a broad  plug.  Setting  up  the  transit  under 
F,  we  sight  at  the  wires  a and  b alternately.  A number  of  methods  for  illumi- 
nating the  wires  have  been  used,  and  are  given  in  textbooks.  The  writer  has 
always  found  those  depending  on  a sight  of  the  wire  across  the  flame  of  a 
lamp  the  hardest  to  obtain,  and  concludes  from  experience  that  the  method 
of  illuminating  the  wires  for  mine  surveying  is  the  best  for  this  also.  A large 
white  target  is  placed  behind  both  wires  and  illuminated  by  a large  lamp 
with  a reflector  behind  it.  The  wire  stands  out  black  against  It  and  can  be 
followed  across  the  target.  As  there  is  considerable  distance  between  the 
wires,  and  as  the  transit  is  comparatively  near  them,  there  will  be  small 
chance  of  getting  a sight  of  one,  when  the  telescope  is  focused  upon  the 
other,  and  so  the  focus  has  to  be  set  between  them.  This  gives  a hazy  sight 
at  each;  but  both  are  shown  against  the  white  background  in  strong  relief. 
After  the  transit  head  is  shifted  so  that  the  line  of  sight  coincides  approxi- 
mately with  both,  focus  upon  them  alternately  and  see  if  the  line  bisects  the 
swing  of  each.  If  so,  the  work  is  done;  if  not,  the  shifting  of  the  transit 
head  must  follow  till  the  end  is  attained.  It  frequently  requires  two  or  more 
hours  of  steady  observation  to  complete  the  work,  and,  when  it  seems  as  if 
the  proper  point  were  secured,  one  of  the  wires  will  show  by  its  swaying  that 
it  has  been  deflected  from  the  vertical  by  a peculiar  slant  of  wind,  and  the 
result  obtained  must  be  checked  again.  When  you  are  through,  there  is  no 
absolute  certainty  that  the  point  you  have  marked  is  in  the  accurate 
extension  of  the  line  a 6 at  the  surface.  Having  decided  on  the  proper  place, 
you  drive  a spad  into  the  plug  overhead;  hang  a plumb-bob  to  it,  and  see  if 
it  be  over  the  axis  of  the  transit,  as  shown  by  the  screw  on  the  telescope.  If 
not,  drive  the  spad  so  that  the  point  of  the  bob  does  so  hang,  and  the  station 
F is  said  to  be  in  the  line  a b.  Measure  F a and  the  angles  to  any  station  of 
the  underground  survey;  the  line  a 5 is  connected  with  the  surveys  at  day- 
light and  below,  and  the  plumb-bobs  may  be  removed. 

Criticism  of  the  Above  Method.— I.  As  has  been  stated,  there  is  no  absolute 
certainty  that  the  point  F is  in  the  line  a b prolonged,  and  this  want  of 
certainty  should  not  exist  in  so  important  a measurement. 

2.  The  work  must  be  performed  by  daylight,  and  the  length  of  time 
necessary  to  complete  it  makes  it  impossible  to  work  the  shaft  for  at  least 
half  a day,  and  may  cause  annoyance  to  the  operators,  or,  if  you  are  ^vorking 
for  a lessee,  lead  them  to  refuse  to  let  you  have  the  use  of  the  shaft  at  the 
time  most  suitable  for  your  purpose. 

3.  It  may  be  hard  to  obtain  a long  sight  below  on  any  line  running 
through  the  larger  axis  of  the  shaft.  Any  Sorter  line  would  give  too  short  a 
base  line  and  would  increase  the  chances  of  error.  To  avoid  these,  another 
method  is  sometimes  used. 

Case  2.— Fig.  2 shows  the  top  set  of  timbers  in  a shaft  of  two  hoisting 
compartments,  down  which  it  is  desired  to  carry  a known  course  or  merid- 
ian on  the  surface  to  the  entry  below.  First  find  out  which  side  of  the 
shaft  is  best  adapted  for  setting  up  the  transit,  as  the  point  to  be  marked  in 
the  mines  will  be  vertically  under  the  point  on  the  surface;  consequently, 


SHAFTS  AND  SLOPES. 


71 


the  side  with  the  widest  opening  leading  from  the  foot  of  the  shaft  should 
be  selected. 

Having  carried  the  meridian  to  a convenient  point  near  the  top  of  the 
shaft,  and  having  found  that  the  south  side  of  the  shaft  is  the  most  accessi- 
ble, determine,  with  an  ordinary  string,  the  location  of  the  point  A,  from 
which  the  hangers  for  the  plumb-lines  will  be  exactly  located  by  means  of 
the  transit.  Now  mark  with  chalk  on 
the  timbers  where  the  strings  cross. 

These  marks,  though  not  accurate, 
serve  as  guides  in  setting  the  hangers. 

Make  a permanent  station  at  the  point 
A and  carry  the  meridian  to  it. 

The  hangers  can  be  made  of  strap 
iron,;i  in.  thick  by  2 in.  wide,  and  at 
least  16  in.  long.  In  one  end  of  the 
iron,  have  a jaw  with  a fine  cut  at  the 
apex,  or  a drill  hole  just  large  enough 
to  contain  the  wire  to  be  used  for 
plumbing.  There  should  be  two  or 
three  countersunk  holes  in  the  hanger, 
through  which  to  fasten  it  to  the  tim- 
bers by  means  of  heavy  wire  nails.  A 
top  view  of  the  hanger  is  shown  in 
Fig.  2. 

In  most  shafts  there  is  a space  from 
2 to  4 in.  wide  between  the  ends  of 
the  cage  and  the  sides  of  the  timbers; 
and  in  order  to  hoist  and  lower  the  cage  to  see  that  the  wires  are  hanging 
freely,  it  is  best  to  set  the  hangers  in  such  a position  on  the  timbers  that 
the  wires  will  hang  in  the  middle  of  the  space. 

Fasten  the  hangers  permanently  over  the  chalk  marks  previously  made 
on  the  north  side  of  the  shaft,  with  the  jaws  pointing  toward  A,  and  on  the 
south  side  of  the  shaft  the  outer  end  of  the  hanger  may  be  fastened 
temporarily. 

Now  set  the  transit  over  the  station  at  A,  take  the  backsight,  foresight  on 
the  wire  hole  of  the  hanger  C and  set  the  wire  hole  of  the  hanger  B on  the 
same  line.  Record  this  course  and  foresight  on  the  wire  hole  of  the  hanger 
F,  fixing  as  before  the  wire  hole  of  the  hanger  D in  the  same  line.  Record 
this  course,  and  then  the  meridian  to  be  carried  into  the  workings  below  is 
established.  Measure  carefully  and  record  the  distances  A to  R,  A to  C, 
and  B to  C,  the  distances  A to  D,  A to  E,  and  D to  E.  and  finally  the  dis- 
tances B to  D and  C to  E.  The  necessity  of  taking  all  these  measurements  is 
for  the  purpose  of  establishing  a point  at  the  bottom  of  the  shaft  vertically 
below  A,  and  checking  the  work  in  the  office. 

The  transit  party  can  now  descend  to  the  bottom  of  the  shaft,  taking  with 
them  four  buckets  of  oil,  the  weights  or  plumb-bobs  to  be  attached  to  the 
wire,  and  all  the  surveying  instruments,  leaving  a responsible  party  on  the 
surface  to  handle  the  wires.  Having  arrived  at  the  bottom  of  the  shaft, 
have  the  cage  hoisted  3 ft.  above  the  landing,  throw  several  pJanks  across 
the  timbers  on  which  to  set  the  buckets  of  oil,  signal  to  the  man  on  top  to 
lower  a wire  and  to  fasten  it  securely,  passing  it  through  the  wire  hole  of 
the  hanger;  now  attach  the  plumb-bob  and  adjust  the  wire  to  such  length 
that,  when  sustaining  the  full  weight  of  the  plumb-bob,  the  latter  will  not 
touch  the  bottom  of  the  bucket.  Insert  the  weight  in  the  oil,  using  care 
not  to  leave  the  full  weight  on  the  wire  with  a jerk,  but  let  the  weight 
down  slowly,  so  that  the  wire  receives  the  full  strain  gradually.  Set  the 
three  remaining  wires  in  a similar  way. 

After  the  wires  have  been  hanging  a few  minutes  with  the  weights 
attached,  the  latter  may  move  from  one  side  to  the  other  of  the  buckets. 
Watch  this  carefully  and  keep  moving  the  buckets  until  all  the  weights 
hang  perfectly  free,  then  leave  everything  alone  until  the  wires  become 
steady.  The  cages  can  now  be  hoisted  and  lowered  for  the  purpose  of 
examining  the  wires  to  see  that  they  hang  free  and  plumb,  care  being  taken 
that  the  cages  are  not  brought  so  close  to  the  landings  as  to  disturb  the 
hangers  at  the  top,  or  the  buckets  at  the  bottom. 

To  find  a point  vertically  below  A,  stretch  a string  along  the  wires  B,  (7, 
being  careful  not  to  touch  them;  stretch  another  along  the  wires  D,  E] 
then,  with  a plumb-line,  determine  a point  on  the  bottom  vertically  below 


72 


SUEVEYING. 


the  intersection  of  the  strings.  Measure  the  distances  A B,  A D,  B J),  and 
C E and  compare  them  with  the  corresponding  distances  at  the  top  of  the 
shaft.  If  these  distances  compare  favorably,  the  wires  are,  in  all  probability, 
steady,  and  the  work  of  determining  the  desired  course  with  the  transit 
may  now  be  begun. 

Set  the  transit  up  over  the  point  of  intersection  just  found;  backsight  on 
the  wires  B,  C ; foresight  on  the  wires  Z),  E,  and  compare^the  included  angle 
and  the  distances  with  the  corresponding  angle  and  distances  at  the 
surface.  If  these  do  not  correspond,  move  the  transit  in  the  direction 
necessary  to  increase  or  decrease  the  angle 
^ or  distances,  as  the  case  may  be.  Repeat 

this  operation  until  the  exact  point  verti- 
cally below  A is  determined. 

A simple  device  that  is  of  great  ad  van; 
tage  is  to  have  three  links  from  an  ordinary 
■ trace  chain  placed  in  the  wires  on  the  side 
toward  the  transit,  and  a few  feet  above 
the  buckets.  This  not  only  enables  the 
wires  to  turn  freely,  but  also  enables  the 
transitman  to  sight  through  one  of  the  links 
to  the  wire  beyond,  whereby  he  can  place 
the  transit  in  exact  line  with  the  wires  more 
easily  than  if  the  links  were  not  there. 

Case  3.— Two,  three,  or  four  wires  are 
employed.  They  are  secured  and  hung  as 
before,  and  are  located  in  the  angles  of  the 
compartments  x,  x,  x,  x,  Fig.  3.  These  are 
connected  with  four  stations  A,  R,  (7,  D,  the 
lines  A B and  C D being  at  right  angles  to 
one  another  for  convenience  in  the  subse- 
quent calculation,  and  are  connected  with 
the  outside  survey.  From  A and  B,  taking 
A R as  a base  line,  the  points  x,  x,  x,  x are 
located.  The  same  is  repeated  from  C and 
D,  taking  CD  as  a base  line.  We  thus  have 
four  locations  of  each  wire.  These  are  tab- 
ulated, and  any  variations  in  a reading 
must  be  followed  by  a repetition  of  the 
same.  The  mean  of  the  readings  gives  the 
location.  (Subsequently,  the  subject  of  cal- 
culating work  will  be  taken  up.)  It  can  be 
briefly  stated  here  that  the  bearings  of  each 
wire  to  each  of  the  others,  as  referred  to  the 
base  line  of  the  survey,  are  then  calculated 
and  the  distance  between  the  wires  accu- 
rately measured.  This  finishes  the  work  at 
daylight. 

There  may  be  two  general  types  of 
arrangements  of  the  bottom  of  the  shaft, 
and  both  arrangements  have  been  sketched 
and  lettered  similarly.  The  first  is  a case 
when  the  shaft  is  arranged  across  the  dip 
of  the  bed,  and  the  second  is  parallel  to  the 
same.  In  both  cases  0 and  7 are  taken  as 
far  apart  as  possible,  and  all  the  wires 
X,  X,  X,  X located  from  each  station  with 
reference  to  the  other.  The  distances  between  the  wires  above  and  below 
are  also  accurately  measured  as  a check.  There  will  be  four  locations  of  0 
and  7 from  the  four  wires,  and  the  mean  of  these  is  taken  as  the  correct  one. 
In  every  case  of  angle  measurement  mentioned,  a series  of  readings  of  each 
angle  is  taken  upon  different  parts  of  the  graduated  limb,  to  avoid  instru- 
mental errors,  and  the  mean  of  these  taken  as  the  true  reading.  From  the 
locations  of  0 and  7,  the  course  between  them,  as  referred  to  the  mean  base 
line,  is  calculated,  and  07  is  the  base  line  for  the  underground  work.  The 
angle  readings  above  and  below  can  be  made  at  the  same  time  with  differ- 
ent instruments,  and,  in  taking  the  readings  below,  it  is  not  necessary  to 
wait  for  absolute  quiet  in  the  wires,  as  that  is  seldom  found.  A small  swing 
can  be  bisected  by  the  cross-hair,  and  the  readings  are  duplicated  until  a 


1 0 ' 

1 

P\i|  4 

1 ^ 

1 

Fig.  3. 


SHAFTS  AND  SLOPES. 


73 


constant  result  is  secured.  By  this  method  a greater  accuracy  and  speed  is 
obtained,  and  the  angles  below  can  be  accurately  measured,  no  matter  how 
the  shaft  may  be  arranged. 

The  T-Square  Method.*— This  ingenious  method  of  taking  the  line  under- 
ground is  especially  valuable  in  shafts  with  several  small  compartments  or 
in  cramped  places  where  one  cannot  line  in 
with  the  wures. 

The  wires  are  placed  in  separate  com- 
partments and  as  far  apart  as  possible.  The 
apparatus  is  made  by  the  carpenter,  and 
consists  of  a straightedge  and  T squares.  The 
former  is  merely  a planed  pine  board  about 
8 in.  X T in.  and  a foot  longer  than  the  distance 
between  the  wires.  It  rests  approximately 
horizontally  on  slats  tacked  across  the  shaft 
for  supports.  It  is  brought  to  about  an  | or 
yV  in.  from  each  wire  and  then  nailed  to  the 
slats  sufficiently  to  prevent  slipping.  One 
man  should  be  at  each  wire.  The  T squares 
are  most  serviceable  if  made  with  a mov- 
able head  clamped  by  a thumbscrew,  and 
of  planed  pine,  about  2|-  in.  X i in.  Except 
in  cramped  quarters,  the  T squares  will  be 
. set  at  right  angles,  and  should  be  placed  together  in  clamping  to  insure 
that  each  is  set  at  precisely  the  same  angle. 

Fig.  4 shows  a cramped  position  such  as  sometimes  arises  and  in  which 
the  movable  head  gives  more  latitude  in  working.  After  clamping,  the 
T squares  are  slid  along  the  straightedge  until  close  to  the  wire,  but  not 
touching  it,  and  are  there  clamped  by  a “ G ” clamp,  both  men  working  at  one 
T square.  The  ends  of  the  T squares,  C and  D,  must  be  supported  on 
blocks  so  that  the  T squares  lie  approximately  in  the  same  horizontal  plane. 
Everything  up  to  the  next  step  need  be  only  approximately  and  quickly 
placed,  but  now  the  greatest  care  must  be  exercised  in  measuring  out  equal 
distances,  A C and  B D,  from  the  wires.  If  the  wire  vibrates,  determine  the 
middle  of  its  swing  by  a pencil  or  pin.  Hold  a footmark  (not  the  end  of  the 
tape)  opposite  the  wire  on  the  T square,  measure  out  an  even  number  of 
feet,  and  mark  the  point  with  a sharp  pencil,  and  insert  a pin.  This  done 
for  both  wires  gives  us  the  parallelogram  ABD  C,in  which  the  only  essential 
is  that  CD  should  be  exactly  parallel  to  A B,  the  line  of  the  wires.  Now  set 
the  transit  over  the  most  convenient  of  the  two  points,  as  D.  To  get  the 
azimuth  of  D C,  and,  consequently,  the  line  of  the  wires,  sight  on  a known 
point  E for  a backsight,  and  measure  the  angle  EDO.  Establish  another 
point  as  F,  on  the  line  of  the  backsight,  in  order  that  its  course  may  be 
preserved  after  the  instrument  and  T square  are  removed. 

By  this  means  the  closing  angle  at  E may  be  read  after  the  wires  are 
removed  from  the  shaft.  Underground,  the  method 
is  the  same,  except  that  D C is  the  known  course, 
and  is  used  as  the  backsight.  To  give  the  coordinates 
of  the  instrument  at  D with  the  greatest  precision, 
the  angle  ADC  and  the  distance  A D should  be 
measured. 

Surveying  Slopes  or  Inclined  Shafts. — Where  a single 
sight  reaches  from  top  to  bottom  of  the  shaft,  the 
problem  is  simple  enough.  A station  can  be  estab- 
lished on  the  inside  of  the  foot-wall  plate  at  the  col  lar 
and  others  in  similar  positions  at  each  level.  The 
instrument  set  up  over  any  station  can  command  the 
whole  shaft  and  the  level  opposite. 

Fig.  5.  Where  the  shaft  is  sunk  on  several  dips,  the  survey 

is  a much  more  difficult  matter.  Fig.  5 illustrates 
cases  of  common  occurrence.  The  shaft  may  be  divided  into  sections  like 
A D EB,  which  are  convex  downwards,  and  others  such  as  E B (7,  which 
are  concave  downwards.  As  a rule  a set-up  can  be  avoided  at  the  convex 
knuckles  if  desired,  and  need  only  be  made  at  those  that  are  concave. 

Bent  Plumb-Line  Method.— A may  be  invisible  from  B,  but  the  survey  may  be 


* See  “Mines  and  Minerals,"  January,  1899,  page  242, 


74 


SURVEYING, 


carried  from  one  point  to  the  other  by  the  ingenious  method  of  the  bent 
plumb-line. 

The  most  complicated  example  which  can  arise  is  shown  in  Fig.  5. 
Establish  a station  at  A,  the  foot- wall  side  of  the  collar,  the  center  point 
being  a small  nail  head  projecting  horizontally.  Attach  a long  plumb-line 
to  this  and  carry  the  other  end  to  B.  Here  it  will  probably  be  necessary  to 
use  a small  screw-eye,  with  its  head  turned  into  the  vertical  plane  of  the 
shaft,  for  the  center  point.  Pass  the  plumb-line  through  this  and  draw  it 
fairly  tight.  Now  attach  a plumb-bob  at  an  intermediate  point  and  regulate 
the  tautness  so  that  the  line  is  clear  at  all  points. 

The  curves  in  the  shaft  may  be  such  that  two  plumb-bobs  may  have  to  be 
hung,  as  at  D and  E,  and  even  a third  may  become  necessary. 

The  plumb-line,  perhaps  100  ft.  long,  is  apt  to  be  disturbed  by  the  air- 
currents,  and  it  is  often  better  to  mark  a point  on  a convenient  timber  near 
D,  and  another  near  E,  so  close  to  the  string  that  there  is  no  doubt  of  the 
points  lying  in  exactly  the  same  vertical  plane  as  the  plumb-line.  If  these 
points  be  once  established,  the  string  and  weights  can  be  taken  out  of  the 
shaft,  leaving  us  four  points  in  the  same  vertical  plane,  and  whose  horizontal 
projections  lie  in  the  same  course. 

Now  set  up  at  A and  measure  the  azimuth  angle  from  the  backsight  to  D, 
thereby  giving  the  bearing  from  A to  B.  If  J)  should  be  invisible  from  B, 
depress  the  telescope  after  sighting  on  D and  locate  the  point  N in  the  same 
vertical  plane,  and  so  situated  that  it  is  visible  from  both  A and  B.  Measure 
the  vertical  angle  and  distance  to  N.  Now  set  up  at  B,  use  the  course  B E for 
a backsight,  and  foresight  to  C.  Measure  the  vertical  angle  and  distance 
B N.  It  is  seen  that  B N might  have  been  used  as  a backsight,  and  E only 
serves  as  an  additional  check.  N is  really  an  intermediate  station,  but  since 
it  lies  in  the  course  AB,a  set-up  there  is  unnecessary.  In  simple  cases,  it  is  a 
very  convenient  method  of  carrying  a survey  from  the  surface  to  the  first 
level,  and  a longer  horizontal  projection  of  the  sight  A D can  be  secured 
than  if  a set-up  were  made  in  the  shaft  at  D\  but  in  complicated  cases,  such 
as  the  one  shown,  it  may  often  be  quicker  to  make  the  extra  set-up  than 
to  use  the  plumb-line.  In  all  sights  for  determining  azimuth,  keep  the 
vertical  angles  as  low  as  possible,  and  the  horizontal  projection  of  the 
course  long. 

Method  by  a Single  Wire  in  the  Shaft. — Stretch  a rather  fine  wire,  free  from 
kinks,  down  the  shaft,  as  shown  in  Fig.  6,  being  careful  that  it  touches 
nowhere  in  the  shaft.  Take  two  plumb-bobs  provided  with  fine  round 
strings.  Suspend  one  from  A and  the  other  from  B so  that  they  nearly  touch 
the  same  side  of  the  wire  M N.  In  order  to  have  the  plumb-lines  as  far  apart 
as  possible,  the  line  at  B must  be  quite  long  and  a can  of  water  should  be 
provided  to  keep  the  bob  from  swinging.  The  plumb-line  is  fastened  to  a 
nail  B nearly  in  the  proper  position.  Have  a bar  of  wood  with  a block 
fastened  to  it  placed  to  one  side  of  B and  a little  below  it. 
^ „ The  block  must  have  a hole  so  that  a small  screw  bolt  can 

easily  screw  through  it.  A spool  is  run  on  the  bolt  having  a 
small  groove  turned  in  it  and  being  sandpapered  and  greased 
so  that  the  string  will  slip  easily  as  the  bolt  is  turned.  Now, 
place  the  transit  in  line  with  the  two  plumb-bobs  as  in  an 
ordinary  case  of  shaft  plumbing.  Repeat  this  operation  below. 
The  plumb-bobs  in  both  cases  hang  in  the  same  vertical  plane 
and  thus  the  true  bearings  are  found  underground.  Even  the 
plumb-lines  could  be  dispensed  with,  but  the  method  would 
not  then  be  so  accurate.  The  instrument  would  be  set  nearly 
in  the  vertical  plane  passing  through  the  wire,  leveled  and 
sighted  at  M.  Dip  the  telescope  until  the  lowest  point  on  the 
wire  is  visible,  note  the  amount  by  which  the  cross-hair  and 
wire  fail  to  coincide  and  shift  the  instrument  accordingly.  But 
if  this  method  were  tried,  the  two  points  sighted  at  would  not  be  nearly  so 
far  apart  horizontally  as  the  plumb-lines,  and  any  error  in  leveling  would 
also  vitiate  the  result.  This  method  of  the  single  wire,  however,  provides 
no  way  of  obtaining  the  coordinates. 


Fig.  6. 


NOTES  ON  MAPPING. 

There  are  no  general  rules  governing  the  minutiae  of  map  making,  so 
that  it  may  be  well  to  note  some  of  the  variations  in  practice.  In  some 
offices  the  area  excavated  isr  shown  by  a light  wash  of  India  ink  in  addition 


NOTES  ON  MAPPING, 


75 


to  the  ink  line  bounding  the  solid  area.  This  makes  a striking  map,  and 
the  workings  stand  out  prominently.  If  the  survey  were  never  to  be 
extended  and  the  map  were  simply  made  to  show  a particular  state  of  the 
workings,  there  would  be  no  objection  to  the  practice;  but  as  such  exten- 
sions have  to  be  made,  and  old  pillars  removed  or  cut  up,  it  requires  con- 
siderable skill  to  tint  the  extensions,  and  especially  the  surfaces  when 
erasures  have  been  made,  so  as  to  produce  an  effect  uniform  with  the  old 
tinted  surface,  especially  as  that  tint  has  been  deepened  by  frequent  han- 
dling. For  these  reasons  many  offices  omit  the  tint  on  the  map,  but  some  tint 
the  back  of  the  tracing  used  by  the  corps,  or  sent  to  the  mine  inspector. 

It  is  an  open  question  whether  the  ends  of  the  chambers  (breasts,  rooms) 
and  gangways  (entries,  levels)  should  be  closed  with  ink.  It  is  well  to  be 
able  to  show  on  your  map  where  the  faces  of  the  workings  were  at  any  given 
time.  Some  place  the  date  of  each  survey  at  the  ends  of  the  gangways  at 
each  posting,  and  of  every  fourth  or  fifth  chamber,  and  thus  note  the  rapid- 
ity with  which  the  mine  is  worked.  Others  use  various  colors  to  denote  the 
successive  postings  of  the  survey,  and  place  across  the  ends  of  gangways  and 
chambers  the  color  appropriate  to  the  survey  that  located  them. 

Where  there  are  a number  of  beds  worked  from  the  same  shaft,  slope,  or 
adit,  the  workings  are  frequently  vertically  above  one  another,  and  their 
location  on  the  same  map  causes  confusion  unless  care  be  taken.  One  of  the 
methods  used  to  distinguish  between  each  bed  is  to  line  in  the  areas  worked 
with  a color  appropriate  to  that  bed.  In  this  way,  three  or  four  beds  have 
been  plotted  on  the  same  map.  A better  way  is  to  make  a map  for  each  bed 
and  to  combine  the  various  beds  on  the  tracings  for  the  officers  and  the  mine 
inspector.  Each  bed  on  this  is  lined  with  its  color,  and  tinted  with  a wash 
of  the  same  color  on  the  back  of  the  tracing  on  the  parts  excavated. 

The  lines  of  survey  are  lightly  drawn  between  stations  with  red  ink,  and 
the  stations  denoted  by  minute  circles  of  the  same  color  as  that  used  for  that 
particular  seam.  The  survey  lines  should  never  cut  the  circumference  of  the 
circle,  as  such  a procedure  might  cause  doubt  as  to  the  exact  location  of  the 
station  in  case  measurements  were  made  on  the  map.  Stations  are  numbered 
as  in  the  mine,  and  beneath  each  is  placed  the  elevation  above  or  below  tide 
of  the  roof  of  the  mine.  If  the  stations  are  numerous  and  the  elevations  fre- 
quently taken,  such  a map  would  furnish  the  means  of  ascertaining  the 
shape  of  the  bed  by  running  contours  through  points  of  equal  elevation. 
This  plan  was  used  by  a number  of  engineers  and  was  adopted  by  the  Second 
Geological  Survey  of  Pennsylvania  in  making  their  mine  sheets"  The  adop- 
tion of  the  scale  of  100  ft.  to  the  inch,  under  the  ventilation  law,  also  fur- 
nished that  survey  with  a means  of  tracing  and  connecting  adjoining 
properties  and  their  workings,  as  had  been  frequently  done  by  large  com- 
panies having  adjacent  collieries,  and  the  maps  of  the  anthracite  regions  of 
the  Second  Geological  Survey  of  Pennsylvania  have  been  thus  compiled  from 
tracings  of  office  maps,  with  little  or  no  inside  work  by  the  corps  of  the  survey. 

The  ground  areas  of  all  buildings  are  tinted  a uniform  red. 

All  railroad  tracks  are  represented  by  red  lines. 

All  bridges,  etc.,  and,  in  fact,  any  improvements  built  by  man,  are  to  be 
colored  red. 

In  the  mine,  the  stations  are  represented  by  a small  circle  (o)  with  the 
number  in  black  beside  it. 

The  lines  of  survey  are  drawn  between  the  circumferences  of  the  circles 

marking  the  station  o o,  so  as  to  leave  the  centers  uncolored.  The 

elevations  above  tide  are  marked. 

All  small  bodies  of  water  are  tinted  with  Prussian  blue;  all  large  bodies 
with  indigo— as  Prussian  blue  is  too  vivid  for  large  areas  of  tint. 

It  is  the  custom  to  allot  a color  to  each  bed,  and  make  each  bed  on  the 
general  tracing  in  its  color.  In  this  way  all  the  beds  may  be  mapped  on  the 
same  tracing,  and  can  be  distinguished  though  the  workings  may  all  under- 
lie the  same  area.  Various  colors  are  sometimes  used  to  denote  the  extent 
of  the  workings  at  the  given  postings. 

The  paper  on  which  the  map  is  made  should  be  of  the  best  quality,  as 
frequent  changes  in  the  workings,  and  the  removal  of  portions  of  old  pillars, 
necessitate  many  erasures.  Ordinary  paper  will  not  work  well  after  erasure 
and  subsequent  handling,  and  the  best  practice  is  to  use  cloth-backed  egg- 
shell paper. 

It  remains  to  note  that  the  temperature  and  humidity  of  the  office,  and  of 
the  place  where  the  maps  are  stored,  should  vary  as  little  as  possible.  As  the 
scale  is  small,  any  variation  in  the  paper  by  contraction  or  expansion  will 


76 


SURVEYING. 


affect  the  scale  on  which  the  map  was  originally  laid  out,  and  will  affect  it 
unequally,  as  the  paper  is  not  homogeneous.  This  can  he  seen  by  making 
measurements  on  old  maps  to  check  work  done  in  former  times.  In  almost 
every  case  the  500' squares  are  slightly*  in  error.  This  must  be  guarded 
against  in  case  measurements  are  taken  from  the  map.  It  is  best  to  calculate 
the  distances  wanted  from  the  coordinates  of  the  ends  of  the  lines,  and 
insure  absolute  accuracy. 

A good  map  is  the  sign  of  a good  draftsman.  The  title  should  be  subordi- 
nate to  the  map.  It  is  common  to  see  the  fifty-cent  map  of  a small  area 
smothered  under  a gorgeous  ten-dollar  title.  The  lettering  should  be  neat 
and  appropriate,  and  a style  should  be  adopted  that  can  be  readily  thrown 
off— as  time  is  quite  an  item  in  the  money  made  by  mapping. 

A neat  title,  the  judicious  use  of  tints  over  the  area  excavated,  and  good 
lettering  of  minor  objects  will  add  dollars  to  the 
value  of  a map.  A small  outlay  of  taste  and  care 
will  make  a beautiful  tracing  out  of  a ragged  one, 
and  double  its  value. 

Locating  Errors.— Errors  in  arc  or  distance  are 
easiljr  located  by  the  method  of  coordinates.  The 
transitman,  at  the  completion  of  a closed  survey, 
should  sum  the  angles  and  see  if  it  be  360°.  Thus, 
before  leaving  the  mine,  a check  will  be  established 
on  the  transit  work.  In  case  of  a variation  from 
360°,  the  notes  are  examined  to  see  if  the  needle 
readings  show  a similar  variation  with  the  vernier. 
In  case  the  notes  are  incomplete,  or,  if  a continuous 
vernier  has  been  carried,  we  table  the  work  before 
leaving  the  mine  and  locate  the  error  as  follows:  Fig.  7 represents  a close  of 
four  stations  and  an  angular  error  at  c.  Starting  from  a we  table  as  follows: 


b 


Sta. 

Course. 

Dist. 

N 

s 

E 

W 

Sums. 

N 

S 

E 

W 

a 

h 

c 

d (d') 
a (a") 
b 

N 

E 

S30E 

S60  W 
N30  W 

100 

100 

100 

100 

100 

86.58 

50 

100 

50 

86.58 

100 

100 

13.42 

36.58 

100 

150 

63.42 

There  is  an  error  in  close  of  30°,  as  the  course  a"h  differs  from  the 
course  a 5 by  30°. 

Reversing  the  order  of  tabling,  and  correcting  each  course  by  30°,  we  have: 


Upon  comparing  the  sums  of  the  northings  and  southings  and  eastings 
and  westings  in  both,  we  find  that  c is  the  only  station  for  which  they  agree. 
Here  the  error  occurred.  The  location  of  c from  either  direction  was  cor- 
rect, and  what  followed  incorrect.  From  this  we  can  deduce  the  rule: 

To  Find  an  Error  in  Arc.— Table  the  close  from  any  station  in  both  directions 
back  to  the  initial  station.  The  station  which  has  a similar  sum  of  eastings 


NOTES  ON  MAPPING. 


77 


and  westings  and  northings  and  southings  in  both  tablings  is  the  one  at 
which  the  error  was  made. 

With  two  or  more  errors  nothing  can  be  done. 

Errors  in  Distance.— These  may  be  found  in  a close  by  tabling.  Suppose 
we  have  a square  ah  cd  so  placed  that  the  magnetic  meridian  passes 
through  h d.  Let  the  distance  c d be  incorrect. 


Sta. 

Course. 

Dist. 

N 

S 

E 

W 

Sums. 

N 

S 

E 

W 

a 

N45E 

100 

70.71 

70.71 

70.71 

70.71 

b 

S 45E 

100 

70.71 

70.71 

141.42 

1 

c 

S 45  W 

150 

106.06 

106.06 

106.06 

35.36 

d 

N45  W 

100 

70.71 

70.71 

35.35 

35. 3o 

a 

The  first  location  of  a is  southings  0,  westings  0;  the  second  location  is 
southings  35.35,  westings  35.35.  The  westings  are  sines  and  the  southings 
cosines,  as  stated  before.  As  sin  cos  = tang  of  course  referred  to  the  base 
line,  we  divide  35.35  by  35.35  and  obtain  1 as  the  natural  tangent  for  45°,  and, 
as  the  error  was  in  sonthings  and  westings,  the  course  on  which  the  error 
was  made  is  S 45°  W.  The  amount  of  the  error  is  found  by  dividing  the  error 
in  eastings  or  westings  as  tabled  by  the  sine  of  the  course  just  found,  or  the 
error  in  northings  or  southings  by  the  cosine  of  the  same.  Both  results 
will  agree,  35.35  -j-  70.71  = .50.  Reducing  the  measured  distance  by  this 
amount,  we  find  the  tabulation  shows  an  accurate  close.  From  this  we 
deduce  the  rule: 

To  Find  an  Error  in  Measurement.— Divide  the  difference  between  the  east- 
ings or  westings  of  the  two  locations  by  the  difference  between  the  northings 
or  southings  of  the  same.  The  quotient  will  be  the  tangent  of  the  course  on 
which  the  error  was  made.  The  extent  of  the  error  is  found  by  dividing  the 
error  in  eastings  or  westings  (as  tabled)  by  the  sine  of  the  above  course,  or 
the  error  in  northings  or  southings  by  the  cosine  of  the  same. 

Locating  Special  Work.— This  last  principle  may  be  used  for  finding  the 
proper  course  and  distance  to  drive  a tunnel  between  two  stations  connected 
by  a survey.  In  outside  tunneling,  the  survey  is  generally  carried  over  the 
surface  in  a straight  line.  In  underground  work  this  is  impossible,  so  that  it 
is  a much  more  difficult  task  to  ascertain  the  distance  and  direction  to  drive, 
from  the  number  of  measurements  to  be  made  in  connection  with  the  two 
stations,  but  if  the  work  is  accurately  done  it  is  much  more  a feat  than  in 
outside  work.  To  include  all  the  elements  that  enter  into  such  a calculation, 
we  will  suppose  that  an  underground  slope  is  to  be  run  between  two  beds  of 
coal.  The  distance  between  the  two  ends  must  be  accurately  obtained,  as 
well  as  the  relation  of  the  two  stations  found.  Having  tabled  the  work,  we 
get  the  difference  between  the  sums  of  sines  and  cosines,  as  just  described, 
for  the  two  points;  the  quotient  from  dividing  the  first  by  the  second  gives 
us  the  course,  and  from  the  last  rule  the  horizontal  distance  is  found.  The 
levels  give  us  the  difference  in  elevation,  and  from  these  data  we  get  the 
slope  per  hundred,  and  the  distance  measured  on  that  slope.  All  of  the  work 
is  done  in  the  mine  and  while  the  transit  is  setting  up  at  one  of  the  end 
stations,  so  that  before  leaving  the  mine,  we  can  give  the  course,  pitch,  and 
distance  of  the  tunnel  and  set  the  first  station  for  lining  in  the  center.  The 
more  important  the  work,  the  greater  need  of  accuracy.  In  one  case  a 
1,000'  chain  was  constructed  to  measure  the  distance  between  two  shafts 
that  were  to  be  connected  by  work  driven  from  both  ends,  and  much 
of  the  outside  work  was  done  on  the  ice  of  the  Susquehanna  River,  and  a 
transit  reading  to  5"  was  used.  The  work  closed  vertically  and  laterally 
within  an  inch. 

Calculation  of  Areas.— In  connection  with  the  mapping  of  the  part  newly 
worked,  the  engineer  of  the  company  sometimes  calculates  the  area 
excavated  since  the  last  posting,  and  estimates  the  royalties  accruing  to  the 
various  parties  whose  lands  are  leased. 

This  method,  at  best,  is  liable  to  grave  errors,  and  requires  a number  of 
accurate  cross-sections  of  the  bed  to  determine  its  composition,  as  well  as 


78 


SURVEYING. 


numerous  determinations  of  the  specific  gravity  to  determine  its  weight. 
The  old  method  of  estimating  workable  coal  in  a property  allowed  1,000  tons 
per  acre  per  foot  of  thickness  of  the  bed.  To  obtain  this  amount,  the  roof 
must  be  good,  the  pillars  of  medium  size,  and  the  bed  near  the  surface; 
or  the  surface  must  be  so  valueless  that  the  pillars  can  be  “drawn”  or 
“robbed.”  As  beds  increase  in  depth,  if  the  surface  be  valuable,  the  ratio 
of  pillars  to  stall  must  increase  or  the  greater  pressure  will  cause  the  mine  to 
cave  in.  It  has  been  found  that,  when  the  surface  is  to  be  kept  up  and  the 
workings  are  to  be  carefully  driven,  but  850  tons  per  acre  per  foot  of  thick- 
ness can  be  used  in  calculation,  under  the  present  system  of  mining.  Efforts 
are  constantly  being  made  to  increase  this  amount,  with  a possible  chance 
of  success. 

To  estimate  the  amount  of  coal  excavated  from  any  property,  the  best 
method  is  to  institute  an  account  of  all  cars  of  coal  taken  out  from  the  work- 
ings under  that  property.  As  soon  as  the  measurements  on  the  mine  tracing 
show  that  a gangway  or  room  has  crossed  the  property  line,  the  office  is 
notified,  and  all  cars  coming  from  those  places  are  credited  to  that  property. 
This  is  the  only  absolutely  accurate  method  of  computation.  The  total 
number  of  cars  of  coal  run  through  the  breaker  is  known,  with  the  total 
weight  of  prepared  coal.  The  ratio  of  the  cars  coming  from  a given  property 
to  the  total  number  of  cars  is  taken  as  the  ratio  between  the  total  prepared 
coal  and  the  coal  sold  from  that  property. 


RAILROAD  CURVES. 

These  are  arcs  of  circles,  and  are  divided  into  simple,  compound,  and 
reverse  curves.  A simple  curve  has  but  one  radius,  a compound  one  is  con- 
tinuous and  has  two  or  more  radii,  and  a 
reverse  one  is  also  continuous  but  com- 
posed of  arcs  described  in  opposite  direc- 
tions. 

Curves  are  designated  by  the  number 
of  degrees  in  the  central  angle,  which  is 
subtended  by  an  arc  whose  chord  is  100  ft. 
long.  Thus,  if  the  angle  BOG,  Fig.  1,  is 
10°  and  .B  is  100  ft.  long,  (x  if  C is  a 10° 
curve. 

The  angle  EEC,  formed  by  the  pro- 
longation of  two  adjacent  straight  por- 
tions of  a railroad,  or  tangents,  as  they  are 
technically  called,  is  termed  an  intersec- 
tion angle. 

The  deflection  angle  of  a curve  is  the 
angle  formed  at  any  point  of  the  curve 
between  a tangent  and  a chord  of  100  ft., 
and  is  therefore  one-half  the  size  of  the 
degree  of  the  curve.  If  the  chord  5 6?  is 
100  ft.,  the  angle  E B G is,  the  defiection  angle  of  the  curve  B G H C,  and  is 
one-half  the  angle  BOG. 

When  the  defiection  angle  D is  given,  the  radius  of  the  curve,  R,  is 
found  by  the  formula 

Sin  D 


The  curve  used  to  connect  two  tangents  is  determined  mainly  by  the  form 
of  the  country.  When  this  is  decided,  the  point  of  beginning,  called  the 
P.  C.  (point  of  curve),  and  the  point  where  the  curve  ends,  called  the  P.  T. 
(point  of  tangent),  must  be  located.  Both  these  points  are  the  same  distance 
from  the  point  of  intersection  of  the  tangents,  called  the  P.  I.  (point  of  inter- 
section). This  distance  is  called  the  tangent  distance  of  a curve,  and  is  found 
by  the  formula 

^ T=  i^tan  i I, 

in  which  tangent  distance; 

R = radius  of  curve; 

I = intersection  angle. 

Having  set  the  tangent  points  B and  C.  Fig.  1,  in  order  to  locate  points  on 
the  curve,  set  up  the  transit  at  B.  the  P.  C.  Set  the  vernier  at  zero-,  and  sight 
to  E,  the  P.  I.  Suppose  .B  to  be  a full  station  on  the  tangent,  and  that  it  has 


RAILROAD  CURVES. 


79 


been  decided  to  set  stakes  at  each  100  ft.  Let  the  central  angle  BOG,  meas- 
ured by  the  100-ft.  chord  B G,  be  10°;  then,  the  deflection  angle  .E  ^ G',  having 
its  vertex  B in  the  circumference,  and  being  subtended  by  the  chord  B G, 
will  equal  ^ BOG,  ox  5°.  Turn  an  angle  of  5°  from  B,  which  in  this  case  will 
be  to  the  right,  measure  100  ft.  from  B,  and  drive  a stake  at  G.  Turn  off  an 
additional  angle  of  5°,  making  10°  from  zero,  and  at  another  100  ft.  measured 
from  G,  and  drive  a stake  at  H.  Continue  this  process  until  20°,  or  one-half 
the  intersection  angle,  has  been  turned  off.  This  last  deflection  will  bring 
the  forechainman  to  the  point  of  tangency  C,  or  the  P.  T. 

When  the  P.  C.  comes  between  two  stations  it  is  called  a substation,  and 
the  chord  between  it  and  the  next  station  on  the  curve  is  called  a subchord. 
Had  the  P.  C.  been  a substation,  say  32  ft.  beyond  a regular  station,  the 
deflection  angle  for  the  measuring  distance  of  100  — 32  = 68  ft.  would  be 
found  in  this  manner:  The  deflection  for  100  ft.  is  5°  = 300';  hence,  for  1 ft. 

300' 

it  is  ~ = 3',  and  for  68  ft.  it  is  3 X 68  = 204'  = 3°  24'.  This  is  turned  off 


and  a stake  set  in  line  68  ft.  from  the  transit.  Other  stations  are  then  located 
as  above,  by  turning  off  an  additional  5°  each  time. 

Rules  for  Measuring  the  Radius  of  a Curve.— Stretch  a string,  say  20  ft.  long,  or 
longer  if  the  curve  is  not  a sharp  one,  across  the 
curve  corresponding  to  the  line  from  A to  C,  in 
Fig.  2.  Then  measure  from  B the  center  of  the 
line  A C,  and  at  right  angles  with  it,  to  the  rail  at 
D.  Multiply  the  distance  A to  B,  or  one-half  the 
length  of  the  string,  in  inches,  by  itself;  measure 
the  distance  D to  ^ in  inches,  and  multiply  it  by  Fig.  2. 

itself.  Add  these  two  products,  and  divide>he  sum 

by  twice  the  distance  from  B to  D,  measured  exactly  in  inches  and  fractional 
parts  of  inches.  This  will  give  the  radius  of  the  curve  in  inches. 

It  may  be  more  convenient  to  use  a straightedge  instead  of  a string.  Care 
must  be  taken  to  have  the  ends  of  the  string  or  straightedge  touch  the  same 
part  of  the  rail  as  is  taken  in  measuring  the  distance  from  the  center.  If  the 
string  touches  the  bottom  of  the  rail  flange  at  each  end,  and  the  center 
measurement  is  made  to  the  rail  head,  the  result  will  not  be  correct. 

In  practice,  it  will  be  found  best  to  make  trials  on  different  parts  of  the 
curve,  to  allow  for  irregularities. 

Example. — Let  A C be  a 20-ft.  string;  half  the  distance,  or  A B,  is  then 
10  ft.,  or  120  in.  Suppose  B D is  found  on  measurement  to  be  3 in.  Then  120 
multiplied  by  120  is  14,400,  and  3 multiplied  by  3 is  9;  14,400  added  to  9 is 
14,409,  which,  divided  by  twice  3,  or  6,  equals  2,401i  in.,  or  200  ft.  1^  in.,  which 
is  the  radius  of  the  curve. 

The  formula  is  thus  stated, 

A ^2  + ^ 2)2 

~2BD~  - 

Or,  applied  to  the  above  example. 


1002  4-  q 

= 2,40U  in.  - 200  ft.  U in. 

2X3 

To  Find  the  Radius  of  a Circular  Railroad  Curve,  the  Straight  Portions  of  a Road 
Being  Given.— If  Q I and  P D,  Fig.  3,  are  the  straight  portions  that  are  to  be 
connected,  the  radius  of  the  curve  I D may  be  found  as  follows: 

Produce  Q I and  P D until  they  meet  and  form  the  angle  T.  Bisect  the 
angle  Q TP  by  the  line  TC.  From  the  point  on  either  line  from  which  the 
curve  is  to  be^n,  in  this  instance  making  the  point  I the  point  of  curve,  erect 
the  line  I C perpendicular  to  Q T,  and  the  point  where  this  joins  the  line  T C, 
or  C,  is  the  center  of  the  curve,  and  the  line  I C is  the  radius.  To  find  the 
end  of  the  curve,  or  point  of  tangent,  as  D,  draw  a line  from  C,  perpendicular 
to  TP.  The  line  CD  will  also  be  a radius  of  the  circle  of  which  I D is  the 
arc,  and  the  point  D will  be  the  point  of  tangent. 

To  Find  the  Radii  of  Compound  Curves  to  Join  Two  Straight  Portions  of  Road. 
This  kind  of  curve  is  adopted  where  the  railroad  is  required  to  pass  through 
given  points,  as  C,  D,  E,  F,  Fig.  3 (6),  or  to  avoid  obstructions. 

Compound  railroad  curves  are  composed  of  straight  lines  and  circular 
arcs,  and  have  common  normals,  OH,  OP,  PI,  QJ,  K R,  and  therefore  com- 
mon tangents  where  the  arcs  are  joined.  The  normals  are  perpendicular  to 
the  straight  portions  of  the  road  also;  OH  is  perpendicular  to  AP,  PP  is 
perpendicular  to  Q A and  KR. 


80 


SURVEYING. 


To  find  the  radii  OB,  C Q,  Fig.  3 (c),  to  connect  two  straight  lines  of  rail- 
road, A B,  DE,  the  rOad  has  to  pass  from  the  point  B,  through  the  point  C, 
and  to  touch  the  straight  road  E F2it  any  point  D. 

Join  B and  C,  make  the  angle  B CO  = 0 B C,  which  is  supposed  to  he 
given,  equal  ^{P—TB  C.  Draw  B 0 perpendicular  to  AB,  then  OB  = CO, 
and  is  the  radius  of  the  arc  B C. 

With  0 B SiS  radius,  describe  the  arc  B C;  draw  CF  perpendicular  to  CQ, 
and  produce  B E to  meet  it  in  F;  make  D F = CF,  and  draw  D Q perpen- 
dicular to  E F,  to  meet  C Q in  Q.  Then  CQ  = QD,  and  the  radii  0 B and 
QD  are  determined. 

Practical  Method  of  Laying  Out  Sharp  Curves  in  a Mine. — Curves  in  a mine  are 
usually  so  sharp  that  they  are  designated  as  curves  of  so  many  feet  radius,, 
instead  of  as  curves  of  so  many  degrees. 

“Suppose  that  it  is  required  to  connect  the  two  headings  A and  B,  Fig.  4 (a), 
which  are  perpendicular  to  each  other,  with  a curve  of  60  ft.  radius.  Pre- 
pare the  device  shown  in  Fig.  4 (&),  by  taking  three  small  wires  or  inelastic 
strings  f g,  g h,  and  g k,  each  10  ft.  long,  and  connecting  one  end  of  each  to 
a small  ring,  and  the  other  end  of  two  to  the  ends  of  a piece  of  wood  If  ft. 
long.  Form  a neat  loop  at  the  end  / of  the  string  g f.  To  use  this  device, 
lay  off  on  the  center  line  of  the  heading  B,  c d and  d e equal  to  60  ft.  and 
10  ft.,  respectively.  Place  the  loop  / of  the 
device  described  over  a small  wire  peg  driven 
in  at  e,  and  the  ring  g over  a similar  peg  at  d. 
Take  hold  of  the  stick  h k,  pull  the  strings  g h 
and  g k taut,  and  place  the  center  mark  on  hk 
on  the  center  line  of  the  heading  B.  Drive  a 
small  peg  in  at  m,  located  by  the  point  k,  which 
is  on  the  curve.  Move  the  device  forward, 
place  the  loop  / over  the  peg  at  d,  the  ring  g 
over  the  peg  at  m,  and  take  hold  of  the  stick 
h k and  pull  until  the  strings  g h and  g k are 


Fig.  4. 


taut,  and  the  strings  f g and  g h are  in  a straight  line.  The  point  k will  fall 
on  the  curve  at  n,  which  mark  by  driving  in  a peg.  To  locate  other 
points,  proceed  exactly  as  in  the  last  step.  The  distance  c d in  any  case 
is  found  by  the  formula  c d ==  R tan  f I,  in  which  R is  the  radius  of  the 
curve,  and  I the  intersection  angle  of  the  center  lines  of  the  headings. 


HINTS  TO  BEGINNERS. 

Abuse  of  Instruments.— Surveying  instruments  of  value  and  precision  are 
not  made  of  cast  iron,  as  one  would  think  from  the  way  they  are  frequently 
handled.  Underground  work  is  transacted  in  places  dark,  dirty,  and  con- 
fined, so  that  extra  care  must  be  observed  to  prevent  accidental  knocks  that 
damage  the  instrument  even  if  they  do  not  destroy  its  accuracy. 


STADIA  MEASUREMENTS. 


81 


As  it  frequently  happens  that  long  distances  must  be  traversed  under- 
ground in  going  between  the  shaft  or  slope  and  the  workings  to  be  surveyed, 
the  transit  and  level  should  be  carried  so  as  to  obviate  all  accidents.  They 
should  never  be  attached  to  the  tripod  and  carried  on  the  shoulder,  and,  if 
the  route  to  be  passed  over  is  up  or  down  a slope  or  working  place,  the 
person  carrying  the  instrument  should  be  the  last  to  descend  and  the  first  to 
ascend,  so  that  loose  stones  or  dirt  that  may  be  dislodged  will  not  affect  or 
endanger  the  instrument  or  trip  the  carrier. 

Be  sure  that  the  tripod  head  is  tightly  screwed  on  to  the  tripod.  The 
writer  remembers  a case  where  the  transitman  and  himself,  when  new  to 
the  work,  spent  over  an  hour  in  endeavoring  to  obtain  two  readings  of  an 
angle  that  would  agree.  The  variations — from  8'  to  2° — were  caused  by  the 
slight  movement  of  an  old  instrument  with  too  much  “ lost  motion,”  and  a 
loose  tripod  head. 

A great  many  engineers  prefer  kerosene  to  fish  oil  for  their  lamps.  Kero- 
sene never  drops  upon  your  book  to  make  an  unsightly  smear,  and  perhaps 
obliterate  part  of  your  notes.  A kerosene  lamp  is  hotter  and,  with  the 
glazed  mine  hat,  is  more  apt  to  produce  headaches.  The  writer,  during  the 
latter  part  of  his  underground  work,  wore  a straw  hat,  had  a piece  of  thin 
sheet  brass  riveted  to  its  front  with  a hole  in  the  top  for  the  lamp  hook.  To 
the  lamp  was  brazed  a narrow  cross-strip  of  the  same  metal,  and  the  strip 
ends,  bent  back  upon  themselves,  were  slid  down  the  sides  of  the  plate  on 
the  hat  and  kept  the  lamp  from  swaying.  With  such  an  arrangement  it  is 
not  necessary  to  remove  the  lamp  to  read  the  vernier,  and  when  the  lamp 
is  used  for  other  purposes,  th6  hat  can  be  removed  with  the  lamp  fastened  to 
it.  This  arrangement  keeps  the  hands  free  from  lamp  smoke  or  oil,  and  a 
cleaner  note  book  is  the  result. 

When  there  is  an  antipathy  to  a lamp  upon  the  head,  and  when,  with  a 
long,  wooden  handle,  one  or  both  hands  are  free  in  going  about  the  work, 
a larger  lamp  is  used  of  “torch”  pattern,  employed  by  wheel  testers  or 
engineers  in  railroad  practice.  Kerosene  can  be  burned  in  this.  The  handle 
can  be  tucked  under  the  left  arm  while  taking  side  notes.  Such  a lamp  is 
convenient  in  finding  old  stations  in  a high  place,  when  there  is  no  firedamp. 

For  plumbing  wet  shafts,  kerosene  resists  the  extinguishing  power  of 
water  better  than  fish  oil,  and  is  less  readily  blown  out  by  a strong  ventilating 
current.  It  makes  more  smoke,  and,  in  tight  headings,  or  mines  with  poor 
ventilation,  with  a large  party,  fouls  the  air  much  more  readily  than  fish  oil. 
Sometimes  a mixture  of  the  two  is  burnt  in  very  drafty  places,  where  it  is 
hard  to  maintain  a light.  Kerosene  is  burned  in  the  plummet  lamp  unless 
it  is  used  with  the  “ safety  ” attachment.  Sweet  oil,  or  any  oil  burning 
without  smoke,  must  then  be  used.  Smoke  clogs  the  openings  in  the  gauze, 
restricts  the  entry  and  escape  of  gases,  and,  especially  if  the  gauze  be  damp 
with  oil,  may  ignite  and  communicate  the  flame  from  within  to  the  outside 
body  of  gas. 

White  lead  or  Dutch  white  (white  lead  and  sulphate  of  baryta  in  equal 
parts)  is  best  for  painting  stations.  Zinc  white  has  been  tried  with  less 
success.  The  mixture  should  not  contain  too  much  linseed  oil— especially 
in  wet  places— or  it  will  run  and  destroy  the  witness. 


THEORY  OF  STADIA  MEASUREMENTS. 

By  Akthuk  Winslow.* 

Late  Assistant  Geologist,  Second  Geological  Survey  of  Pennsylvania,  State 
Geologist  of  Missouri. 

The  fundamental  principle  on  which  stadia  measurements  are  based  is 
the  geometrical  one  that  the  lengths  of  parallel  lines  subtending  an  angle  are 
proportional  to  their  distances  from  its  apex.  Thus  if,  in  Fig.  1 (a),  a represents 
the  length  of  a line  subtending  an  angle  at  a distance  d from  its  apex,  and  a' 
the  length  of  a line,  parallel  to,  and  twice  the  length  of,  a subtending  the 
same  angle  at  a distance  d'  from  its  apex,  then  d'  will  equal  2d. 


* Mr.  Winslow’s  calculations  and  tables  have  been  proved  practically  correct  by  the  several 
corps  of  the  Second  Geological  Survey  of  Pennsylvania.  The  corps  in  the  anthracite  regions,  under 
directions  of  Mr.  Frank  A.  Hill,  geologist  in  charge,  took  over  30,000  stadia  sights,  and  better 
results  were  obtained  when  tie  surveys  were  made  than  in  previous  work  in  which  distances 
were  chained. 


82 


SURVEYING. 


This  is,  in  a general  way,  the  underlying  principle  of  stadia  work;  the 
nature  of  the  instruments  used,  however,  introduces  several  modifications, 
and  these  will  be  best  understood  by  a consideration  of  the  conditions  under 
which  such  measurements  are  generally  made. 

There  are  placed  in  the  telescopes  of  most  instruments  fitted  for  stadia 
work,  either  two  horizontal  wires  (usually  adjustable),  or  a glass  wuth  two 
etched  horizontal  lines  at  the  position  of  the  cross-wires  and  equidistant 
from  the  center  wire.  A self-reading  stadia  rod  is  further  provided,  gradu- 
ated according  to  the  units  of  measurements  used.  In  a horizontal  sight 

with  such  a telescope  and  rod, 
the  positions  of  the  stadia  wires 
are  projected  upon  the  rod,  and 
intercept  a distance  which,  in 
Fig.  1 (6),  is  represented  by  a. 

In  point  of  fact,  there  is 
formed,  at  the  position  of  the 
stadia  wires,  a small  conjugate 
image  of  the  rod  that  the  wires 
intersect  at  points  h and  c, 
which  are,  respectively,  the 
foci  of  the  points  B and  C on 
the  rod.  If,  for  the  sake  of 
simplicity,  the  object  glass  be 
considered  a simple  biconvex 
lens,  then,  by  a principle  of 
optics,  the  rays  from  any  point 
of  an  object  converge  to  a focus  at  such  a position  that  a straight  line,  called 
a secondary  axis,  connecting  the  point  with  its  image,  passes  through  the 
center  of  the  lens.  This  point  of  intersection  of  the  secondary  axes  is 
called  the  optical  center.  Hence,  it  follows  that  lines  such  as  c C and  h B, 
in  Fig.  l{b),  drawn  from  the  stadia  wires  through  the  center  of  the  object 
glass,  will  intersect  the  rod  at  points  corresponding  to  those  that  the  wires 
cut  on  the  image  of  the  rod.  From  this  follows  the  proportion: 

d _ a 
'p  ~ 1' 

d = ^ a,  (1) 

where  d = distance  of  rod  from  center  of  objective; 

p = distance  of  stadia  wires  from  center  of  objective; 
a = distance  intercepted  on  rod  by  stadia  .vires; 

I = distance  of  stadia  wires  apart. 


If  p remained  the  same  for  all  lengths  of  sight,  then  ^ could  be  made  a 

desirable  constant  and  d would  be  directly  proportional  to  a.  Unfortunately, 
however,  for  the  simplicity  of  such  measurements,  p (the  focal  length)  varies 
with  the  length  of  the  sight,  increasing  as  the  distance  diminishes  and  vice 
versa.  Thus,  the  proportionality  between  d and  a is  variable.  The  object, 
then,  is  to  determine  exactly  what  function  a is  of  d and  to  express  the  rela- 
tion in  some  convenient  formula. 

The  following  is  the  general  formula  for  biconvex  lenses: 

/ is  the  principal  focal  length  of  the  lens,  and  p and  p'  are  the  focal  distances 
of  image  and  object,  and  are,  approximately,  the  same  as  p and  d,  respectively, 
in  equation  (1): 

Therefore,  — + i i approximately, 

, ^ ''d  , 

and  _ = _ _ 1. 

^ ^ ^ 
d a 


From  (1), 


Whence, 


P 


I f 
»=  T « + /• 


(S) 


STADIA  MEASUREMENTS. 


83 


In  this  formula,  it  will  be  noticed  that  as  / and  I remain  constant  for 
sights  of  all  lengths,  the  factor  by  which  a is  to  be  multiplied  is  a constant, 
and  that  d is  thus  equal  to  a constant  times  the  length  of  a,  plus/.  This  for- 
mula would  seem,  then,  to  express  the  relation  desired,  and  it  is  generally 
considered  as  the  fundamental  one  for  stadia  measurements.  As  above 


stated,  however,  the  equation  — -f  -^  = i is  only  approximately  true,  and 
p a j 

the  conjunction  of  this  formula  with  (2)  being,  therefore,  not  rigidly  admissi- 
ble, equation  (3)  does  not  express  the  exact  relation.*  The  equation  express- 
ing the  true  relation,  though  differing  from  (3)  in  value,  agrees  with  it  in 

f 

form,  and  also  in  that  the  expression  corresponding  to  ~ is  a constant,  and 
that  the  amount  to  be  added  remains,  practically,  /.  The  constant  corre- 
sponding to  -y  may  be  called  lc\,  and  thus  the  distance  of  the  rod  from  the 


objective  of  the  telescope  is  seen  to  be  equal  to  a constant  times  the  reading 
on  the  rod,  plus  the  principal  focal  length  of  the  objective.  To  obtain  the 
exact  distance  to  the  center  of  the  instrument,  it  is  further  necessary  to  add 
the  distance  of  the  objective  from  that  center  to/;  which  sum  may  be  called  c. 
The  final  expression  for  the  distance,  with  a horizontal  sight,  is  then 
d = k a A c.  (4) 

The  necessity  of  adding  c is  somewhat  of  an  encumbrance.  In  the  stadia 
work  of  the  U.  S.  Government  surveys,  an  approximate  method  is  adopted  in 
which  the  total  distance  is  read  directly  from  the  rod.  For  this  method  the 
rod  is  arbitrarily  graduated,  so  that,  at  the  distance  of  an  average  sight,  the 
same  number  of  units  of  the  graduation  are  intercepted,  between  the  stadia 
wires  on  the  rod,  as  units  of  length  are  contained  in  the  distance.  For  any 
other  distance,  however,  this  proportionality  does  not  remain  the  same;  for, 
according  to  the  preceding  demonstration,  the  reading  on  the  rod  is  propor- 
tional to  its  distance,  not 
from  the  center  of  the  in- 
strument, but  from  a point 
at  a distance  “ c ” in  front 
of  that  center,  so  that, 
when  the  rod  is  moved 
from  the  position  where 
the  reading  expresses  the 
exact  distance,  to  a point 
say  half  that  distance  from 
the  instrument  center,  the 
readings  expresses  a dis- 
tance less  than  half;  and, 
at  a point  double  that  dis- 
tance from  instrument  cen- 
ter, the  distance  expressed 
by  the  reading  is  more 
than  twice  the  distance. 

The  error  for  all  distances 
less  than  the  average  is 
minus,  and  for  greater  dis- 
tances, plus.  The  method 
is,  however,  a close  approx- 
imation, and  excellent  re- 
sults are  obtained  by  its  use. 

Another  method  of  get- 
ting rid  of  the  necessity  of 
adding  the  constant  was 
devised  by  Mr.  Porro,  a 
Piedmontese,  who  constructed  an  instrument  in  which  there  was  such  a 
combination  of  lenses  in  the  objective  that  the  readings  on  the  rod,  for  all 
lengths  of  sight,  were  exactly  proportional  to  the  distances.  I The  instrument 


* This  is  demonstrated  later  on. 

t ft  is  dependent  on  I,  and  can  therefore  be  made  a convenient  value  in  any  instrument  fitted 
with  adjustable  stadia  wires.  It  is  generally  made  equal  to  100,  so  that  a reading  on  the  rod  of  1' 
corresponds  to  a distance  of  100'  -f-  /. 

t A notice  of  this  instrument  will  be  found  in  an  article  by  Mr.  Benjamin  Smith  Lyman, 
entitled  “ Telescopic  Measurements  in  Surveying,”  in  “Journal  Franklin  Institute,”  May  and 
June,  1868,  and  a fuller  description  is  contained  in  “ Annales  des  Mines,”  Vol.  XVI,  fourth  series. 


84 


SURVEYim. 


was,  however,  bulky  and  difficult  to  construct,  and  never  came  into 
extensive  use. 

For  stadia  measurements  with  inclined  sights,  there  are  two  modes  of 
procedure.  One  is  to  hold  the  rod  at  right  angles  to  the  line  of  sight;  the 
other,  to  hold  it  vertical.  With  the  first  method,  ft  will  be  seen,  by  reference 
.to  Fig.  2(a),  that  the  distance  read  is  not  to  the  foot  of  the  rod  E,  but  to  a point 
/,  vertically  under  the  point  F,  cut  by  the  center  wire.  A correction  has, 
therefore,  to  be  made  for  this.  An  objection  to  this  method  is  the  difficulty 
of  holding  the  rod  at  the  same  time  in  a vertical  plane  and  inclined  at  a 
definite  angle.  Further,  as  the  rod  changes  its  inclination  with  each  new 
position  of  the  transit,  the  vertical  angles  of  backsight  and  foresight  are  not 
measured  from  the  same  point. 

The  method  usually  adopted  is  the  second  one,  where  the  rod  is  always 
held  vertical.  Here,  owing  to  the  oblique  view  of  the  rod,  it  is  evident  that 
the  space  intercepted  by  the  wires  on  the  rod  varies,  not  only  with  the  dis- 
tance, but  also  with  the  angle  of  inclination  of  the  sight.  Hence,  in  order 
to  obtain  the  true  distance  from  station  to  station,  and  also  its  vertical  and 
horizontal  components,  a correction  must  be  made  for  this  oblique  view  of 
the  rod.  In  Fig.  2 (&), 

A B = a = reading  on  rod; 

me  = d ^ inclined  distance  = c + GF  = c + k,  CH\ 

MP  = D = horizontal  distance  = d cos  w; 

FP  = Q = vertical  distance  = D tan  n\ 

n = vertical  angle; 

AG  B = 2m. 

It  is  first  required  to  express  d in  terms  of  a,  n,  and  m. 

From  the  proportionality  existing  between  the  sides  of  a triangle  and  the 
sines  of  the  opposite  angles, 

AF  __  

GF  ~ sin  [90°  + (w  — m)] ’ 


or, 

and 

or, 

or 


AF  = GFsinm 


cos  {n  — m)* 
BF  _ sin  m 

GF  ~ sin  [90°  — (7t -f  m)]  ’ 

1 


B F = G F sin  m 
A F B F = G F sin  m 
AF  F BF  = a,  and  GF  = 


cos  {n  -{-my 

r 1 + ] 

Lcos(w  — m)  cos(7i-[-m) 

CR ^ CH  cos  m 

2 tan  m ~~  2 sin  m' 
By  substituting  and  reducing  to  a common  denominator, 


CR  cos  m [cos  (ti  + m)  + cos  (n  — m)] 
2 cos  (?^ -J-m)  cos(n  — m) 


Reducing  this  according  to  trigonometrical  formulas. 


^ cos2  n cos2  m — sin^  n sin2  m 

CR  = a T , 

cos  n cos2  m 


as  d = M F = c -{■  k.  CR. 

, , - cos2  n cos2  m — sin^  n sin-  m 

d = c -{■  ka 5 . 

cos  n cos2  m 

The  horizontal  distance,  D — d cos  n. 

J)  = c cos  n -{-  k a cos^ n~ka  sin^ n tan^ m. 

The  third  member  of  this  equation  may  safely  be  neglected,  as  it  is 
very  small  even  for  long  distances  and  large  angles  of  elevation  (for 
1,500'  n = 45°  and  k = 100,  it  is  but  0.07').  Therefore,  the  final  formula  for 
distances  with  a stadia  rod  held  vertically,  and  with  wires  equidistant  from 
the  center  wire,  is  the  following: 

D = c cos  n ak  cos-  n.  (5) 


STADIA  MEASUREMENTS. 


85 


The  vertical  distance  Q is  easily  obtained  from  the  relation:  Q — i)tanw. 

Q = c sinn -{- ak  cosn  Sinn; 

• . 7 sin27i 

or,  Q = c sin  w 4-  a A:  — - — . (6)* 

With  the  aid  of  formulas  (5)  and  (6),  the  horizontal  and  vertical  distances 
can  be  immediately  calculated  when  the  reading  from  a vertical  rod  and 
the  angle  of  elevation  of  any  sight  are  given.  From  these  formulas,  the 
stadia  reduction  tables  following  have  been  calculated.  The  values  of  a A:  cos-  n 

and  ak  were  separately  calculated  for  each  2 minutes  up  to  30° 

of  elevation;  but,  as  the  value  of  c sin  n and  c cos  n has  quite  an  inappre- 
ciable variation  for  1°,  it  was  thought  sufficient  to  determine  these  values 
only  for  each  degree.  As  c varies  with  different  instruments,  these  last  two 
expressions  were  calculated  for  three  different  values  of  c,  thus  furnishing 
a ratio  from  which  values  of  c sin  n and  c cos  n can  be  easily  determined 
for  an  instrument  having  any  constant  (c). 

Similar  tables  have  been  computed  by  J.  A.  Ockerson  and  Jared  Teeple, 
of  the  United  States  Lake  Survey.  Their  use  is,  however,  limited,  from  the 
fact  that  the  meter  is  the  unit  of  horizontal  measurement,  while  the  eleva- 
tions are  in  feet.  The  bulk  of  the  tables  furnishes  differences  of  level  for 
stadia  readings  up  to  400  meters,  but  only  up  to  10°  of  elevation.  Supple- 
mentary tables  give  the  elevations  up  to  30°  for  a distance  of  1 meter.  For 
obtaining  horizontal  distances,  reference  has  to  be  made  to  another  table^ 
which  is  somewhat  an  objectionable  feature,  and  a multiplication  and  a 
subtraction  has  to  be  made  in  order  to  obtain  the  result.  Last,  but  not  least, 
these  tables  are  apparently  only  accurate  when  used  with  an  instrument 
whose  constant  is  .43  meter. 

The  many  advantages  of  stadia  measurements  in  surveying  need  not  be 
dwelt  on  here,  both  because  attention  has  been  repeatedly  called  to  them, 
and  because  they  are  self-evident 'to  every  engineer.  Neither  will  it  be 
within  the  compass  of  this  article  to  describe  the  various  forms  of  rods  and 
instruments,  or  the  conventionalities  of  stadia  work. 

It  is  seen  that,  in  the  deduced  formula,  the  factor  by  which  the  reading 
on  the  rod  is  multiplied  is  a constant  for  each  instrument.  The  question 
now  arises.  Does  this  remain  the  case  with  a compound  objective? 

In  view  of  the  difficulty  of  demonstrating  this  mathematically,  it  was 
decided  to  make  a practical  test  of  this  point  with  a carefully  adjusted 
instrument.  The  readings  were  taken  from  two  targets  set  so  that  the  sight 
should  be  horizontal,  thus  preventing  any  personal  error  or  prejudice  from 
affecting  the  reading.  A distance  of  500  ft.  was  first  measured  off  on  a level 
stretch  of  ground,  and  each  50-ft.  point  accurately  located.  From  one  end 
of  this  line,  three  successive  series  of  stadia  readings  were  then  taken  from 
the  first  50-ft.  and  each  succeeding  100-ft.  mark.  The  following  table  con- 
tains the  results: 


Distances. 

Feet. 

Spaces  Intercepted  on  the  Rod. 

1st  Series. 
Feet. 

2d  Series. 
Feet. 

3d  Series. 
Feet. 

Mean. 

Feet. 

50 

.485 

.4860 

.4855 

.4855 

100 

.985 

.9870 

.9830 

.9850 

200 

1.985 

1.9860 

1.9840 

1.9850 

300 

2.989 

2.9875 

2.9870 

2.9878 

400 

3.983 

3.9800 

3.9890 

3.9840 

500 

4.985 

4.9850 

4.9900 

4.9867 

Multiplying  the  mean  of  these  readings  by  100,  and  subtracting  the  result 
from  the  corresponding  distance,  we  obtain  the  following  table: 


*The  above  demonstration  is  substantially  that  given  by  Mr.  George  J.  Specbt  in  an  article 
on  Topographical  Surveying  in  “Van  Nostrand’s  Engineering  Magazine,”  February,  1880, 
though  enlarged  and  corrected. 


86 


SUEVEVING. 


Distances. 

Feet. 

Mean  of 
Stadia  Readings 
Times  100. 

Feet. 

Differences. 

Feet. 

Variations 
From  Mean. 
Feet. 

50 

48.55 

1.45 

+ .02 

100 

98.50 

1.50 

+ .07 

200 

198.50 

1.50 

+ .07 

300 

298.78 

1.22 

— .21 

400 

398.40 

1.60 

+ .17 

600 

498.67 

1.33 

— .10 

Sum  of  differences  = 8.60;  mean  of  difference  = 1.43. 

The  variations  between  the  numbers  of  the  column  of  differences  are 
slight,  the  maximum  from  a mean  value  of  1.43  ft.  being  only  .21  ft.  A 
study  of  the  tables  will  show  that  these  variations  have  no  apparent  rela- 
tion to  the  length  of  the  sight,  and  as,  in  the  maximum  case,  .the  variation 
corresponds  to  a reading  on  the  rod  of  onlj'  .0021  ft.  (an  amount  much 
within  the  limits  of  accuracy  of  any  ordinary"  sight),  we  are  perfectly  justified 
in  concluding  that  these  variations  are  accidental,  and  that  the  “difference” 
is  a constant  value. 

We  thus  see  that  with  a telescope  having  a compound,  plano-convex 
objective,  the  horizontal  distance  is  equal  to  a constant  times  the  reading  on 
the  rod,  plus  a constant,  and  may,  as  in  other  cases,  be  expressed  by  the 
equation  d — a A:  + c. 

A few  precautions,  necessary  for  accurate  work,  should,  however,  be 
emphasized.  First,  as  regards  the  special  adjustments:  Care  should  be 
taken  that  in  setting  the  stadia  wires*  allowance  be  made  for  the  instru- 
ment constant,  and  that  the  wires  are  so  set  that  the  reading,  at  any  dis- 
tance, is  less  than  the  true  distance  by  the  amount  of  this  constant.! 

For  accurate  stadia  work,  it  is  better  to  take  both  distances  and  elevations 
only  at  alternate  stations,  and  then  to  take  them  from  both  backsight  and 
foresight  in  such  a manner  that  the  vertical  angle  is  always  read  from  the 
same  position  on  each  rod,  which  should  be  the  average  height  of  the 
telescope  at  the  different  stations. 

Cases  will,  of  course,  occur  where  this  method  will  be  impracticable,  and 
then  the  mode  of  procedure  must  be  left  to  the  judgment  of  the  surveyor.  If 
it  be  desired  to  have  the  absolute  elevation  of  the  ground  under  the  instru- 
ment, the  height  of  telescope  at  each  station  will  have  to  be  measured  by  the 
rod,  and  the  difference  between  this  measurement  and  the  average  height 
used  in  sighting  to  the  rod  either  added  or  subtracted,  as  the  case  may  be. 
This  difference  will  ordinarily  be  so  small  that  in  a great  deal  of  stadia 
work  no  reduction  will  be  necessary.  In  sighting  to  the  rod  for  the  angle  of 
depression  or  elevation,  the  center  horizontal  wire  must  always  be  used.  By 
this  means  an  exactly  continuous  line  is  measured.  For  theoretical  exact- 
ness it  is  necessary  that  the  stadia  wires  should  be  equidistant  from  the 
horizontal  center  wire,  for,  if  this  is  not  the  case,  the  distance  read  is  for  an 
angle  of  elevation  differing  from  thh  true  one  by  an  amount  proportional  to 
the  displacement  of  the  wires. 

With  reasonable  care  a high  degree  of  accuracy  can  be  attained  in  stadia 
measurements.  The  common  errors  of  stadia  reading  are  unlike  the  common 
errors  of  chaining,  the  gross  ones  (such  as  making  a difference  of  a whole 
hundred  feet)  being,  in  general,  the  only  important  ones,  and  these  are 
readily  checked  by  double  readings.  To  facilitate  the  subtraction  of  the 
reading  of  one  cross-hair  from  that  of  another,  one  should  be  put  upon  an 


*This  applies  to  an  instrument  with  movable  stadia  wires,  and  not  to  one  with  etched  lines  on 
glass.  In  the  latter  case,  the  graduation  of  the  rod  is  the  adjustable  portion.  It  has  been 
claimed  as  an  advantage  for  etched  lines  on  glass,  that  they  are  not  affected  by  variations  of 
temperature,  while  the  distance  between  stadia  wires  is.  A series  of  tests  made  with  one  of 
Heller  k Brightly's  transits,  to  determine  this  point,  showed  no  appreciable  alteration  in  the 
space  between  the  wires,  as  measured  on  a rod  500  ft.  distant,  with  a range  of  temperature 
between  that  produced  in  the  instrument  by  the  sun  of  a hot  summer’s  day  and  that  produced  by 
enveloping  the  telescope  in  a bag  of  ice. 

tAs  the  difference  is  evidently  proportional  to  the  length  of  sight,  with  a 1,000'  sight  it  would 
amount  to  22.5',  etc. 


STADIA  MEASUREMENTS. 


87 


even  footmark,  and  in  the  check,  reading  the  other  one.  This  is  assuming 
the  measurements  to  be  made  by  the  ordinary  method,  and  not  by  the 
approximate  one  of  the  United  States  Engineers. 


HORIZONTAL  DISTANCES  AND  DIFFERENCES  OF  LEVEL  FOR 
STADIA  MEASUREMENTS. 


The  formulas  used  in  the  computation  of  the  following  tables  were  those 
given  by  Mr.  George  J.  Specht  in  an  article  on  Topographical  Surveying, 
published  in  “ Van  Nostrand’s  Engineering  Magazine”  for  February,  *1880. 
These  formulas  furnish  expressions  for  horizontal  distances  and  differences 
of  level  for  stadia  measurements,  with  the  conditions  that  the  stadia  rod 
he  held  vertical,  and  the  stadia  wires  be  equidistant  from  the  center  wire. 
They  are  as  follows: 

D = c cos  n ak  cos^  n; 


Q 


D tan  n = c sin  n + 


ak  sin2w^ 
2 ’ 


1)  = horizontal  distance; 

Q = difference  of  level; 

c = distance  from  center  of  instrument  to  center  of  object  glass,  plus  focal 
length  of  object  glass; 

k = focal  length  of  object  glass  divided  by  distance  of  stadia  wires  apart; 
a = reading  on  stadia  rod; 
n = vertical  angle; 

ak  = reading  on  rod  multiplied  by  fc, which  is  a constant  for  each  instrument 
(generally  100). 

In  the  tables,  the  vertical  columns  consist  of  two  series  of  numbers  for 
each  degree,  which  series  represent,  respectively,  the  different  values  of 

ak  cos2  n and  sm2yi  qyqyy  2 minutes,  when  ak  = 100.  To  obtain  the 

horizontal  distance  or  the  difference  of  level  in  any  case,  the  corresponding 
value  of  c cos  n or  c sin  n must  further  be  added;  and  the  mean  of  each  of 
these  expressions,  for  each  degree,  with  three  of  the  most  common  values  of 
c,  is  given  under  each  column. 

As  an  example,  let  it  be  required  to  find  the  horizontal  distance  and  the 
difference  of  level  when  n = + 6°  18',  ak  = 570,  and  the  instrument 
constant  c = .75.  In  the  column  headed  6°,  opposite  18'  in  the  series  for 
“ Hor.  Dist.,”  we  find  98.80  as  the  expression  for  ak  cos^n  when  ak  = 100; 
therefore,  when  ak  = 570, 

a k cos2  n = 98.80  X 5.70  = 563.16. 

To  this  must  be  added  c cos  ti,  which,  in  this  case,  is  found  in  the  subjoined 
column  to  be  .75. 

In  a.  similar  manner,  the  required  difference  of  level  is 
(+10.91  X 5.70)  + .08  = + 62.27. 

One  multiplication  and  one  addition  must  be  made  in  each  case. 

It  is  to  be  noticed  that,  with  the  smaller  angles,  cos  n in  the  expressions 
c cos  n and  c sin  n may  be  entirely  neglected  without  appreciable  error. 

For  values  of  c,  which  differ  from  those  given,  an  approximate  correction, 
proportional  to  the  amount  of  difference,  may  very  easily  be  made  in  these 
two  expressions. 


88 


STADIA  MEASUREMENTS. 


o 

o 

Diff. 

Elev. 

l>l>I>t^t>t^I>I>t^I>l>l>I>t^l>I>-l^OOQOOOCOCOGOQOODQOOOOOOOCOOO 

i-IrHTHrHr-lTHrHT-lT-lT-H^T-lr-l^rHrHrHT-lTHrHrHrHrHrHrHT-lT-lT-li-HrHTH 

'-i 

Hor. 

Dist. 

96.98 

96.96 

96.94 

96.92 

96.90 

96.88 

96.86 

96.84 

96.82 

96.80 

96.78 

96.76 

96.74 

96.72 

96.70 

96.68 

96.66 

96.64 

96.62 

96.60 

96.57 

96.55 

96.53 

96.51 

96.49 

96.47 

96.45 

96.42 

96.40 

96.38 

96.36 

2 

s. 

Difr. 

Elev. 

15.45 

15.51 

15.56 

15.62 

15.67 

15.73 

15.78 

15.84 

15.89 

15.95 

16.00 

16.06 

16.11 

16.17 

16.22 

16.28 

16.33 

16.39 

16.44 

16.50 

16.55 

16.61 

16.66 

16.72 

16.77 

16.83 

16.88 

16.94 

16.99 

17.05 

17.10 

CO 

'-i 

Hor. 

Dist. 

S 

§0 

.*s  i 

13.78 

gSg8SS?5SS8!§SSSSE2gS8S5 

383^ 

i 

lO.ZO 

15.34 

15.40 

15.45 

S 

Hor. 

Dist. 

S 

o 

Diff. 

Elev. 

12.10 

T2.15 

iilli 

XZi.UU 

12.60 

12.66 

12.72 

12.77 

12.83 

12.88 

12.94 

13.00 

13.05 

13.11 

13.17 

13.22 

13.28 

13.33 

13.39 

13.45 

Id.OJL 

13.‘73 

13.78 

S 

S 

Hor. 

Dist. 

iiSiiSliiSiiiiiiliiiliii 

^SS8 

gggg 

TtH 

I-'; 

S 

Diff. 

Elev. 

10.40 

10.45 

10.51 

10.57 

10.62 

10.68 

10.74 

10.79 

10.85 

10.91 

10.96 

11.02 

11.08 

11.13 

11.19 

11.25 

11.30 

11.36 

11.42 

11.47 

11.53 

11.59 

iX.OX 

11.87 

11.93 

11.98 

12.04 

12.10 

S 

Hor. 

Dist. 

98.91 

mm 

98.88 

98.87 

98.86 

98.85 

98.83 

98.82 

98.61 

98.60 

98.58 

98.57 

98.56 

98.54 

98.53 

98.51 

s 

0 

Diff. 

Elev. 

8.68 

8.74 

8.80 

8.85 

8.91 

8.97 

9.03 

9.08 

9.14 

9.20 

9.25 

9.31 

9.37 

9.43 

9.48 

9.54 

9.60 

9.65 

9.71 

9.77 

9.83 

9.88 

9.94 

10.00 

10.05 

10.11 

10.17 

10.22 

10.28 

10.34 

10.40 

o 

lO 

Hor. 

Dist. 

2 

' o 

Diff. 

Elev. 

«Di>t>i>t^i^i^i>i>i>i>i>i>-'t-‘i>i>x>i>-‘i>oidQ6odo6cx5c6odo6odo6o6o6 

s 

S 

O 

j 

1 

Hor. 

Dist. 

gggggsggsggsgsggsgsggggsggsgsgs 

8 

a 

o 

CO 

Diff. 

Elev. 

u:j  lO  lO  lO  »o  lO  lO  lO  lO  id  id  id  lO  lO  o CO  «:>  'sd  cd  cd  CO  cd  cd  cd  o CO  IU5  CO  ;d  ;d 

s 

o 

Hor. 

Dist. 

99.73 

99.72 

99.71 

99.71 

99.70 

99.69 

99.69 

99.68 

99.68 

99.67 

99.66 

99.66 

99.65 

99.64 

99.63 

99.63 

99.62 

99.62 

99.61 

99.60 

99.59 

99.59 

99.58 

99.57 

99.56 

99.56 

99.55 

99.54 

99.53 

99.52 

99.51 

8 

r-; 

2 

Diff. 

Elev. 

§ 

S 

S 

Hor. 

Dist. 

§8SSS5SgSSSSS8S8S§3SS8gSSSSf:E:gges:SE2f; 

gggggggggggsggggggsggsssgsggggg 

8 

2 

Diff. 

Elev. 

2S222ii33§i3liii§S5issii5iiasis 

§ 

§ 

Hor. 

Dist. 

ggggggggggggggggggg-gggggggggggg 

8 

rH- 

2 

o 

o 

ta  > 

S w 

O OT 

Wq 

O 

S 

S 

88SSSg888SS8SgggggggggggggggSSS 

i§i§ii§ii^§i*8g8gSgg8gg88ggggg 

I 

2 

V) 

c = 1.00  1 

c = 1.25  1 

STADIA  MEASUREMENTS. 


89 


o 

Diflf. 

Elev. 

32.14 

32.18 

32.23 

32.27 

32.32 

32.36 

32.41 

32.45 

32.49 

32.54 

32.58 

32.63 

32.67 

32.72 

32.76 

32.80 

32.85 

32.89 

32.93 

32.98 

33.02 

33.07 

33.11 

33.15 

ill 

O CO  CO  CO 

O CO  CO  CO 

lO 

CO 

Hor. 

Dist. 

88.30 

88.26 

88.23 

»».ll 

88.08 

88.04 

88  00 

o 

19°  1 

Diff. 

Elev. 

30.78 

30.83 

30.87 

30.92 

30.97 

31.01 

31.06 

OJ-.J-U 

•31.15 

iiii 

gss 

gsg 

g885 

i 31.65 

31.69 

31.74 

31.78 

31.83 

31.87 

31.92 

31.96 

32.01 

32.05 

32.09 

32.14 

lO 

CO 

CO 

Hor, 

Dist. 

89.40 

89.36 

89.33 

89.29 

89.26 

89.22 

89.18 

89.15 

89.11 

89.08 

89.04 

89.00 

88.96 

88.93 

ill 

88.71 

88.67 

88.64 

88.60 

88.56 

88.53 

88.49 

88.45 

88.41 

88.38 

88.34 

88.30 

H 

18°  1 

Diflf. 

Elev. 

29.39 

29.44 

29.48 

29.53 

29.58 

29.62 

29.67 

29.72 

29.76 

29.8  L 
29.86 
29.90 

29.95 

30.00 

30.04 

30.09 

30.14 

30.19 

30.23 

30.28 

30.32 

30.37 

30.41 

30.46 

au.oi 

30.55 

30.60 

30.65 

30.69 

30.74 

30.78 

CO 

Hor. 

Dist. 

iO(MQOu: 

8888 

vyj.oo 

90.31 

90.28 

90.24 

90.21 

90.18 

90.14 

90.11 

90.07 

90.04 

90.00 

89.97 

89.93 

89.90 

89.86 

89.83 

89.79 

89.76 

89.72 

89.69 

89.65 

89.61 

89.58 

89.54 

89.51 

89.47 

89.44 

89.40 

rH 

lO 

05 

1 1.19; 

o 

Diflf. 

Elev. 

27.96 

28.01 

28.06 

z,o.ou 

28.34 

28.39 

28.44 

28.49 

28.54 

28.58 

28.63 

28.68 

28.73 

28.77 

28.82 

28.87' 

28.92 

28.96 

29.01 

29.06 

29.11 

29.15 

29.20 

29.25 

29.30 

29.34 

29.39 

CO 

o 

CO 

S' 

Hor. 

Dist. 

91.45 
91.42 
91.39 
91.35 
91.32 
91.29 
91.26 
91.22 
91.19 
91.16 
91.12 
91.09 
91.06 
91.02 
90.99 
90  96 

Sggggggggggg 

90.52 

90.48 

90.45 

lO 

leri  J 

16°  1 

Diflf. 

Elev. 

sags 

26.69 

26.74 

26.79 

26.84 

26.89 

26.94 

26.99 

j 

Hor. 

Dist. 

92.40 

92.37 

92.34 

92.31 

92.28 

92.25 

92.22 

92.15 

92.12 

92.09 

92.06 

92.03 

92.00 

91.97 

91.93 

91.90 

91.87 

91.84 

91.81 

91.77 

91.74 

91.71 

91.68 

91.65 

91.61 

91.58 

91.55 

91.52 

91.48 

91.45 

r 

1 1 

Diflf, 

Elev. 

25.00 

25.05 

25.10 

25.15 

25,20 

25.30 

25.35 

25.40 

25.45 

25.50 

25.55 

25.60 

25.65 

25.70 

25.75 

ggggggsss 

sag? 

sag? 

Z,U.O-J 

26.40 

26.45 

26.50 

Hor. 

Dist. 

93.30 

93.27 

93.24 

92.80 

92.77 

92.74 

92.71 

92.68 

92.65 

92.62 

92.59 

92.56 

92.53 

92.49 

92.46 

92.43 

92.40 

(M 

CO 

05 

S 

ol-I 

Diflf. 

Elev. 

23.47 

23.52 

23.58 

23.63 

23.68 

23.73 

23.78 

23.83 

23,88 

23.93 

23.99 

24.04 

24.09 

24.14 

24.19 

24.24 

24.29 

24.34 

24.39 

24.44 

24.49 

24.55 

24.60 

24.65 

24.70 

24.75 

24.80 

24.85 

24.90 

24.95 

25.00 

05 

s 

Hor. 

Dist. 

94.15 

94.12 

94.09 

94.07 

94.04 

94.01 

93.98 

93.90 

93.87 

93.84 

93.81 

93.79 

93.76 

93.73 

93.70 

93.67 

93.65 

93.62 

93.59 

93.56 

93.53 

93.50 

93.45 

93.42 

93.39 

93.36 

93.33 

93.30 

CO 

05 

1 1.211 

13° 

Diflf. 

Elev. 

(Nr-(NOOCO( 

OSClOOr-li 

sasiss! 

S83? 

gj  g|  si  gj  gj  S gj  ?l  85  ?5  S 

sags 

^0.0^ 

23.37 

23.42 

23.47 

I> 

1-H 

Hor. 

Dist. 

94.94 

94.91 

94.89 

94.86 

94.84 

94.81 

94.79 

94.76 

94.73 

94.71 

94.68 

94.66 

94.63 

94.60 

94.58 

94.55 

94.52 

94.50 

94.47 

94.44 

94.42 

94.39 

94.36 

94.34 

94.31 

94.28 

94.26 

94.23 

94.20 

94.17 

94.15 

CO 

I> 

05 

2 

12°  1 

Diflf. 

Elev. 

20.34 

20.39 

20.44 

20.55 

20.60 

20.66 

20.71 

20.76 

nSS 

Zi.DU 

21.66 

21.71 

21.76 

21.81 

21.87 

21.92 

CO 

05 

<N 

s 

o ,2-. 

W(? 

95.68 

95.65 

95.63 

95.61 

95.58 

8SI: 

gSS 

95.34 

95.32 

95.29 

95.27 

95.24 

95.22 

95.19 

95.17 

95.14 

95.12 

95.09 

95.07 

95.04 

95.02 

94.99 

94.97 

94.94 

CO 

1> 

2 

o 

rH 

Diflf. 

Elev. 

18.73 

18.78 

18.84 

±o.ov 

18.95 

19.00 

19.05 

19.11 

19.16 

19.21 

19.27 

19.32 

19.38 

19.43 

19.48 

19.54 

19.59 

19.64 

19.70 

19.75 

19.80 

19.86 

19.91 

19.96 

20.02 

20.07 

20.12 

20.23 

1 20.28 

20.34 

lO 

s 

Hor. 

Dist. 

96.36 

96.34 

96.32 

96.29 

96.27 

96.25 

96.23 

96.21 

96.18 

96.16 

96.14 

96.12 

96.09 

96.07 

96.05 

96.03 

96.00 

95.98 

95.96 

95.93 

95.91 

95.89 

95.86 

95.84 

95.79 

95.77 

95.75 

95.72 

95.70 

95.68 

CO 

11 

V 

= 1.00  1 

a 

II 

V 

90 


STADIA  MEASUREMENTS. 


% 

CO 

Diff. 

Pllev. 

43.30 

43.33 

43.36 

43.39 

43.42 

43.45 

43.47 

43.50 

43.53 

43.56 

43.59 

43.62 

43.65 

43.67 

43.70 

43.73 

43.76 

43.79 

43.82 

43.84 

43.87 

43.90 

43.93 

43.95 

43.98 

44.01 

44.04 

44.07 

44.09 

44.12 

44.15 

s 

Hor. 

Dist. 

2 

0 

01 
C<J 

Diflf. 

Elev. 

42.40 

42.43 

42.46 

42.49 

42.53 

42.56 

42.59 

42.62 

42.65 

42.68 

42.71 

42.74 

42.77 

42.80 

42.83 

42.86 

42.89 

? 

g 

Hor. 

Dist. 

76.50 

76.45 

76.40 

76.35 

76.30 

76.25 

76.20 

76.15 

76.10 

76.05 

76.00 

75.95 

75.90 

75.85 

75.80 

75.75 

75.70 

75.65 

75.60 

75.55 

75.50 

75.45 

75.40 

75.35 

75.30 

75.25 

75.20 

75.15 

75.10 

75.05 

75.00 

2 

1 

Diflf. 

Elev. 

41.45 

41.48 

41.52 

41.55 

41.61 

41.65 

41.68 

41.71 

41.74 

41.77 

41.81 

41.84 

41.87 

41.90 

41.93 

41.97 

42.00 

42.03 

42  06 

42.09 

42.12 

42.15 

42.19 

42.22 

42.25 

42.28 

42.31 

42.34 

42.37 

42.40 

s 

Hor. 

Dist. 

§ 

o 

(M 

Diflf. 

Elev. 

40.45 

40.49 

40.52 

40.55 

40.59 

40.62 

40.66 

40.69 

40.72 

40.76 

40.79 

40.82 

40.86 

S 

S 

Hor. 

Dist. 

79.39 

79.34 

79.30 

79.25 

79.20 

79.15 
79.11 

79.06 

79.01 

78.96 
78.92 
78.87 
78.82 
78.77 
78.73 
78.68 
78.63 
78.58 
78.54 
78.49 
78.44 

78.39 

78.34 

78.30 

78.25 

78.20 

78.15 

78.10 

78.06 

78.01 

77.96 

S 

5 

& 

(N 

Diflf. 

Elev. 

??l 

S 

Hor. 

Dist. 

80.78 

80.74 

80.69 

80.65 

8n  AO 

’i 

S 

% 

Diflf. 

Elev. 

38.30 

38.34 

38.38 

38.41 

38.45 

38.49 

38.53 

38.56 

38.60 

38.64 

38.67 

38.71 

38.75 

38.78 

38.82 

uo.ou 

38.89 

38.93 

38.97 

39.00 

39.04 

39.08 

39.11 

39.15 

39.18 

39.22 

39.26 

39.29 

39.33 

39.36 

39.40 

^1 

s 

Hor. 

Dist. 

82.14 
82.09 
82.05 
82.01 
81  QA 

81.92 

81.87 

81.83 

533S53  5SS5SSS53S5Si 

81.24 

81.19 

81.15 

81.10 

81.06 

81.01 

80.97 

80.92 

80.87 

80.83 

80.78 

$ 

8 

2 

% 

Diflf. 

Elev. 

« 

g: 

Hor. 

Dist. 

83.46 
83.41 
83.37 
83.33 
88  08 

liiiiiiiliiliiiiiliiiii 

S 

2 

1 

Diflf. 

Elev. 

35.97 

36.01 

36.05 

36.09 

36.13 

36.17 

36.21 

36.25 

36.29 

36.33 

36.37 

36.41 

36.45 

36.49 

36.53 

36.57 

36.61 

36.65 

36.69 

36.73 

36.77 

36.80 

36.84 

36.88 

36.92 

36.96 

37.00 

37.04 

37.08 

37.12 

37.16 

s 

Hor. 

Dist. 

84.73 

84.69 

84.65 

84.61 

84.57 

84.52 

84.48 

84.44 

84.40 

84.35 

84.31 

84.27 

84.23 

84.18 

84.14 

84.10 

84.06 

84.01 

83.97 

83.93 

83.89 

83.84 

83.80 

83.76 

83.72 

83.67 

83.63 

83.59 

83.54 

83.50 

83.46 

$ 

g 

! 

(M 

Diflf. 

Elev. 

1 34.73 

34.77 

34.82 

34.86 

34.90 

34.94 

34.98 

.35.02 

S;: 

SS?5l 

'■SSffil 

35.56 

35.60 

35.64 

35.68 

35.72 

35.76 

35.80 

35.85 

a5.89 

35.93 

35.97 

?! 

Hor. 

Dist. 

85.97 

85.93 

85.89 

III 

85.76 

85.72 

85.68 

85.64 

85.60 

85.56 

85.52 

85.48 

85.44 

85.40 

s 

g 

O 

<N 

Qg 

o .2 
Kq 

33.67 

33.72 

33.76 

33.80 

33.84 

33.89 

33.93 

33.97 

34.01 

34.06 

34.10 

34.14 

34.18 

34.23 

34.27 

34.31 

34.35 

34.40 

34.44 

34.48 

34.52 

34.57 

34.61 

34.65 

34.69 

34.73 

S 

1 

§ 

to 

n 

i 

1 

87.16 

87.12 

87.08 

87.04 

87.00 

86.96 

86.92 

86.88 

86.84 

86.80 

86.77 

86.73 

86.69 

86.65 

86.61 

86.57 

86.53 

eo.4y 

86.45 

86.41 

86.37 

86.33 

86.29 

86.25 

86.21 

86.17 

SSSoS 

g 

n 

ELEMENTS  OF  MECHANICS. 


91 


ELEMENTS  OF  MECHANICS. 

Only  the  elements  of  machines  are  here  treated,  as  all  machinery,  how- 
ever complicated,  is  merely  a combination  of  the  six  elementary  forms,  viz.: 
the  lever,  the  wheel  and  axle,  the  pulley,  the  inclined  plane,  the  wedge,  and 
the  screw;  and  these  six  can  be  still  further  reduced  to  the  lever  and  the 
inclined  plane.  They  are  termed  mechanical  powers,  but  they  do  not 
produce  force;  they  are  only  methods  of  applying  and  directing  it. 

The  law  of  all  mechanics  is: 

The  power  multiplied  by  the  distance  through  which  it  moves  is  equal  to  the 
weight  multiplied  by  the  distance  through  which  it  moves. 

Thus,  20  lb.  of  power  moving  through  5 ft.  = 100  lb.  of  weight  moving 
through  1 ft.  In  the  following  discussion  friction  is  not  considered,  the 
idea  being  to  give  an  elementary  knowledge  of  the  principles  of  the 
elements  of  mechanics. 

Levers. — There  are  three  classes  of  levers.  They  are:  (1)  power  at  one 
end,  weight  at  the  other,  and  fulcrum  between;  (2)  power  at  one  end, 
fulcrum  at  the  other,  and  weight  between;  (3)  weight  at  one  end,  fulcrum 
at  the  other,  and  power  between. 

The  handle  of  a blacksmith’s  bellows  is  a lever  of  the  first  class.  The 
hand  is  the  power  and  the  bellows  the  weight,  with  the  pivot  between 
as  the  fulcrum.  A crowbar  as  used  for  prying  down  top  rock  is  a lever  of 
the  second  class.  The  hand  is  the  power,  the  rock  to  be  barred  down 
the  weight,  and  the  point  in  the  roof  against  which  the  bar  presses 
is  the  fulcrum.  The  treadle  of  a grindstone  is  a lever  of  the  third  class. 
The  foot  is  the  power,  the  hinge  at  the  back  of  the  foot  is  the  fulcrum, 
and  the  moving  of  the  machinery  is  the  weight. 

A lever  is  in  equilibrium  when  the  arms  balance  each  other.  The  dis- 
tances through  Which  the  power  and  the  weight  move  depend  on  the 
comparative  length  of  the  arms.  Let  L represent  power’s  distance  from 
the  fulcrum  ( C),  I the  weight’s  distance,  and  a the  distance  between  power 
and  weight;  then,  if  L is  twice  I,  the  power  will  move  twice  as  far  as  the 
weight.  Substituting  these  terms  in  the  law  of  mechanics,  we  have 


P \ W \ :i  \L.  PL  = Wl. 
P = Fi  w ^ PL 
L I 

I _ T _ 

“ w+p’  ~ 1lTp‘ 


P : W ::  I : L.  PL  = Wl. 
^ Wa  , Pa 


W—P' 


W-P' 


' P \ W ::l  : 


T _ 

^ “ P-W' 


L. 


PL 
W = 

I = 


= Wl. 
PL 
I * 

Pa 

P-W' 


In  first-  and  second-class  levers,  as  ordinarily  used,  we  gain  power  and 
lose  time;  in  the  third  class,  we  lose  power  and  gain  time. 

Example. — Having  a weight  of  2,000  lb.  to  lift  with  a lever,  the  short  end 
of  which  is  2 ft.  from  the  fulcrum  and  the  long  end  10  ft.,  how  much  power 
will  be  required? 

L : I : : W : P,  or  10  : 2 ::  2,000  : 400 lb. 


92 


ELEMENTS  OF  MECHANICS, 


The  compound  lever,  Fig.  1,  consists  of  several  levers  so  constructed  that 
the  short  arm  of  the  first  acts  on  the  long  arm  of  the  second,  and  so  on  to 
the  last. 

If  the  distance  from  A to  the  fulcrum  he  four  times  the  distance  from  the 

fulcrum  to  B,  then  a power  of 
5 lb.  at  A will  lift  20  lb.  at  B. 
If  the  arms  of  the  second  lever 
are  of  the  same  comparative 
length,  the  20-lb.  power  obtained 
at  B will  exert  a pressure  of  80 
lb.  on  E)  and  if  the  third  lever 
has  the  same  comparative 
lengths,  this  80  lb.  at  E will  lift  320  lb.  at  O.  Thus,  a power  of  5 lb.  at 
A will  balance  a weight  of  320  lb.  at  G.  But,  in  order  to  raise  the  weight 
1 ft.,  the  power  must  pass  through  or  64  ft. 

The  wheel  and  axle,  Fig.  2,  is  a modification  of  the  lever.  The  ordinary 
windlass  is  a common  form.  The  power  is  applied  to  the 
handle,  the  bucket  is  the  weight,  and  the  axis  of  the 
windlass  is  the  fulcrum.  The  long  arm  of  the  lever  is 
the  handle,  and  the  short  arm  is  the  radius  of  the  axle. 

Thus,  F is  the  fulcrum,  Fc  the  long  arm,  and  Fb  the 
short  arm.  The  wheel  and  axle  has  the  advantage  that 
it  is  a kind  of  perpetual  lever.  We  are  not  obliged  to 
prop  up  the  weight  and  readjust  the  lever,  but  both 
arms  work  continuously. 

By  turning  the  handle  or  wheel  around  once,  the 
rope  will  be  wound  once  around  the  axle,  and  the 
weight  will  be  lifted  that  distance.  Applying  the  law  of 
mechanics,  we  have  power  x the  circumference  of  the 
wheel  '=  the  weight  X circumference  of  the  axle;  or, 
as  the  circumference  of  circles  are  proportional  to  their  radii,  we  have 


P : W ::  r : R.  PR  = Wr. 

R P 

...  RP  RP 

W = . r = 

r W 

A train,  Fig.  3,  consists  of  a series  of 
wheels  and  axles  that  act  on  one  another 
on  the  principle  of  a compound  lever. 
The  driver  is  the  wheel  to  which  power 
is  applied.  The  driven^  or  follower,  is 
the  one  that  receives  motion  from  the 
driver.  The  pinion  is  the  small  gear- 
wheel on  the  axle. 

If  the  diameter  of  the  wheel  A is  16 
in.,  and  of  the  pinion  B 4 in.,  a pull  of 
1 lb.  applied  at  P will  exert  a force  of 
4 lb.  on  the  wheel  C;  if  the  diameter 
of  (7  is  6 in.,  and  of  P 3 in.,  a force  of  4 lb.  on  C will  exert  a force  of  8 lb.  on 
E.  If  E is  16  in.  in  diameter,  and  P 4 in.,  a force  of  8 lb.  on  E will  raise  a 
weight  of  32  lb.  on  F.  In  order,  however,  to  lift  this  amount,  according  to 
the  principle  already  named,  the  weight  will  only  pass  through  ^ of  the 
distance  of  the  power.  Thus,  power  is  gained  and  speed  lost.  To  reverse 
this,  we  apply  power  to  the  axle,  and,  with  a correspondingly  heavy 

f)ower,  gain  speed.  Referring  to  Fig.  4,  applying  the 
aw  of  mechanics,  * ' 


P = 


W r r'r" 
RR'R"' 
n : n"  ; : 


W = 


PR  R'R" 


: RR'^/ 
R R'R". 


n,  n',  n"  = number  of  revolutions; 

V,  v'  = velocity  or  speed  of  rotation; 
r,  r',  r",  etc.  = radii  of  the  pinions; 

R,  R',  R",  etc.  = radii  of  the  wheels. 


Fig.  4. 


ELEMENTS  OF  MECHANICS. 


93 


Fig.  5. 


The  Inclined  Plane.— In  Fig.  5 we  see  that  the  power  must  descend  a dis- 
tance equal  to  J.  (7  in  order  to  elevate  the  weight  to  the  height  B C;  hence, 
we  have  P X length  of  the  inclined  plane  = IF  X the  height  of  the  inclined 
plane,  or  P : W:  : height  of  inclined  plane  : length  of  inclined  plane;  or, 

I h sin  a 

To  Find  the  Weight  Required  to  Balance  Any  Weight  on  Any  Inclined  Plane. 

Multiply  the  given  weight  by  the  sine  of  the  angle 
of  inclination. 

Thus,  to  find  the  weight  required  to  balance  a 
loaded  car  weighing  2,000  lb.  on  a plane  pitching 
18°,  we  multiply  2,000  by  the  sine  of  18°,  or  2,000  X 
.3090170  = 618.034  lb. 

Or,  if  the  length  of  the  plane  and  the  vertical 
height  are  given,  multiply  the  load  by  the  quotient 
of  the  vertical  height  divided  by  the  length. 

Thus,  if  a plane  between  two  levels  is  300  ft. 
long  and  rises  92.7  ft.,  and  the  load  is  2,000  lb.,  the  balancing  weight  is 
found  as  follows; 

92  7 

2.0«<»X3(X)  = 

Case  1. — To  find  the  horsepower  required  to  hoist  a given  load  up  an 
inclined  plane  in  a given  time,  use  the  formula 

I r vertical  height  4 

Load  (in  lb.)  + weight  of  hoisting  rope  (in  lb.)  X ^ through  which  the  > 
^ J ( load  is  raised  (in  ft.  )j  ^ 

33.000  X time  of  hoisting  (in  minutes) 

Example.— Find  the  horsepower  required  to  raise,  in  3 minutes,  a car 
weighing  1 ton  and  containing  1 ton  of  material  up  an  inclined  plane  1,000 
ft.  long  and  pitching  30°,  if  the  rope  weighs  1,500  lb. 

The  total  load  equals  car  + contents  + rope  = 2,000  + 2,000  + 1,500  = 
5,500  lb. 

The  vertical  height  through  which  the  load  is  hoisted  equals 

1.000  X sin  30°  = 1,000  X .5  - 500  ft. 


33,000  X 3 

Case  2. — When  the  power  acts  parallel  to  the  base,  use  the  formula 
W X height  of  inclined  plane  = P X length  of  base. 

These  rules  are  theoretically  correct,  but  in  practice  an  allowance  of 
about  30^  must  be  made  for  friction  and  contingencies. 

The  screw  consists  of  an  inclined  plane  wound  around  a cylinder.  The 
inclined  plane  forms  the  thread,  and  the  cylinder,  the  body.  It  works  in  a 
nut  that  is  fitted  with  reverse  threads  to  move  on  the  thread  of  the  screw. 
The  nut  may  run  on  the  screw,  or  the  screw  in  the  nut.  The  power  may  be 
applied  to  either,  as  desired,  by  means  of  a wrench  or  a lever. 

When  the  power  is  applied  at  the  end  of  a lever,  it  describes  a circle  of 
which  the  lever  is  the  radius  r.  The  distance  through  which  the  power  passes 
is  the  circumference  of  the  circle;  and  the  height  to  which  the  weight  is 
lifted  at  each  revolution  of  the  screw  is  the  distance  between  two  of  the 
threads,  called  the  pitch  (p).  Therefore  we  have  P X circumference  of 
circle  = WX  pitch,  or  P : W : : p : 2 n r. 

2 TT  r p ' 

The  power  of  the  screw  may  be  increased  by  lengthening  the  lever 
or  by  diminishing  the  distance  between  the 
threads. 

Example.— How  great  a weight  can  be  raised 
by  a force  of  40  lb.  applied  at  the  end  of  a wrench 
14  in.  long,  using  a screw  with  5 threads  per  inch  ? 
WX^  = 40  X 28  X 3.1416. 

W = 17,593  lb. 

The  wedge  usually  consists  of  two  inclined 
planes  placed  back  to  back.  (Fig.  6.)  In  theory, 
the  same  formula  applies  to  the  weage  as  to  tne 
inclined  plane.  Case  2. 


Fig.  6. 


P : W w thickness  of  wedge  ; length  of  wedge. 


94 


ELEMENTS  OF  MECHANICS. 


Friction,  in  the  other  mechanical  powers,  materially  diminishes  their 
efficiency;  in  this  it  is  essential,  since,  without  it,  after  each  blow  the  wedge 
would  fly  back  and  the  whole  effect  be  lost.  Again,  in  the  others  the  power 
is  applied  as  a steady  force;  in  this  it  is  a sudden  blow,  and  is  equal  to  the 
momentum  of  the  hammer. 

The  pulley  is  simply  another  form  of  the  lever  that  turns  about  a fixed 
axis  or  fulcrum.  With  a single  fixed  pulley 
shown  in  Fig.  7,  there  can  be  no  gain  of  power 
or  speed,  as  the  force  P must  pull  down  as  much 
as  the  weight  IF,  and  both  move  with  the  same 
velocity.  It  is  simply  a lever  of  the  first  class 
with  equal  arms,  and  is  used  to  change  the 
direction  of  the  force. 

V = velocity  of  W.  v'  = velocity  of  P. 

P = W.  V = V'. 

Movable  Pulley. — A form  of  the  single  pulley, 
where  it  moves  with  the  weight,  is  shown  in 
Fig.  8.  In  this,  one  half  of  the  weight  is  sus- 
tained by  the  hook,  and  the  other  half  by  the 
power.  Since  the  power  is  only  one-haff  the 
weight,  it  must  move  through  twice  the  space;  in  other  words,  by  taking 
twice  the  time,  we  can  lift  twice  as  much.  Here  power  is  gained  and  time 
lost.  P = ^ W.  v'  — 2 V. 

Combinations  of  Pulleys.— (1)  In  Fig.  9,  we  have  the  IF sustained  by  three 
cords,  each  of  which  is  stretched  by  a tension  equal  to  the  P,  hence,  1 lb.  of 
power  will  balance  3 lb.  of  weight.  (2)  In  Fig.  10,  a power  of  1 lb.  will  in  the 


Fig.  7. 


Fig.  9.  Fig.  10.  Fig.  11. 


S 4 21  » 


Fig.  12. 


same  manner  sustain  a IF  of  4 lb.,  and  must  descend  4 in.  to  raise  the  IF 
1 in.  (3)  Fig.  11  represents  the  ordinary  tackle  block  used  by  mechanics, 
which  can  be  calculated  by  the  following  general  rule: 

Rule. — In  any  combination  of  pulleys  where  one  continuous  rope  is  used,  a 
load  on  the  free  end  will  balance  a weight  on  the  movable  block  as  many  times  a*? 
great  as  the  load  on  the  free  end  as  there  are  parts  of  the  rope  support- 
ing ttw  load,  not  counting  the  free  end. 

(4)  In  the  cord  marked  1, 1,  Fig.  12,  each  part  has  a tension 
equal  to  P;  and  in  the  cord  marked  2, 2,  each  part  has  a tension 
equal  to  2 P,  and  so  on  with  the  other  cords.  The  sum  of  the 
tensions  acting  on  IF  is  16;  hence,  IF  = 16  P.  If  n = number  of 
pulleys, 

p = \Y  = 2"  P. 


Differential  Pulley.— Fig.  13.  IF  = 


V-y 
Fig.  13. 


FRICTION  AND  LUBRICATION. 


95 


In  all  combinations  of  pulleys,  nearly  one-half  the  effective  force  is  lost 
by  friction. 

Composition  of  Forces.— When  two  forces  act  on  a body  at  different  angles, 
their  result  may  be  obtained  by  the  following  rule: 

Rule. — Through  a point  draw  two  lines  parallel  to  the  directions  of  the  lines  of 
action  of  the  two  forces.  With  any  convenient  scale,  measure  off,  from  the  point 
of  intersection,  distances  corresponding  to  the  magnitudes  of  the  respective  forces, 
and  complete  the  parallelogram.  From  the  comm.on  point  of  application,  draw  the 
diagonal  of  the  parallelogram;  this  diagonal  will  he  the  resultant,  and  its  magni- 
tude can  be  measured  with  the  same  scale  that  was  used  to  measure  the  two  forces. 
When  more  than  two  forces  act  on  a body  simultaneously , find  the  resultant  of 
any  two  of  them  as  above;  then,  by  the  same  method,  combine  this  resultant  with  a 
third  force,  and  this  resultant  with  the  fourth  force,  and  so  on. 


FRICTION  AND  LUBRICATION. 

Friction.— Friction  is  the  resistance  to  motion  due  to  the  contact  of 
surfaces.  It  is  of  two  kinds,  sliding  and  rolling.  If  the  surface  of  a body 
could  be  made  perfectly  smooth,  there  would  be  no  friction;  but,  in  spite  of 
the  most  exact  polish,  the  microscope  reveals  minute  projections  and  cavities. 
We  fill  these  with  oil  or  grease,  and  thus  diminish  friction.  Since  no  surface 
can  be  made  perfectly  smooth,  some  separation  of  the  two  bodies  must,  in  all 
cases,  take  place  in  order  to  clear  such  projections  as  exist  on  the  surfaces. 
Therefore,  friction  is  always  more  or  less  affected  by  the  amount  of  the 
perpendicular  pressure  that  tends  to  keep  them  together. 

The  ultimate  friction  is  the  greatest  frictional  resistance  that  one  body 
sliding  over  another  is  capable  of  opposing  to  any  sliding  force  when  at  rest. 

The  coefficient  of  friction  is  the  proportion  that  the  ultimate  friction  in  a 
given  case  bears  to  the  perpendicular  pressure.  The  coefficient  of  friction  is 
usually  expressed  in  decimals;  but  sometimes,  as  in  the  case  of  cars  and 
engines,  it  is  expressed  in  pounds  (of  friction)  per  ton. 

The  coefficient  of  friction  equals  the  ultimate  friction  divided  by  the 
perpendicular  pressure,  and  the  ultimate  friction  equals  the  perpendicular 
pressure  multiplied  by  the  coefficient  of  friction.  Thus,  if  we  have  a block 
weighing  100  lb.  standing  on  another  block,  and  it  takes  35  lb.  pressure  to 
slide  it,  the  coefficient  of  friction  = or  .35. 

Table  of  Coefficients  of  Fkiction. 


Materials. 

Smooth,  Clean, 
and  Dry  Plane 
Surfaces. 

Smooth  Plane  Sur- 
faces, Perfectly 
Lubricated  With 
Tallow. 

Oak  on  oak  

.40 

.079 

Wrought  iron  on  oak  

.62 

.085 

Wrought  iron  on  cast  iron 

.19 

.103 

Wrought  iron  on  wrought  iron 

.14 

.082 

Wrought  iron  on  brass 

.17 

.103 

Cast  iron  on  cast  iron 

.15 

.100 

Cast  iron  on  brass 

.15 

.103 

S*teel  on  cast  iron  

.20 

.105 

Steel  on  steel  

.14 

Steel  on  brass 

.15 

.056 

Brass  on  cast  iron 

.22 

.086 

Brass  on  wrought  iron 

.16 

.081 

Brass  on  brass 

.20 

Oak  on  cast  iron 

.080 

Oak  on  wrought  iron  

.098 

Cast  iron  on  oak 

.078 

Steel  on  wrought  iron 

.093 

The  above  coefficients  are  only  approximate,  for  the  coefficient  will  vary 
with  the  intensity  of  the  pressure  and  the  velocity,  and  also  with  the  condi- 
tions of  the  atmosphere.  But  they  are  correct  enough  for  practical  purposes. 


9G 


ELEMENTS  OF  MECHANICS. 


The  friction  of  liquids  moving  in  contact  with  solid  bodies  is  independent 
of  the  pressure,  because  the  forcing  of  the  particles  of  the  fluid  over  the  pro- 
jections on  the  surface  of  the  solid  body  is  aided  by  the  pressure  of  the 
surrounding  particles  of  the  liquid,  which* tend  to  occupy  the  places  of  those 
forced  over.  Therefore,  the  coeflicients  of  Motion  of  liquids  over  solids  do 
not  correspond  with  those  of  solids  over  solids.  The  resistance  is  directly  as 
the  area  of  surface  or  contact. 


Coefficients  of  Friction  in  Axles. 


Axle. 

Bearing. 

Ordinary 

Lubrication. 

Lubricated 

Continuously. 

Bell  metal 

Bell  metal  

.097 

Cast  iron  

Bell  metal  

.07 

.049 

Wrought  iron 

Bell  metal  

.07  • 

.05 

Wrought  iron 

Cast  iron  

.07 

.05 

Cast  iron  

Cast  iron  

.07 

.05 

Cast  iron  

Lignum  vitse 

.10 

Wrought  iron 

Lignum  vitae  

.12 

Friction  naturally  varies  with  the  character  of  the  surfaces,  lubrication, 
and  the  nature  of  the  lubricant.  The  best  lubricants  for  the  purposes 
should  always  be  used,  and  the  supply  should  be  regular.  When  machinery 
is  well  lubricated,  the  lubricant  keeps  the  surfaces  apart,  and  the  frictional 
resistance  becomes  very  small,  or  about  the  same  as  the  friction  of  liquids. 


Frictional  Resistance  of  Shafting. — 

Let  K = coefficient  of  friction; 

W = work  absorbed  in  foot-pounds; 

P = weight  of  shafting  and  pulleys  -f  the  resultant  stress  of  belts; 
H = horsepower  absorbed; 

D = diameter  of  journal  in  inches; 

R = number  of  revolutions  per  minute. 

Then, 

Ordinary  Oiling.  Continuous  Oiling. 


W = .0182 XPXE;  .0112 X P X P; 

H = .000000556  X P X P X P;  .000000339  X P X P X P; 

K = .066.  .044. 

As  a rough  approximation,  100  ft.  of  shafting,  3 in.  diameter,  making 
120  revolutions  per  minute,  requires  1 horsepower. 

For  friction  of  air  in  mines,  see  “Coefficient  of  Friction,”  under  Venti- 
lation. 

Friction  of  Mine  Cars. — The  friction  of  mine  cars  varies  so  much  that  it  is 
impossible  to  give  a formula  for  calculating  it  in  every  case.  No  two  mine 
cars  will  show  the  same  frictional  resistance,  when  tested  with  a dynamome- 
ter, and,  therefore,  nothing  but  an  average  friction  can  be  dealt  with.  The 
construction  of  the  car,  the  condition  of  the  track,  and  the  lubrication  are 
important  factors  in  determining  the  amount  of  friction. 

In  this  connection,  we  may,  however,  state  some  of  the  requisites  of  good 
oil  box  and  journal  bearings.  Tightness  is  a prerequisite,  and,  in  dry  mines 
where  the  dust  is  very  penetrating,  this  is  especially  important;  the  bear- 
ings should  be  sufficiently  broad;  the  oil  box  large  enough  to  hold  sufficient 
oil  to  run  a month  without  renewal,  and  so  constructed  that,  while  it  may 
be  quickly  and  easily  opened,  it  will  not  open  by  jarring  or  by  being  acci- 
dentally struck  by  a sprag  or  a lump  of  coal. 

There  are  a number  of  patented  self-oiling  wheels  that  are  improvements 
on  the  old-style  plain  wheels,  and  each  of  these  has  undoubtedly  some 
point  of  superiority  over  the  old  style. 

Among  the  most  extensively  used  of  these  patented  wheels  are  those  with 
annular  oil  chambers,  and  those  with  patent  bushings.  Their  superiority 
consists  in  the  fact  that,  if  properly  attended  to,  a well-lubricated  bearing  is 
secured  with  greater  regularity  and  less  work  than  when  the  old-style  wheel 
was  used. 

With  a view  of  adopting  a standard  wheel,  the  Susquehanna  Coal  Co., 
of  Wilkesbarre,  Pa.,  experimented  for  a number  of  years  with  different 


FRICTION  AND  LUBRICATION 


97 


styles  of  self-lubricating  wheels,  and  as  a result  of  the  experiments  it  adopted 
a wheel  patented  by  its  chief  engineer,  Mr.  Jas.  H.  Bowden. 

Mr.  R.  Van  A.  Norris,  E.  M.,  Assistant  Engineer,  made  a series  of  989  tests 
with  old-style  wheels,  some  of  which  had  patent  removable  bushings,  and 
others  annular  oil  chambers,  and  the  Bowden  wheel.  The  old  wheels  were 
found  to  be  practically  alike  in  regard  to  friction.  All  the  wheels  were  of 
the  loose  outside  type,  16  in.  in  diameter,  mounted  on  2|  in.  steel  axles, 
with  journals  5i  in.  long.  The  axles  passed  loosely  through  solid  cast 
boxes,  bolted  to  the  bottom  sills  of  the  cars,  and  were  not  expected  to 
revolve. 

The  table  of  friction  tests  shows  the  results  obtained  with  both  old-  and 
new-style  wheels,  and  is  of  interest  to  all  colliery  managers,  inasmuch  as 
the  figures  given  for  the  old-style  wheels  alone  are  the  most  complete  in 
existence,  and,  as  stated  before,  they  are  good  averages. 

Tests  were  made  on  the  starting  and  running  friction  of  each  style  of 
wheel,  under  the  conditions  of  empty  and  loaded  cars,  level  and  grade 
track,  curves,  and  tangents.  The  instruments  used  were  a Pennsylvania 
Railroad  spring  dynamometer,  graduated  to  3,000  lb.,  with  a sliding  recorder, 
a hydraulic  gauge  (not  recording)  reading  to  10,000  lb.,  graduated  to  25  lb., 
and  a spring  balance,  capacity  300  lb.,  graduated  to  3 lb.  All  these  were 
tested  and  found  correct  previous  to  the  experiments. 

Most  of  the  observations  on  single  cars  were  made  with  the  300-lb. 
balance.  The  two  types  of  “old-style  ” wheels  have  been  classed  together  in 
the  table.  Each  car  was  carefully  oiled  before  testing,  and  several  of  each 
type  were  used,  the  results  being  averages  from  the  number  of  trials  shown 
in  the  table. 

In  the  experiments  on  the  slow  start  and  motion,  the  cars  were  started 
very  slowly  by  a block  and  tackle,  and  the  reading  was  taken  at  the  moment 
of  starting.  They  were  then  kept  just  moving  along  the  track  for  a 
considerable  distance,  and  the  average  tractive  force  was  noted,  the  whole 
constituting  one  experiment. 

The  track  selected  for  these  experiments  was  a perfectly  straight  and 
level  piece  of  42  in.  gauge,  about  200  ft.  long,  in  rather  better  condition  than 
the  average  mine  track.  The  cars  were  41f  in.  gauge,  3^  ft.  wheel  base,  10  ft. 
long,  capacity  about  85  cu.  ft.,  with  6-in.  topping. 

To  ascertain  the  tractive  force  required  at  higher  speeds,  trips  of  one,  four, 
and  twenty  cars,  both  empty  and  loaded,  were  attached  to  a mine  locomotive 
and  run  about  a mile  for  each  test,  the  resistance  at  various  points  on  the 
track,  where  its  curve  and  grade  were  known,  being  noted,  care  also  being 
taken  to  run  at  a constant  speed.  Unfortunately,  only  four  of  the  “new- 
style”  cars  were  available  on  the  tracks  where  these  trials  were  made. 

The  remarkably  low  results  for  the  twenty-car  trips  are  attributed  to 
variations  in  the  condition  of  the  track,  and  the  fact  that  the  whole  train 
was  seldom  pulling  directly  on  the  locomotive,  the  cars  moving  by  jerks,  so 
that  correct  observations  were  impracticable.  The  hydraulic  gauge  was  used 
for  these  twenty-car  tests,  and  the  needle  showed  vibrations  from  1 to  4 tons 
and  back.  The  mean  was  taken  as  nearly  as  possible.  The  gauge  was 
rather  too  quickly  sensitive  for  the  work,  and  the  Pennsylvania  Railroad 
dynamometer  was  not  strong  enough  to  stand  the  starting  jerks  and  the 
strain  of  accelerating  speed. 

The  tests  marked  “rope  haul”  were  made  on  an  empty-car  haulage 
system,  about  500  ft.  long,  with  overhead  endless  rope  running  continuously 
at  a speed  of  180  ft.  per  min.,  the  cars  being  attached  to  the  moving  rope  by 
a chain,  a ring  at  the  end  of  which  was  slipj)ed  over  a pin  on  the  side  of  the 
car.  The  increase  of  friction  on  the  heavier  grades  was  due  to  the  rope 
pulling  at  a greater  angle  across  the  car.  Correction  was  not  made  for  this 
angularity  at  the  time,  and  the  rope  has  since  been  rearranged,  so  that  the 
correction  cannot  now  be  made.  There  were  not  enough  curve  experi- 
ments to  permit  the  deduction  of  any  general  formula  for  the  resistance 
of  these  cars  on  curves. 

The  experiments  on  grade  agree  fairly  well  with  those  on  a level,  the 
rather  higher  values  obtained  being  probably  due  more  to  the  greater  effort 
required  in  moving  them,  and  the  consequent  jerkiness  of  the  motion,  than 
to  any  real  increase  in  resistance.  As  the  experiments  on  all  styles  of 
wheels  were  made  in  an  exactly  similar  manner,  the  comparative  value 
of  the  results  is  believed  to  be  nearly  correct,  the  probable  error  in  each  set  of 
experiments,  as  computed  by  the  method  of  least  squares,  varying  from  about 
if  for  slow  start  and  motion  to  12^  for  the  rapid  motion  and  twenty-car  trips. 


Summary  of  Friction  Tests  on  Susquehanna  Coal  Co.’s  Mine  Cars,  April,  1889. 


98 


ELEMENTS  OF  MECHANICS. 


No.  of 
Tests. 

•papBoi 

<M  CO  O rt<  00  t» 

i-H  lO  tOC>.  1-1 

OXCO  ^ 

O00l>l> 

1276  [286 

•i!^draa 

COCOTt^t^COCOCCO 
i-ICOiOtH  tH 

0X0^ 

O lO  lO 
rH 

1 Old-Style  Wheels.  | 

Loaded.  | 

•iqSx9jii 

JO  oSEjaaojaj 

1 Level. 

OCOOC^  OlO 

00  lO  CO  CO  coos 

CO  hc}5  c4  CO  iH  r-H 

1 Grade. 

1 3.94 

2.00 

2.79 

i>  Cars  pulled  from  side. 

J 

1 Curve. 

oooo 

I>  CO  CO  rJH 

CO  rH  1-H 

1 Total  number  of  tests 

•noi'joTjj 

oj  9na  uox 

JOd  OOJO^i  OAIJOTJJX 

lOi-noOTf  os--^ 

C»  O U01>  <N  'Hj' 

«|S 

§8^  S 

CO  OX  CO  OX 
OjOCOCO 

•uotjou^ 
oj  otia’jBO 

jod  oojto^j  SAijaEJj, 

Ii01>i001  l>iO 

C^J  lO  O CO  1-11:^ 

CO  CO  <N  <N  rH  I-H 

311 

161 

220 

OOXCOCO 

O 05  Tti  ox 

tJH  O rH  rH 

•ijTA'BJf)  oj  and 
90LO  J aAIJOEJJ, 

1,639 

1,639 

205 

227 

'JEQ  lad 

OOJOJ^  aAlJOBJJj 

lO  t>  »0  <N  I>  lO 

OX  lO  O CO  I-Il'' 

CO  CO  ox  (M  1-1  I-H 

1,950 

1,800 

425 

O 05  CO  CO 

O rH  Tf  ox 

TJH  GC  rH  I-H 

UBO  JO  jq3i9A\. 

8,500 

7,885 

7,885 

7,885 

9,000 

9,000 

7,885 

7,885 

7,885 

OOOO 
OOOO 
lO  t-^^o^o 
oefod  05”of 

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COCCOXOiOOOSOX 
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OO  O CO  CO 

lO  OOOXtJH 

lO  ox  Tl? 

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oj  arid  ’uox 

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OCDCOrtHOXt^COO 

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O 00  ox  ox  lO  CO  CO 
1—1  CO  CO  CO  GO  I-H  I-H 
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125 

62 

50 

100 

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jad  aojod  aAijoEJj, 

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OGOiOCOCO^tiOSCO 
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lO  »C  O ox  UO  CO  CO 

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rH  1-H  I— ( 

125 

62 

50 

100 

•iCjiATSjf)  oj  ana 

aoaoa  aAijonjj, 

lO  tO  tto  OO  00  ox  o 
^ rfi  CO  05  o Tf 

^ OX  OX 

•JBO  jad 

aojo^  aAijoBJjj 

oco-^oxoTt^coo 
OGOiococoTjiaico 
rH  CO 

O O lO  O CO  lO  CO 

lO  I-H  ox  Tf  00  I-H  O 
lO  lO  rH  rH  rH  CO  CO 

125 

62 

50 

100 

•JBO  JO  jqSiaji 

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OXt-IiHi-IOXOXOXOX 

ox’'  ox”  of  of  of  of  ox”  ox” 

ooo  oooo 

Tf  Tf  Tf  Tf  TTH 

rH  rH  rH  OX  OX  OX  OX 

of  of  of  of  of  of  of 

2,240 

2,240 

2,240 

2,240 

C5  ^ 
o 0.2, 
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B Bto 

■ o3  o3  jii 

oT  CO  oT 
o OJ  <D 
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bX)tX)b£)tyDfcJCfcyc6ctiX) 

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CO  I— I rH 

o o o o 
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^ f-l  fH 

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SS8sS88 


doooooco 

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OOOOOiDOP 

bcbcbcbcbctuctxibx) 

o3o3c3^c3'^do3 


rQ  V-(  Vh '♦H 

dooo 

rlic  lO  lO 
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Q C) 


Summary  of  Friction  Tests  on  Susquehanna  Coal  Co.’s  Mine  Cars,  April,  im— {Continued). 


FRICTION  AND  LUBRICATION. 


99 


O CO  (N  Oi 

CSJ  rtH>  CO 

CO  (N  rH  CO  CO 
CC  00 

2.20 

2.36 

1.63 

1.93 

05  CO  CO  CO 
lO  CO 

8§?SS 

(M  rH  tH  iH 

OCOCOOO 
005CO  lO 

d I— 1 t— t iH 

lOOOO 
d CO  CO  CO 

oToococo 

OO  00  CO  00  CO 
1>  TjJ  CO  Tf  lO 
d d iH  r-l  r-5 

aj5-|2®l2„i4. 

d lOI>  CO 

CO  lO  CO  CO  CO 

S’doS’t^ 

COCOTtiCOCO 

<s|n  to|o  bIm 

codocoi> 

CO  CO  Tfi  CO  CO 

UO  lO  lO  lO  iC 

I—t  I— 1 T-H  rH  T—* 

ddd"(dd 

ddcoco 

dcoco 

3.73 

1.58 

1.85 

1.69 

SoOT^  W 

O d lO  ^ 
CO  iH  rH  -H 

CO  CO  05  d 

05  05  Tfl  I— 1 

CO  CO  d d 

2,000 

1,825 

400 

350 

1 8,160 

8,160 

[8,160 

1 8,160 

4.06 

1.56 

1.12 

«e-g 

0»0i0 

O5C0d 

O0QOt>- 

05COd 

502 

502 

73 

ooo 

s^s 

2,415 

2,415 

2,415 

JO  og'BjuaoJoj; 


•uopoij^j 

oj  on’a  uox 
jad  aoaojj  aAijoBix 


•aoijOTJjj 

oj  ana 

jad  aojo^d  aAijonax 


•^fjiAnjf)  oj  ana 
aoio^i  aAijoBJx 


•j'BQ  jad 
aoJOjj  aAjiOTSJx 


•a«0  JO  jqSia^ 


•jqSia^Vi 

JO  aS'Bjuaoja^ 


•aotjouj 

01  an'a  *aox 
jad  aojo^i  aAiioBJx 


•UOIlOtJ^J 
01  ana  •I'BO 
jad  aojo^j  aAjio'BJx 


•^fljA'BJf)  01  ana 
aojoj^  aAiioisjX 


•JBO  Jad 
Oojo^i  aAjio'BJx 


•JBo  JO  jqSioji 


- ^ 
'N  CO 


<NiO 


T— ( 

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^ 2 ^ 

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od  ^ 
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0)  0)  0)  o»  0) 
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o3  ^ o3  q ^ 

;h  ;h  M M ;-i 
O)  0)  0>  0)  0) 
^>  > > > 


U f-i 

03  o3 

O O 


esa 
'a 


o o 
Onft 

O)  . . 

o o 


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tq  43  "q 

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q c3  ^ c3 

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0)  0)  o>  0) 
> > > > 


be  CO 


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q q 0 


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tn  M 

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■Sto  ^ 

SS-* 

O)  02 

0)  O)  o 

o o o 
>>> 


100 


ELEMENTS  OF  MECHANICS. 


Lubrication. — There  is  probably  no  factor  that  has  a more  direct  bearing 
on  the  cost  of  production  per  ton  of  coal  and  ores  than  the  lubrication  of 
mine  machinery,  and  yet  it  is  doubtful  if  there  is  another  item  connected 
with  the  operation  of  a mine  less  understood  by  owners,  their  managers,  and 
engineers  in  charge. 

Steam  plants  are  equipped  with  boilers  of  the  highest  known  efficiency; 
heaters  are  used  that,  by  utilizing  waste  steam,  will  heat  the  feedwater  for 
boilers  to  the  highest  point.  Modern  engines  that  will  develop  a horsepower 
with  the  least  amount  of  steam  are  installed;  bends,  instead  of  elbows,  are 
placed  in  steam  and  exhaust  pipes,  so  that  the  friction  and  back  pressure 
may  be  reduced  to  a minimum.  In  a word,  everything  is  done  in  the  equip- 
ment of  a plant  to  secure  economy  in  its  operation.  After  all  this  is  done, 
frequently  a long  step  is  taken  in  the  opposite  direction  by  the  use  of  an  oil 
unsuited  to  the  existing  conditions,  and  those  in  charge  of  the  plant  are  led 
to  believe  that  the  lubrication  is  all  that  could  be  desired,  simply  because 
the  engines  and  machinery  run  quietly  and  the  temperature  of  the  bearings 
does  not  become  alarmingly  high.  The  office  of  a lubricant  is  not  merely  to 
secure  this  result,  but,  primarily,  to  reduce  friction  and  wear  to  a minimum; 
and  an  oil  that  will  do  this  is  the  best  oil  to  use,  no  matter  what  the  price 
per  gallon  may  be. 

Few  realize  the  great  loss  in  power  due  to  the  friction  of  wearing  parts. 
One  of  the  greatest  living  authorities  on  lubrication  writes: 

“ It  may  probably  be  fairly  estimated  that  one-half  the  power  expended 
in  the  average  case,  whether  in  mill,  mine,  or  workshop,  is  wasted  on  lost 
work,  being  consumed  in  overcoming  the  friction  of  lubricated  surfaces.” 

He  adds  that  a reduction  of  50^  in  the  work  lost  by  friction  has  often  been 
secured  by  a change  of  lubricants. 

As  one  of  many  instances  showing  the  loss  that  will  occur  by  the  use  of 
inferior  lubricants,  attention  is  called  to  two  flour  mills  located  in  one  of  the 
Middle  States.  One  of  the  plants  was  equipped  with  a condensing  engine 
capable  of  developing  a horsepower  on  24  lb.  of  water  per  hour;  the  other 
plant  had  a simple  engine,  taking  30  lb.  of  water  per  hour.  The  plant  con- 
taining the  condensing  engine  was  purchased  by  the  owner  of  the  plant 
containing  the  simple  engine.  The  new  owner  of  the  plant  was  surprised  to 
learn  that  the  cost  of  operation  per  barrel  of  flour  manufactured  was  equally 
as  great  in  the  new  plant  as  in  the  old  one.  The  engines  were  indicated, 
and  valves  found  to  be  properly  adjusted  and  the  engine  working  within 
the  economical  range,  so  far  as  load  was  concerned.  The  loss  was  then 
attributed  to  the  boilers,  but  an  evaporative  test  proved  that  there  was  no 
practical  difference  here,  as  the  boilers,  in  both  instances,  were  evaporating 
a fraction  over  8 lb.  of  water  per  pound  of  coal.  At  this  point,  the  question 
of  lubrication  was  taken  up,  and,  on  the  advice  of  an  expert  sent  by  a 
prominent  manufacturer  of  lubricants  to  look  over  the  plant,  an  entire 
change  was  made  in  the  lubricants  used,  and,  as  a result,  a money  saving  of 
over  :$2.25  per  day  (practically  ^700  per  annum— this  in  a plant  of  less  than 
250  horsepower)  was  effected,  notwithstanding  the  fact  that  the  new  lubri- 
cants used  cost  considerably  more  per  gallon  than  those  formerly  used. 
This  simply  indicates  that  the  price  of  an  oil  is  of  little  importance  in 
comparison  with  its  friction-reducing  power.  Friction  costs  money,  because 
it  means  greater  cost  of  operation  per  unit  of  output. 

Among  the  expenses  chargeable  to  waste  power,  due  to  inferior  lubrica- 
tion, may  be  included:  (1)  The  cost  of  power  produced  in  excess  of  that 
really  required  to  operate  the  mine  per  ton  of  output.  In  this  calculation 
should  be  included  the  proper  proportion  of  salaries  of  engineers,  and  all 
other  items  that  contribute  to  the  cost  of  the  motive  department,  as  well  as 
the  cost  of  mining  the  fuel  consumed  in  producing  this  excess  power. 
(2)  Wear  and  tear  of  machinery,  which  is  constantly  doing  more  work  per 
ton  of  coal  mined  than  should  be  required  of  it. 

There  is  also  an  element  of  danger  that  ought  to  receive  serious  consid- 
eration, as,  while  it  is  true  that  cylinder  and  bearing  lubricants  of  indifferent 
merit  will,  under  ordinary  conditions,  keep  the  cylinders  from  groaning  and 
the  bearings  from  becoming  hot,  experiments  have  proved  that,  in  accom- 
])lishing  such  results,  the  oils  in  use  were  being  taxed  to  their  utmost;  and 
there  is  record  of  many  instances  where,  as  a result  of  using  oils  of  such 
limited  endurance,  accidents  of  a serious  nature  have  occurred,  necessarily 
causing  shut-downs  just  at  the  time  when  the  operation  of  a plant  to  its 
fullest  capacity  was  imperative. 

It  is  most  difficult,  in  an  article  of  this  character,  to  do  much  more  than 


FRICTION  AND  LUBRICATION. 


101 


.point  out  the  danger  due  to  the  use  of  inferior  lubricants,  leaving  it  to  the 
purchaser  himself  to  determine  as  to  the  intrinsic  worth  of  the  lubncante 
offered  to  him.  In  making  his  selection  he  would  do  well  to  consult  with 
and  heed  the  advice  of  some  highly  responsible  manufacturer  of  lubricants 
who  has  given  to  the  question,  in  all  its  phases,  the  most  careful  study,  and 
who  would  most  probably  have  the  benefit  of  a wide  experience  in  the  applica- 
tion as  well  as  the  manufacture  of  lubricants.  Some  buyers  have,  to  then 
ultimate  regret,  ^opted,  as  a method  of  determining  the  merits  of  lubri- 
cants, a schedule  of  laboratory  tests.  Such  a method  is  not  only  useless,  but 
it  is  misleading  to  any  one  other  than  a manufacturer  of  lubricants,  who 
makes  use  of  it  merely  as  a means  of  insuring  uniformity  in  his  manu- 
factured products,  and  not  as  a measure  whereby  to  judge  their  practical 
value.  Indeed,  many  oils  can  be  very  properly  described  by  practically  the 
same  schedule  of  tests,  and  yet  are  widely  apart  when  their  utility  for  a 
given  service  is  considered.  _ . i x,  • x- 

As  a general  guide  in  purchasing  cylinder  oil  for  mine  lubrication,  it 
might  be  said  that  a dark-colored  oil  is  of  greater  value,  as  a rule,  than  one 
that  has  been  filtered  to  a red  or  light  amber  color,  as  the  process  of  filtration 
necessarily  takes  from  the  oil  a considerable  percentage  of  its  lubricating 
value,  and  at  the  same  time  the  process  is  an  expensive  one.  In  short,  if  a 
light-colored  oil  is  insisted  upon,  a high  price  must  be  paid  for  an  inferior 
lubricant.  As  a word  of  caution,  however,  it  would  be  well  to  add  ri^nt 
here  that  irresponsible  manufacturers  frequently  take  advantage  of  the  fact 
that  the  most  efficient  and  best  known  cylinder  oils  are  dark-colored,  and 
endeavor,  with  more  or  less  success,  to  market  as  “ cylinder  oil  products 
absolutely  unsuited  to  the  lubrication  of  steam  cylinders,  and  that  would 

consequently  be  expensive  could  they  be  procured  without  cost. 

For  the  lubrication  of  engine  bearings,  where  modern  appliances  for 
feeding  are  used,  an  engine  oil  of  a free  running  nature  is  best,  as  it  more 
quickly  reaches  the  parts  requiring  lubrication  than  an  oil  of  a more  sluggish 
nature.  It,  of  course,  must  not  be  an  oil  susceptible  to  temperature  changes, 
but  must  be  capable  of  performing  the  service  required  of  it  under  the  most 
severe  conditions,  where  an  oil  of  less  “backbone  ” would  fail.  Such  an  oil 
would  also  be  suitable  for  the  lubrication  of  dynamos,  and  should  also  give 
satisfaction  where  used  in  lubricating  the  cylinders  of  air  compressors. 
Where  the  machinery  is  of  an  old  type  and  loose-jointed,  or  when  the  bear- 
ings are  open  and  the  oil  is  applied  directly  to  them  by  means  of  an  oiler, 
an  engine  oil  of  a more  sluggish,  or  viscid,  nature  is  best. 

Perhaps  of  equal  importance  to  the  lubrication  of  power  machinery 
must  be  considered  the  lubrication  of  the  axles  of  mme  cars.  This  is 
important,  first,  because  of  the  fact  that  perhaps  three-fourths  of  the  oil 
used  about  a coal  mine  is  used  for  this  purpose,  and,  secondly,  becai^e  there 
is  really  a marked  difference  in  the  quality  and,  therefore,  in  the  efficiency 
of  lubricants  used  for  this  purpose.  Fully  nine-tenths  of  the  prominent 
railroads  of  this  country  are  today  using  car-axle  oil,  costing  perhaps  as 
much  per  gallon  as  much  of  the  so-called  cylinder  oil  that  is  used  in  coal 
mines,  they  having  discovered,  by  exhaustive  experiments,  that  the  increased 
efficiency  gained  by  using  an  oil  of  such  quality  many  times  offsets  the 
difference  in  the  co'st  per  gallon  and  enables  them  to  secure  a greater  mile- 
age without  any  increase  in  their  power  or  other  fixed  charges.  This,  we  are 
certain,  would  apply  just  as  forcibly  to  the  lubrication  of  coal  cars,  no 
matter  whether  the  power  is  derived  from  “long-eared  mules’  or  electric 
motors,  and  we  believe  this  feature  of  lubrication  of  mine  equipment  should 
receive  more  careful  attention  than  it  does  receive,  as  a rule.  , 

There  is  a considerable  amount  of  waste  in  the  lubrication  of  mine  cars. 
This  waste  is  hard  to  avoid,  and,  naturally,  makes  the  buyer  hesitate  before 
adopting  the  use  of  a car  oil  that  costs  very  much  per  gallon;  but  we  believe 
it  can  be  demonstrated,  even  in  the  face  of  this  waste,  that  the  increased 
efficiency  secured  by  the  use  of  a high-grade  car  oil  would  warrant  its  use. 
Such  waste  is  pretty  hard  to  correct  in  mines  where  the  old-fashioned  style 
of  car  axles  is  still  in  use,  and  where  the  oil  is  applied  through  an  ordinary 
spout  oil  can  into  the  axle  box,  and  allowed  to  drip  off  the  axles  and  on  to 
the  ground.  When  axles  are  equipped  in  the  same  manner  as  those  of 
freight  cars,  or  where  cars  are  equipped  with  one  of  the  several  different 
styles  of  patent  car  wheels  and  axles  that  are  coming  into  use  quite 
extensively,  it  is  possible  to  regulate  the  feeding  of  the  oil  to  the  axles,  ^ ^ 
to  reduce  the  waste  to  a minimum.  One  of  these  patent  car  wheels,  which 
is  perhaps  better  known  than  any  other,  is  constructed  with  a hollow  hub 


102 


STRENGTH  OF  MATERIALS. 


that  acts  as  a reservoir  for  the  oil,  the  oil  passing  from  this  reservoir  through 
small  holes  onto  a felt  washer,  which  it  must  saturate,  and  by  which  it  is 
applied  to  the  axles.  Such  w^heels  require  a limpid  oil,  as  a heavy,  sluggish 
oil  w’ould  not  so  readily  saturate  the  felt  w asher  referred  to.  A tight  cap  is 
adjusted  to  the  end  of  the  axle,  to  prevent  waste  of  oil.  These  wheels  will 
run  quite  a length  of  time  without  reoiling  after  the  reservoir  is  once  filled. 

Of  course,  it  costs  something  to  equip  mine  cars  with  these  patent  axles, 
but  w e are  convinced  that  such  an  outlay  w^ould  result  in  more  economical 
operation,  particularly  if  at  the  same  time  the  very  best  quality  of  car  oil 
obtainable  is  used. 


BEST  LUBRICANTS  FOR  DIFFERENT  PU  R POSES  (tH  U RSTOn). 

Low  temperatures,  as  in  rock  drills)  

driven  iy  compressed  air | Light  mineral  lubricating  oils. 

Very  great  pressures,  slow  speed { ‘lubS^®’ 

Heavy  pressures,  with  slow  speed | ''' 

HeaiT  pressures  and  high  speed { ^Sral' 0"!^” 

Light  pressures  and  high  speed  e-oft^e 

Lard  oil,  tallow^  oil,  heavy  mineral 
oils,  and  the  heavier  vegetable 
oils. 

Steam  cylinders  -j  Heavy  mineral  oils,  lard,  tallow. 

(Clarified  sperm,  neat’s  foot,  x>or- 
Watches  and  other  delicate  mechanism.  ^ poise,  olive,  and  light  mineral 

( lubricating  oils. 

For  mixture  with  mineral  oils,  sperm  is  best;  lard  is  much  used;  olive 
and  cottonseed  are  good. 


Ordinary  machinery.. 


STRENGTH  AND  WEIGHT  OF  MATERIALS 


WOODEN  BEAMS. 

To  Find  the  Quiescent  Breaking  Load  of  a Horizontal  Square  or  Rectangular  Beam 
Supported  at  Both  Ends  and  Loaded  at  the  Middle.— Multiply  the  breadth  in 
inches  by  the  square  of  -depth  in  inches,  divide  the  product  by  distance  in 
feet  betw^een  the  supports,  and  multiply  the  quotient  by  the  constant  given 
in  the  table  on  the  next  page.  Take  safe  w orking  load  one-third  of  break- 
ing load. 

To  Find  the  Quiescent  Breaking  Load  of  a Horizontal  Cylindrical  Beam.— Divide 
the  cube  of  the  diameter  in  inches  by  the  distance  betw’een  the  supports  in 
feet,  and  multiply  the  quotient  by  the  constant. 

When  the  load  is  uniformly  distributed  on  the  beam,  the  results  obtained 
by  the  above  rules  should  be  doubled. 

Example  1.— Find  the  quiescent  breaking  load  and  safe  w orking  load  of 
a yellow-pine  collar  8 in.  square,  12  ft.  between  legs. 

8^8^ 

Breaking  load  = — — X 500  = 21,333  lb.  for  seasoned,  and  10,666  lb.  for 
green  timber. 

Safe  w’orking  load  = 7,111  lb.  for  seasoned,  and  3,556  lb.  for  green  timber. 

Example  2.— Find  the  quiescent  breaking  load,  and  the  safe  w'orking 
load  of  a hemlock  collar  10  in.  diameter,  7 ft.  betw  een  legs. 

Breaking  load  — ^ x 236  = 33,714  lb.  for  seasoned  timber,  and 
=*  16,857  lb.  for  green  timber. 

OQ  714  11  9*^ 

Safe  w’orking  load  = — -- — = 11,238  lb.  for  seasoned,  and  — or  — — 
= 5,619  lb.  for  green  timber. 

To  Find  the  Load  a Rectangular  Collar  Will  Support  When  Its  Depth  Is  Increased. 
When  the  length  and  width  remain  constant,  the  load  varies  as  the  square  of 
the  depth. 


IRON  AND  STEEL  BEAMS. 


103 


Example.— A rectangular  collar  10  in.  deep  supports  15,000  lb.  What  will 
it  support  if  its  depth  is  increased  to  12  in.? 

10-'  : 122  : : 15^000  : 21,600.  Ans. 

Having  the  Length  and  Diameter  of  a Collar,  to  Find  the  Diameter  of  a Longer  Collar 
to  Support  the  Same  Weight.— For  the  same  load,  the  strength  of  collars  varies 
as  the  cubes  of  their  diameters,  and  inversely  as  their  lengths. 

Example.— If  a collar  6 ft.  long  and  8 in.  diameter  supports  a certain 
weight,  what  must  be  the  diameter  of  a collar  12  ft.  long  to  support  the  same 
weight?  _ _ 

if  6 : if  12  : : 8 in.  : 10+  in.  Ans. 

Having  the  Loads  of  Two  Beams  of  Equal  Length  and  the  Diameter  of  One,  to 
Find  the  Diameter  of  the  Other. — ^When  the  lengths  are  equal,  the  diameters 
vary  as  the  cube  roots  of  the  loads,  or  the  cubes  of  the  diameters  vary  as  the 
loads. 

Example  1. — A beam  11  in.  in  diameter  supports  a load  of  32,160  lb.  What 
will  be  the  diameter  of  another  beam  the  same  length,  to  support  a load 

of  19,440  lb.?  

if  32,160  : ^19,440  : : 11 ; 9.  Ans. 

Example  2.— A beam  8 in.  in  diameter  will  support  a load  of  10,240  lb. 
What  load  will  a beam  the  same  length  and  7 in.  in  diameter  support  ? 

8^ : : : 10,240  : 6,860.  Ans. 

Table  of  Constants. 

Calculated  for  seasoned  timber.  For  green  timber,  take  one-half  of  these 
constants.  Safe  working  load  is  one-third  of  breaking  load. 


Woods. 

Square  or 
Rectan- 
gular. 

Round. 

Woods. 

Square  or 
Rectan- 
gular. 

Round. 

Ash,  white 

650 

383 

Locust  

600 

353 

Ash,  swamp 

400 

236 

Lignum  vitae 

650 

383 

Ash,  black 

300 

177 

Larch 

400 

236 

Balsam,  Canada 

350 

206 

Maple  

550 

324 

Beech,  white 

450 

265 

Oak,  red  or  black ... 

550 

324 

Beech,  red 

550 

324 

Oak,  white 

600 

353 

Birch,  black 

450 

265 

Oak,  live 

600 

353 

Birch,  yellow  

450 

266 

Pine,  white 

450 

265  • 

Cedar,  white 

250 

147 

Pine,  yellow  

500 

295 

Chestnut  

450 

265 

Pine,  pitch 

550 

324 

Elm 

350 

206 

Poplar  

550 

324 

Elm,  rock  

600 

353 

Spruce  

450 

265 

Hemlock  

400 

236 

Sycamore 

500 

295 

Hickory  

650 

383 

Willow  

350 

206 

Ironwood  

600 

353 

To  Find  the  Diameter  of  a Collar  When  the  Weight  Increases  in  Proportion  to  the 
Length.— Find  the  required  diameter  to  support  the  same  weight  as  the  short 
collar.  Then  the  length  of  the  short  collar  is  to  the  length  of  the  long  one 
as  the  diameter  found  to  support  the  original  weight  is  to  the  required 
diameter. 

Example. — If  a collar  6 ft.  long,  8 in.  in  diameter,  supports  a certain  weight, 
what  must  be  the  diameter  of  a collar  12  ft.  long  to  support  twice  the  weight? 

83  ( 13 

1:2::^:  or  1 : 2 : : 2 X 83 : ( )3, 

or  if  r : if  2 : : 8if  2 : ( ) = 12.7.  Ans. 


IRON  AND  STEEL  BEAMS. 

Constants  for  use  in  calculating  strength  of  iron  and  steel  beams: 


Cast  iron  2,000 

Wrought  iron  2,200 

Steel  ^ 5,000 


Safe  Loads  Uniformly  Distributed  for  Standard  and  Special  I Beams. 

{Tons  of  2,000  Pounds.) 


104 


STRENGTH  OF  MATERIALS, 


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Safe  loads  given  include  weight  of  beam.  Maximum  fiber  stress,  16,000  lb.  per  sq.  in. 

Bor  spacings  below  the  heavy  lines,  the  deflections  will  be  greater  than  the  allowable  limit  for  plastered  ceilings,  equaling  span. 


PILLARS  OR  PROPS. 


105 


Hard  steel  will  break  the  same  as  cast  iron.  Soft  steel  will  bend  like 
wrought  iron.  The  elastic  limit  of  wrought  iron  is  reached  at  about  2,200  lb. 
As  it  does  not  break,  we  use  the  limit  of  elasticity. 

To  Find  the  Quiescent  Breaking  Load  of  a Horizontal  Square  or  Rectangular 
Iron  or  Steel  Beam  Supported  at  Both  Ends  and  Loaded  at  the  Middle.— Multiply 
the  square  of  its  deptn  in  inches  by  its  breadth  in  inches;  multiply  this  result 
by  the  constant  for  the  material  used,  and  divide  by  the  length  in  feet 
between  the  supports.  For  the  neat  load,  subtract  one-half  the  weight  of 
the  beam. 

To  Find  the  Quiescent  Breaking  Load  of  a Cylindrical  Iron  or  Steel  Beam. 

Find  the  breaking  load  of  a square  beam  the  sides  of  which  are  equal  to  the 
diameter  of  the  round  one,  and  multiply  by  .6. 

Safe  working  load  in  each  of  the  preceding  cases  is  one-third  of  the  breaking 
load.  If  the  load  is  equally  distributed  over  the  beam,  it  will  be  twice  as 
great. 


PILLARS  OR  PROPS. 

To  Find  the  Crushing  Load  of  Either  Square  or  Rectangular  Wooden  Pillars  or 
Props.— Call  one  side  of  the  square  or  the  least  side  of  the  rectangle  the 
breadth.  Divide  the  square  of  the  length  in  inches  by  the  square  of  the 
breadth  in  inches,  multiply  the  quotient  by  .004,  add  1 to  the  product,  and 
divide  the  constant  in  the  following  table  by  the  result.  Then  multiply 
this  quotient  by  the  number  of  square  inches  in  the  end  of  the  prop. 

Or,  breaking  load  in  lb.  = Xbd, 

(^X  .004) +1 

when  I = length  in  inches,  b = breadth  in  inches,  and  d = depth  in  inches. 
Crushing  Loads  of  Well-Seasoned  American  Woods. 


Wood. 


Ash  

Beech 

Birch  

Cedar,  red 

Cedar,  white 

Chestnut  

Hemlock 

Hickory 

Linden 

Locust,  black,  yellow 

Locust,  honey 

Maple,  broad-leafed 
Oregon 


Crushing 
Load.  Lb. 
per  Sq.  In. 

Wood. 

Crushing 
Load.  Lb. 
per.  Sq.  In. 

6,800 

Maple,  sugar,  black 

8,000 

7,000 

Maple,  white, red....  1^... 

6,800 

8,000 

Oak,  white,  red,  black 

7,000 

6,000 

Oak,  scrub,  basket  

6,000 

4,400 

Oak,  chestnut,  live 

7,500 

5,300 

Oak,  pin  

6,500 

5,300 

Pine,  white 

5,400 

8,000 

Pine,  pitch 

5,000 

5,000 

Pine,  Georgia 

8,500 

9,800 

Poplar  

5,000 

7,000 

Spruce,  black 

5,700 

Spruce,  white 

4,500 

5,300 

Willow 

4,400 

For  green  timber,  take  one-half  of  the  constants  or  crushing  strength. 
Safe  working  load  equals  one-third  of  crushing  load. 

Example.— What  is  the  breaking  load  of  a well-seasoned  hemlock  post 
10  in.  by  8 in.  and  12  ft.  long? 

5,300-i-  [l+  X -00^)]  = 2,308.41b.  per  sq.  in.  of  area.  2,308.4  X 80 

= 184,672  lb.  Ans. 

To  Find  the  Breaking  Load  of  a Cylindrical  Wooden  Prop.— Find  the  breaking 
load  of  a square  prop  whose  ends  are  equal  in  area  to  those  of  the  cylin- 
drical one,  and  proceed  according  to  foregoing  rule. 

Example.— What  is  the  safe  working  load  for  a hemlock  mine  prop  10  in. 
diameter,  10  ft.  long  ? 

The  area  of  the  end  of  the  prop  = 78.54  sq.  in.  A square  of  equal  area 
will  have  sides  equal  to  i/  78.54  = 8.86+  in. 

Then,  5,300  ^ j^l  + X *004^  j = 3,058.3  lb.  per  each  sq.  in.  of  area. 


106 


STRENGTH  OF  MATERIALS. 


And  3,058.3  X 78.54  -=  240,198  lb.  This  is  the  crushing  strength  of  a similar 
prop  of  seasoned  timber,  but,  as  mine  timber  is  used  in  its  green  state,  we 
take  one-half  of  240,198  lb.,  or  120,099  lb.,  as  the  crushing  load  of  the  prop  in 
question.  Then,  the  safe  working  load  is  one-third  of  this,  or  40,033  lb. 

The  strength  of  similar  props  varies  as  the  cubes  of  their  diameters,  and 
inversely  as  their  lengths. 

Safe  Loads,  in  Tons  of  2,000  Pounds,  for  Hollow  Cylindrical  Cast-Iron 
Columns. 

( The  Carnegie  Steel  Co.^  Limited.) 


Outside  Diam.  I 

Inches. 

Thickness  of 
Metal. 

Length  of  Columns  in  Ft. 

1 Sectional  Area. 

1 Inches. 

Weight  in  Lb.  of 

Columns  per 

Ft.  of  Length. 

8 

10 

12 

14 

16 

1 

20 

22 

24 

Tons. 

Tons. 

Tons. 

Tons. 

Tons.  Tons. 

Tons. 

Tons. 

Tons. 

6 

JL 

26.2 

23.0 

20.1 

17.5 

15.2 

13.2 

11.5 

8.6 

26.95 

6 

% 

37.5 

33.0 

28.8 

25.0 

21.7 

18.9 

16.5 

12.4 

38.59 

6 

1 

42.7 

37.6 

32.8 

28.5 

24.7 

21.5 

18.8 

14.1 

43.96 

6 

1 

47.6 

41.9 

36.5 

31.8 

27.6 

24.0 

21.0 

15.7 

49.01 

6 

li 

52.2 

46.0 

40.1 

34.8 

30.2 

26.3 

23.0 

17.2 

53.76 

7 

47.7 

43.1 

38.5 

34.3 

30.4 

26.9 

23.9 

21.2 

18.9 

14.7 

45.96 

7 

1 

61.1 

55.2 

49.3 

43.8 

38.9 

34.4 

30.6 

27.1 

24.2 

18.9 

58.90 

7 

li 

67.2 

60.8 

54.3 

48.3 

42.8 

37.9 

33.7 

29.9 

26.7 

20.8 

64.77 

8 

57.9 

53.3 

48.6 

44.1 

39.7 

35.8 

32.2 

28.9 

26.1 

17.1 

53.29 

8 

1 

74.6 

68.7 

62.5 

56.7 

51.1 

46.0 

41.4 

37.3 

33.6 

22.0 

68.64 

8 

li 

89.9 

82.8 

75.5 

68.4 

61.7 

55.5 

49.9 

44.9 

40.5 

26.5 

82.71 

9 

68.1 

63.6 

58.9 

54.2 

49.6 

45.2 

41.2 

37.5 

34.1 

19.4 

60.65 

9 

1 

88.0 

82.3 

76.2 

70.0 

64.1 

58.4 

53.2 

48.4 

44.1 

25.1 

78.40 

9 

li 

106.6 

99.6 

92.2 

84.8 

77.6 

70.8 

64.4 

58.7 

53.4 

30.4 

94.94 

9 

U 

123.8 

115.7 

107.1 

98.5 

90.1 

82.2 

74.8 

68.1 

62.0 

35.3 

110.26 

9 

u 

139.6 

130.5 

120.8 

111.1 

101.6 

92.7 

84.4 

76.8 

69.9 

39.9 

124.36 

10 

1 

101.4 

95.9 

89.8 

83.6 

77.4 

71.5 

65.8 

60.5 

55.5 

28.3 

88.23 

10 

li 

123.3 

116.5 

109.1 

101.6 

94.1 

86.8 

79.9 

73.4 

67.5 

34.4 

107.23 

10 

U 

143.7 

135.8 

127.3 

118.5 

109.7 

101.2 

93.2 

85.6 

78.7 

40.1 

124.99 

10 

n 

162.7 

153.8 

144.1 

134.1 

124.2 

114.6 

105.5 

97.0 

89.1 

45.4 

141.65 

11 

1 

114.8 

109.4 

103.5 

97.3 

91.0 

84.8 

80.2 

73.1 

67.7 

31.4 

98.03 

11 

u 

139.9 

133.3 

126.1 

118.6 

110.9 

103.3 

97.8 

89.4 

82.5 

38.3 

119.46 

11 

H 

163.5 

155.9 

147.5 

138.6 

128.7 

120.8 

114.3 

104.1 

96.4 

44.8 

139.68 

11 

U 

185.7 

177.1 

167.5 

157.5 

147.3 

137.2 

129.8 

118.3 

109.5 

50.9 

158.68 

11 

2 

206.6 

196.9 

186.3 

175.1 

163.8 

152.6 

144.4 

131.5 

121.8 

56.6 

176.44 

12 

1 

128.0 

122.9 

117.2 

111.0 

104.7 

98.4 

92.2 

86.1 

80.4 

34.6 

107.51 

12 

li 

156.4 

150.1 

143.1 

135.7 

127.9 

120.2 

112.6 

105.2 

98.2 

42.2 

131.41 

12 

u 

183.3 

175.9 

167.7 

159.0 

149.9 

140.9 

132.0 

123.3 

115.1 

49.5 

154.10 

12 

u 

208.7 

200.4 

191.0 

181.1 

170.7 

160.4 

150.3 

140.5 

131.1 

56.4 

175.53 

12 

2 

232.7 

223.4 

213.0 

201.9 

190.4 

178.9 

167.6 

156.6 

146.1 

62.8 

195.75 

13 

1 

141.2 

136.3 

130.7 

124.7 

118.5 

112.1 

105.8 

99.5 

93.5 

37.7 

117.53 

13 

u 

172.8 

166.8 

160.0 

152.7 

145.0 

137.2 

129.4 

121.8 

114.4 

46.1 

143.86 

13 

U 

203.0 

195.9 

187.9 

179.3 

170.3 

161.1 

152.0 

143.1 

134.3 

54.2 

168.98 

13 

n 

231.6 

223.6 

214.5 

204.7 

194.4 

183.9 

173.5 

163.3 

153.3 

61.9 

192.88 

13 

2 

258.9 

249.9 

239.7 

228.7 

217.3 

205.5 

193.9 

182.5 

171.3 

69.1 

215.56 

14 

1 

154.3 

149.6 

144.3 

138.5 

132.3 

125.9 

119.5 

113.1 

106.8 

40.8 

127.60 

14 

u 

189.2 

183.4 

176.9 

169.7 

162.2 

154.4 

146.5 

138.6 

131.0 

50.1 

156.31 

14 

u 

222.6 

215.8 

208.1 

199.7 

190.8 

181.7 

172.3 

163.1 

154.1 

58.9 

183.67 

14 

u 

254.4 

246.7 

237.9 

228.3 

218.1 

207.6 

197.0 

186.5 

176.2 

67.4 

210.00 

14 

2 

284.8 

276.2 

266.4 

255.6 

244.2 

232.4 

220.6 

208.8 

197.2 

75.4 

235.12 

15 

1 

167.4 

162.9 

157.8 

152.1 

146.0 

139.7 

133.3 

126.8 

120.4 

44.0 

137.28 

15 

u 

205.5 

200.0 

193.7 

186.7 

179.3 

171.5 

163:6 

155.7 

147.9 

54.0 

168.48 

15 

H 

242.1 

235.7 

228.2 

220.0 

211.2 

202.1 

192.8 

183.5 

174.2 

63.6 

198.74 

15 

U 

277.2 

269.8 

261.3 

251.9 

241.9 

231.4 

220.7 

210.1 

199.5 

72.9 

227.45 

15 

2 

310.8 

302.5 

293.0 

! 

282.5 

271.2 

259.5 

247.5 

235.5 

1 

223.6 

81.7 

254.90 

SPECIFIC  GRAVITY. 


107 


Minimum  Safe-Bearing  Values  of  Masonry  Materials. 


Materials. 


Tons  per  Sq.  Ft. 


Granite,  capstone 

Squared  masonry 

Sandstone,  capstone 

Squared  masonry 

Rubble,  laid  in  lime  mortar 

Rubble,  laid  in  cement  mortar 

Limestone,  capstone 

Squared  masonry 

Rubble,  laid  in  lime  mortar 

Rubble,  laid  in  cement  mortar 

Bricks,  hard,  laid  in  lime  mortar 

Hard,  laid  in  Portland  cement  mortar  

Hard,  laid  in  Rosendale  cement  mortar  ... 
Concrete,  1 Portland,  2 sand,  5 broken  stone 


50 

25 

25 

12 

5 

10 

36 

18 

5 

10 

7 

14 

10 

10 


SPECIFIC  GRAVITY,  WEIGHT,  AND  PROPERTIES  OF  MATERIALS,  ETC. 

The  specific  gravity  of  a body  is  the  ratio  of  its  weight  to  the  weight  of 
an  equal  bulk  of  pure  water,  at  a standard  temperature  (62°  F.  = 16.670°  C.). 

Some  experimenters  have  used  60°  F.  as  the  standard  temperature,  others 
32°  and  still  others,  39.1°.  To  reduce  a specific  gravity,  referred  to  water 
at  39.1°  F.,  to  the  standard  of  water  at  62°  F.,  multiply  by  1.00112. 

Given  specific  gravity  referred  to  water  at  62°  F.,  multiply  by  62.355  to 
find  the  weight  of  a cubic  foot  of  the  substance.  Given  weight  per  cubic 
foot,  to  find  specific  gravity,  multiply  by  0.016037.  ^ 

Given  specific  gravity,  to  find  the  weight  per  cubic  inch,  multiply  by 

To  Find  the  Specific  Gravity  of  a Solid  Heavier  Than  Water. — Weigh  the  body 
both  in  air  and  in  water,  and  divide  the  weight  in  air  by  the  difference  of 
the  weights  in  air  and  water. 

Example. — A piece  of  coal  weighs,  say,  480  grains.  Loss  of  weight 
when  weighed  in  water,  398  grains. 

Then,  §§§  = 1.206,  specific  gravity  of  the  coal  compared  with  water  at 

As  a cubic  foot  of  water  weighs,  approximately,  1,000  oz.,  the  weight  of  a 
cubic  foot  of  anv  substance  can  be  found  by  multiplying  its  specific  gravity 
by  1,000. 

To  Find  the  Specific  Gravity  of  a Solid  Lighter  Than  Water.— Attach  to  it 
another  body  heavy  enough  to  sink  it;  weigh  severally  the  compound  mass 
and  the  heavier  body  in  water,  divide  the  weight  of  the  body  in  air  by  the 
weight  of  the  body  in  air  plus  the  weight  of  the  sinker  in  water  minus  the 
combined  weight  of  the  sinker  and  body  in  water. 

To  Find  the  Specific  Gravity  of  a Fluid.— Weigh  both  in  and  out  of  the  fiuid 
a solid  (insoluble)  of  known  specific  gravity,  and  divide  the  product  of  the 
weight  lost  in  the  fiuid  and  the  specific  gravity  of  the  solid  by  the  weight  of 
the  solid. 

The  weight  of  a cubic  foot  of  water  at  a temperature  of  62°  is  about 
1,000  oz.  avoirdupois,  and  the  specific  gravity  of  a body,  water  being  1,000, 
shows  the  weight  of  a cubic  foot  of  that  body  in  ounces  avoirdupois. 
Then,  if  the  magnitude  of  the  body  be  known,  its  weight  can  be  com- 
puted; or,  if  its  weight  be  known,  its  magnitude  can  be  calculated,  provided 
we  know  its  specific  gravity;  or,  of  the  magnitude,  weight,  and  specific 
gravity,  any  two  being  known,  the  third  may  be  found. 

To  Find  the  Magnitude  of  a Body  in  Cubic  Feet  From  Its  Weight.— Divide  the 
weight  of  the  body  in  ounces  by  1,000  times  the  specific  gravity  of  the  body. 

To  Find  the  Weight  of  a Body  in  Ounces  From  Its  Magnitude.— Divide  the 
weight  of  the  body  in  ounces  by  the  specific  gravity  of  the  substance  mul- 
tiplied by  1,000. 

Note. — The  specific  gravity  of  any  substance  is  equal  to  its  weight  in 
^ grams  per  cubic  centimeter.  (See  table  of  metric  weights  and  measures.) 

45-  oa ooqqo^:^7g} 

9 ^ e^«Licc/7  0TT 


108 


WEIGHT  OF  MATERIALS. 


Specific  Gravity  of  Substances. 


Substance. 

Average 

Specific 

Gravity. 

Average 
Weight  per 
Cu.  Ft.  Lb. 

Air,  atmospheric;  at  60°  F.  under  pressure  of  1 at- 
mosphere, or  14.7  lb.  per  sq.  in 

.00123 

.0765 

Alcohol,  pure  

.793 

49.43 

Alcohol,  of  commerce 

.834 

52.1 

Aluminum 

2.66 

166.0 

Anthracite*  coal 

1.5 

93.5 

Asphaltum 

1.4 

87.3 

Brass,  cast  , 

8.1 

504.0 

Brass,  rolled  

8.4 

524.0 

Bronze,  gun  metal 

8.5 

529.0 

Brick,  best  pressed 

150.0 

Brick,  common  hard 

125.0 

Carbonic-acid  gas 

.00187 

.1167 

Clay,  dry,  in  lumps,  loose 

Clay,  potters’,  dry 

Coke,  t loose,  of  good  coal 

63.0 

1.9 

119.0 

27.5 

Coal,  bituminous  t 

1.35 

84.0 

Coal,  bituminous,  broken  loose 

50.0 

Coal,  bituminous,  moderately  shaken 

54.0 

Copper,  cast 

8.7 

542.0 

Copper,  rolled 

8.9 

555.0 

Cork  

.25 

15.6 

Earth,  common  loam,  perfectly  dry,  loose 

76.0 

Earth,  common  loam,  perfectly  dry,  shaken 

87.0 

Earth,  common  loam,  perfectly  dry, moderately  packed 

95.0 

Earth,  common  loam,  slightly  moist,  loose  

78.0 

Earth,  common  loam,  more  moist,  loose 

80.0 

Earth,  common  loam,  more  moist,  shaken 

90.0 

Earth,  common  loam,  more  moist,  packed 

96.0 

Earth,  common  loam,  as  a soft  flowing  mud 

108.0 

Earth,  common  loam,  as  a soft  mud  packed 

115.0 

Gold,  cast,  pure  or  24  carat 

19.26 

1,204.0 

Gravel  

98.0 

Gutta  percha 

.98 

61.1 

Gypsum  (plaster  of  Paris) 

2.27 

141.6 

Gypsum,  in  irregular  lumps 

82.0 

Gypsum,  ground,  loose 

56.0 

Gypsum,  ground,  well  shaken 

64.0 

Gypsum,  calcined,  loose 

56.0 

Hydrogen  gas,  14^  times  lighter  than  air  and  16  times 
lighter  than  oxygen 

.00527 

Ice 

.92 

57.4 

Iron,  cast - 

7.21 

450.0 

Iron,  rolled  bars 

7.65 

480.0 

Iron,  sheet 

485.0 

Iron,  wrought 

7.77 

485.0 

Lead 

11.38 

709.6 

Lime,  quick 

1.5 

95.0 

Lime,  quick,  ground,  loose,  per  struck  bushel,  66  lb. 

53.0 

Mercury,  at  32°  F 

13.62 

849.0 

Mercury,  at  60°  F 

13.58 

846.0 

Mercury,  at  212°  F 

13.38 

836.0 

Nitrogen  gas,  gV  part  lighter  than  air 

.0744 

Oils,  whale,  olive 

.92 

57.3 

# Anthracite  increases  about  75  per  cent,  in  bulk  when  broken  to  any  market  size.  A ton 
loose,  averages  from  40  to  43  cu.  ft. 

+ A heaped  bushel,  loose,  weighs  from  35  to  42  lb.  A ton  occupies  80  to  97  cu.  ft. 

} A heaped  bushel,  loose,  weighs  about  74  lb.,  and  a ton  occupies  from  43  to  48  cu.  ft.  Bitumi* 
nous  coal,  when  broken,  occupies  75  per  cent,  more  space  than  in  the  soli<I. 


SPECIFIC  GRAVITY, 


109 


Specific  Gravity  of  Substances— ( (7o?i^mwed). 


Substance. 


Oxygen  gas,  yV  part  heavier  than  air 

Petroleum  

Powder 

Rosin 

Silver 

Slate  

Steel  

Sulphur  

Tallow 

Tin,  cast 

Water,  pure,  rain  or  distilled,  at  32°  F.,  Barom.  30  in. 
Water,  pure,  rain  or  distilled,  at  62°  F.,  Barom.  30  in. 
Water,  pure,  rain  or  distilled,  at  212°  F.,  Barom.  30  in. 

Water,  sea,  average 

Zinc  


Average 

Specific 

Gravity. 

Average 
Weight  per 
Cu.  Ft.  Lb. 

.00136 

.0846 

.878 

54.8 

1.5-1.85 

105.0 

1.1 

68.6 

10.5 

655.0 

2.8 

175.0 

7.85 

490.0 

2.0 

125.0 

.94. 

58.6 

7.35 

459.0 

62.417 

1.00 

62.355 

59.7 

1.028 

64.08 

7.00 

437.5 

The  following  table  gives  the  specific  gravities  of  various  coals: 


Name  of  Coal. 

Sp.  Gr. 

Weight  of  a 
Cu.  Ft.  Lb. 

Weight  of  a 
Cu.Yd.  Tons. 

Newcastle  Hartley,  England 

1.29 

80.6 

.972 

Wigan,  4 ft.,  England 

1.20 

75.0 

.914 

Portland,  England  

1.30 

81.2 

.978 

Anthracite,  Wales 

1.39 

86.9 

1.047 

Eglington,  Scotland 

1.25 

78.1 

.941 

Anthracite,  Irish 

1.59 

99.4 

1.193 

Anthracite,  Pennsylvania 

1.55 

96.9 

1.167 

Bituminous,  Pennsylvania 

1.40 

87.5 

1.054 

Block  coal,  Indiana 

1.27 

79.4 

.956 

SPECIFIC  GRAVITY  AND  WEIGHT  OF  PREPARED  ANTHRACITE  COAL. 

To  Mr.  Irving  A.  Stearns, ' General  Superintendent  of  the  Pennsylvania 
Railroad  Co.’s  Coal  Department,  we  are  indebted  for  the  following  sum- 
mary of  tests  made  by  the  mining  engineers  of  the  company. 

In  a series  of  tests  to  ascertain  the  specific  gravity  of  the  coal  from  differ- 
ent seams  worked  by  the  company,  it  was  found  that  the  average  specific 
gravity  was  1.4784,  and  the  average  weight  per  cubic  foot  was  92.50  lb.  This 
was  calculated  for  space  filled  at  breaker  without  settling.  Add  5^  for 
packed  spaces  of  large  heaps. 

Weight  per  Cubic  Foot  of  Susquehanna  Coal  Co.’s  White  Ash  Anthra- 
cite Coal. 


/ 

Size. 

Size  of  Mesh. 

Weight  per 
Cu.  Ft. 
Pounds. 

Cu.Ft.  Froml 
Cu.  Ft.  Solid. 

Over. 

Through. 

Lump 

4i"  to  9 " 

57 

1.614 

Broken 

21"  to  2i" 

3i"  to  4i" 

53 

1.755 

Egg 

11"  to  2i" 

2f"  to  2i" 

52 

1.769 

Large  stove 

li"  to  li" 

li"  to  2i" 

51i 

1.787 

Small  stove 

1 " to  li" 

li"  to  li" 

51i 

1.795 

Chestnut 

F'to  i" 

1 " to  li" 

51 

1.804 

Pea 

f"to  1" 

r'to  i" 

50i 

1.813 

No.  1 buckwheat 

iV'to  i" 

rto  r 

50i 

1.813 

No.  2 buckwheat 

TV'tO  1" 

50i 

1.813 

110 


WEIGHT  OF  MATERIALS. 


LINE  SHAFTING. 

Shafting  is  usually  made  cylindrically  true,  either  by  a special  rolling 
process,  when  it  is  known  as  cold-rolled  shafting,  or  it  is  turned  up  in  a 
machine  called  a lathe.  In  the  latter  case,  it  is  called  bright  shafting.  What 
is  known  as  black  shafting  is  simply  bar  iron  rolled  by  the  ordinary  process 
and  turned  where  it  receives  the  couplings,  pulleys,  bearings,  etc. 

Bright  turned  shafting  varies  in  diameter  by  i in.  up  to  about  in.  in 
diameter;  above  this  diameter  the  shafting  varies  by  i in.  The  actual 
diameter  of  a bright  shaft  is  in.  less  than  the  commercial  diameter,  it 
being  designated  from  the  diameter  of  the  ordinary  round  bar  iron  from 
which  it  is  turned.  Thus,  a length  of  what  is  called  3"  bright  shafting  is 
only  2^1  in.  in  diameter. 

Cold-rolled  shafting  is  designated  by  its  commercial  diameter;  thus,  a 
length  of  what  is  called  3"  shafting  is  3 in.  in  diameter. 

Cold-rolled  iron  is  considerably  stronger  than  ordinary  turned  wrought 
iron;  the  increased  strength  being  due  to  the  process  of  rolling,  which  seems 
to  compress  the  metal  and  so  make  it  denser — not  merely  skin  deep,  but 
practically  throughout  the  whole  diameter. 


STRENGTH  OF  SHAFTING. 

Let  D = diameter  of  shaft; 

R = revolutions  per  minute; 

H = horsepower  transmitted; 

C = constant  given  in  table. 
Constants  for  Line  Shafting. 


In  the  accompanying  table  the  bearings  are  supposed  to  be  spaced  so 

to  rplipvp  thp  nf 

Material  of  Shaft. 

No  Pulleys 
Between 
Bearings. 

Pulleys  excessive  bending;  also, 

Betw'een  in*  the  third  vertical  col- 

Bearings  nmn,  an  average  num- 

® ■ her  and  weight  of  pulleys 

Steel  or  cold-rolled  iron 

Wrought  iron 

Cast  iron  

65 

70 

90 

and  power  given  off  is 
assumed. 

In  determining  the 
constants  given  in  the 

accompanying  table,  al- 
lowance has  been  made  to  insure  the  stiffness  as  w^ell  as  strength  of  the  shaft. 


H ^ 


IFXR 

c • 


^ 


R = 


CXH 

j)i  • 


Shafts  are  subject  to  forces  that  produce  stresses  of  two  kinds— transverse 
and  torsional.  When  the  machines  to  be  driven  are  below  the  shaft,  there 
is  a transverse  stress  on  the  shaft,  due  to  the  weight  of  the  shaft  itself,  of  the 
pulley  and  tension  of  the  belt.  Sometimes  the  power  is  taken  off  horizon- 
tally on  one  side,  in  which  case  the  tension  of  the  belt  produces  a horizontal 
transverse  stress,  while  the  weight  of  the  pulley  acts  with  the  weight  of  the 
shaft  to  produce  a vertical  transverse  stress.  When  the  machinery  to  be 
driven  is  placed  on  the  floor  above  the  shaft,  the  tension  of  the  belt  produces 
a transverse  stress  in  opposite  direction  to  that  due  to  the  weight  of  the 
shaft  and  pulley. 

The  torsional  strength  of  shafts,  or  their  resistance  to  breaking  by  twisting, 
is  proportional  to  the  cube  of  their  diameter.  Their  stiffness  or  resistance  to 
bending  is  proportional  to  the  fourth  power  of  their  diameters,  and  inversely 
proportional  to  the  cube  of  the  lengths  of  their  spans.  No  simple  general 
formula  can  be  given  that  will  safely  apply  to  enmne  and  other  shafting 
that  is  subjected  to  the  bending  stresses  produced  by  overhung  cranks,  the 
weight  of  heavy  flywheels,  the  pull  of  large  belts,  or  to  severe  shocks  pro- 
duced by  the  intermittent  action  of  the  power  or  load.  The  calculations  for 
such  shafts  should  always  be  based  on  the  special  conditions  involved. 

In  the  following  table  is  given  the  maximum  distance  between  the  bear- 
ings of  some  continuous  shafts  that  are  used  for  the  transmission  of  power. 

Pulleys  from  which  considerable  power  is  to  be  taken  should  always 
be  placed  as  close  to  a bearing  as  possible. 

The  diameters  of  the  different  lengths  of  shafts  composing  a line  of  shaft- 
ing may  be  proportional  to  the  quantity  of  power  delivered  by  each  respective 
length.  In  this  connection,  the  positions  of  the  various  pulleys  depend 


WEIGHT  OF  CASTINGS. 


Ill 


on  the  distance  between  the  pulley  and  the  bearing,  and  on  the  amount  of 
power  given  off  by  the  pulleys.  Suppose,  for  example,  that  a piece  of  shaft- 
ing delivers  a certain  amount  of 
power;  then,  it  is  obvious  that  the 
shaft  will  deflect  or  bend  less  if  the 
pulley  transmitting  that  power  be 
placed  close  to  a hanger  or  bear- 
ing, than  if  it  be  placed  midway 
between  the  two  hangers  or  bear- 
ings. It  is  impossible  to  give  any 
rule  for  the  proper  distance  of  bear- 
ings that  could  be  used  univer- 
sally, as  in  some  cases  the  require- 
ments demand  that  the  bearings 
be  nearer  together  than  in  others. 

If  the  work  done  by  a line  of  shaft- 
ing. is  distributed  quite  equally 
along  its  entire  length,  and  the 
power  can  be  applied  near  the 
middle,  the  strength  of  the  shaft 
need  be  only  half  as  great  as  would 
be  required  if  the  power  were  applied  at  one  end  of  the  shaft. 

WEIGHT  OF  CASTINGS. 

To  Find  the  Approximate  Weight  of  a Casting.— For  iron,  multiply  the  weight 
of  the  pattern  by  20.  Copper  is  I heavier;  lead,  f heavier;  brass,  \ heavier; 
and  zinc  is  as  heavy. 


Diameter 
of  Shaft. 
Inches. 

Distance  Between  Bearings. 
Feet. 

Wrought-Iron 

Shaft. 

Steel  Shaft. 

2 

11 

11.50 

3 

13 

13.75 

4 

15 

15.75 

5 

17 

18.25 

6 

19 

20.00 

7 

21 

22.25 

8 

23 

24.00 

9 

25 

26.00 

Thickness 

or 

Diameter. 

Inches. 

Weight  of 
a Square 
Foot. 
Pounds. 

Weight  of  a 
Square  Bar 

1 Ft.  Long. 
Pounds. 

Weight  of  a 
Round  Bar 

1 Ft.  Long. 
Pounds. 

Thickness 

or 

Diameter. 

Inches. 

Weight  of 
a Square 
Foot. 
Pounds. 

Weight  of  a 
Square  Bar 

1 Ft.  Long. 
Pounds. 

Weight  of  a 
Round  Bar 

1 Ft.  Long. 
Pounds. 

JL 

9.375 

.195 

.154 

4i 

168.7 

63.33 

49.71 

f 

14.06 

.440 

.346 

4f 

173.4 

66.86 

52.52 

1 

3 

18.75 

.781 

.610 

4f 

178.1 

70.52 

55.39 

I 

23.44 

1.221 

.959 

4f 

182.8 

74.27 

58.34 

f 

28.12 

1.758 

1.381 

5 

187.5 

78.12 

61.37 

32.81 

2.393 

1.880 

5i 

196.9 

86.14 

67.65 

l" 

37.50 

3.125 

2.455 

206.2 

94.54 

74.26 

1? 

42.19 

3.955 

3.107 

215.6 

103.3 

81.16 

It 

46.87 

4.883 

3.835 

6 

225.0 

112.5 

88.36 

If 

51.57 

5.909 

4.640 

6i 

234.4 

122.1 

95.89 

u 

56.26 

7.033 

5.523 

6i 

243.8 

132.0 

103.7 

If 

60.94 

8.253 

6.484 

6^ 

253.1 

142.4 

111.9 

u 

65.63 

9.572 

7.518 

7 

262.5 

153.2 

120.2 

If 

70.32 

10.99 

8.630 

7t 

271.9 

164.2 

129.0 

2 

75.01 

12.50 

9.821 

7i 

281.3 

175.8 

138.1 

79.70 

14.11 

11.09 

7f 

290.7 

187.7 

147.4 

2i 

84.40 

15.83 

12.43 

8 

300.0 

200.1 

157.0 

2f 

89.07 

17.63 

13.85 

8t 

309.4 

212.7 

167.0 

2i 

93.75 

19.54 

15.34 

84 

318.8 

225.8 

177.3 

2f 

98.44 

21.54 

16.56 

8f 

328.2 

239.3 

187.9 

2f 

103.2 

23.64 

18.56 

9 

337.4 

253.1 

198.8 

2f 

107.8 

25.84 

20.29 

9i 

346.8 

267.4 

210.0 

3 

112.6 

28.13 

22.10 

9i 

356.2 

282.1 

221.5 

i| 

117.3 

30.52 

23.97 

9f 

365.6 

297.0 

233.3 

121.8 

33.01 

25.93 

10 

375.0 

312.5 

245.5 

3f 

126.5 

35.60 

27.95 

lOi 

384.4 

328.4 

257.8 

3f 

131.2 

38.28 

30.07 

lOi 

393.7 

344.5 

270.6 

3f 

135.9 

41.07 

32.25 

lOJ 

403.1 

361.2 

283.7 

3f 

140.6 

43.95 

34.51 

11 

412.5 

378.2 

297.0 

3f 

145.3 

46.93 

36.85 

lU 

421.9 

395.5 

310.6 

4 

150.0 

50.01 

39.27 

IH 

431.2 

413.3 

324.6 

4i 

154.7 

53.18 

41.77 

Ilf 

440.6 

431.4 

338.8 

4f 

4f 

159.3 

164.0 

56.46 

59.82 

44.33 

46.99 

12 

450.0 

450.0 

353.4 

112 


WEIGHT  OF  MATERIALS, 


WEIGHTS  OF  SHEETS  AND  PLATES  OF  STEEL,  WROUGHT  IRON, 
COPPER,  AND  BRASS. 

(Cambria  Steel  Co.) 

American,  or  Brown  Sharpe,  Gauge. 


No. 

of 

Gauge. 

Thickness. 

Inch. 

Weight  Per  Square  Foot. 

Steel. 

Iron. 

Copper. 

Brass. 

0000 

.460000 

18.7680 

18.4000 

20.8380 

19.6880 

oao 

.409642 

16.7134 

16.3857 

18.5568 

17.5327 

00 

.364796 

14.8837 

14.5918 

16.5253 

15.6133 

0 

.324861 

13.2543 

12.9944 

14.7162 

13.9041 

1 

.289297 

11.8033 

11.5719 

13.1052 

12.3819 

2 

.257627 

10.5112 

10.3051 

11.6705 

11.0264 

3 

.229423 

9.3605 

9.1769 

10.3929 

9.8193 

4 

.204307 

8.3357 

8.1723 

9.2551 

8.7443 

5 

.181940 

7.4232 

7.2776 

8.2419 

7.7870 

6 

.162023 

6.6105 

6.4809 

7.3396 

6.9346 

7 

.144285 

5.8868 

5.7714 

6.5361 

6.1754 

8 

.128490 

5.2424 

5.1396 

5.8206 

5.4994 

9 

.114423 

4.6685 

4.5769 

5.1834 

4.8973 

10 

.101897 

4.1574 

4.0759 

4.6159 

4.3612 

11 

.090742 

3.7023 

3.6297 

4.1106 

3.8838 

12 

.080808 

3.2970 

3.2323 

3.6606 

3.4586 

13 

.071962 

2.9360 

2.8785 

3.2599 

3.0800 

14 

.064084 

2.6146 

2.5634 

2.9030 

2.7428 

15 

.057068 

2.3284 

2.2827 

2.5852 

2.4425 

16 

.050821 

2.0735 

2.0328 

2.3022 

2.1751 

17 

.045257 

1.8465 

1.8103 

2.0501 

1.9370 

18 

.040303 

1.6444 

1.6121 

1.8257 

1.7250 

19 

.035890 

1.4643 

1.4356 

1.6258 

1.5361 

20 

.031961 

1.3040 

1.2784 

1.4478 

1.3679 

21 

.028462 

1.1612 

1.1385 

1.2893 

1.2182 

22 

.025346 

1.0341 

1.0138 

1.1482 

1.0848 

23 

.022572 

.92094 

.90288 

1.0225 

.96608 

24 

.020101 

.82012. 

.80404 

.91058 

.86032 

25 

.017900 

.73032 

.71600 

.81087 

.76612 

26 

.015941 

.65039 

.63764 

.72213 

.68227 

27 

.014195 

.57916 

.56780 

.64303 

.60755 

28 

.012641 

.51575 

.50564 

.57264 

.54103 

29 

.011257 

.45929 

.45028 

.50994 

.48180 

30 

.010025 

.40902 

.40100 

.4M13 

.42907 

31 

.008928 

.36426 

.35712 

.40444 

.38212 

32 

.007950 

.32436 

.31800 

.36014 

.34026 

33 

.007080 

.28886 

.28320 

.32072 

.30302 

34 

.006305 

.25724 

.25220 

.28562 

.26985 

'35 

.005615 

.22909 

.22460 

.25436 

.‘21032 

36 

.005000 

.20400 

.20000 

.22650 

.21400 

37 

.004453 

.18168 

.17812 

.20172 

.19059 

38 

.003965 

.16177 

.15860 

.17961 

.16970 

39 

.003531 

.14406 

.14124 

.15995 

.15113 

40 

.003144 

.12828 

• .12576 

.14242 

.13456 

CAST-IRON  PIPE. 


113 


WEIGHT  OF  CAST-IRON  PIPE  PER  FOOT  IN  POUNDS. 

These  weights  are  for  plain  pipe.  For  hautboy  pipe,  add  8 in.  in  length 
for  each  joint.  For  copper,  add  for  lead,  for  welded  iron, 


Diam- 


Thickness  of  Pipe.  Inches. 


Bore. 

Inches. 

i 

f 

a 

1 

1 

8 

1 

li 

li 

It 

li 

If 

2 

1 

3.07 

5.07 

7.38 

li 

3.69 

6.00 

8.61 

li 

4.30 

6.92 

9.84 

U 

4.92 

7.84 

11.10 

2 

5.53 

8.76 

12.30 

16.2 

2i 

6.15 

9.69 

13.50 

17.7 

2i 

6.76 

10.60 

14.80 

19.2 

24.0 

2^ 

7.37 

11.50 

16.00 

20.8 

25.9 

3 

7.98 

12.50 

17.20 

22.3 

27.7 

33.4 

9.21 

14.30 

19.70 

25.4 

31.4 

37.7 

4 

10.30 

16.10 

22.20 

28.5 

35.1 

42.0 

4i 

11.70 

18.00 

24.60 

31.5 

38.8 

46.3 

5 

12.90 

19.80 

27.10 

34.6 

42.5 

50.6 

14.20 

21.70 

29.50 

37.7 

46.1 

54.9 

6 

15.40 

23.50 

32.00 

40.8 

49.8 

59.2 

68.9 

16.60 

25.40 

34.50 

43.8 

53.5 

63.5 

73.8 

84.4 

7 

17.80 

27.20 

36.90 

46.9 

57.2 

67.8 

78.7 

89.4 

n 

19.10 

29.10 

39.40 

50.0 

60.9 

72.1 

83.7 

95.5 

108 

8 

20.30 

30.90 

41.80 

53.1 

64.6 

76.4 

88.6 

101.0 

114 

127 

21.50 

32.80 

44.30 

56.1 

68.3 

80.7 

93.5 

107.0 

120 

134 

148 

9 

22.80 

34.60 

46.80 

59.2 

72.0 

85.1 

98.4 

112.0 

126 

140 

155 

9i 

24.00 

36.40 

49.20 

62.3 

75.7 

89.3 

103.0 

118.0 

132 

147 

163 

10 

25.10 

38.30 

51.70 

65.3 

79.4 

93.6 

108.0 

123.0 

138 

164 

170 

202 

11 

27.60 

42.00 

56.60 

71.5 

86.7 

102.0 

118.0 

134.0 

151 

168 

185 

220 

12 

30.00 

45.70 

61.50 

77.7 

94.1 

111.0 

128.0 

145.0 

163 

181 

199 

237 

275 

13 

32.50 

49.40 

66.40 

83.8 

102.0 

120.0 

138.0 

156.0 

175 

195 

214 

254 

294 

14 

35.00 

53.10 

71.40 

89.4 

109.0 

128.0 

148.0 

168.0 

188 

208 

229 

271 

314 

15 

37.40 

56.70 

76.30 

96.1 

116.0 

137.0 

158.0 

179.0 

200 

222 

244 

289 

334 

16 

39.10 

60.40 

81.20 

102.0 

124.0 

145.0 

167.0 

190.0 

212 

235 

258 

306 

353 

17 

42.30 

64.10 

86.10 

108.0 

131.0 

154.0 

177.0 

201.0 

225 

249 

273 

323 

373 

18 

44.80 

67.80 

91.00 

115.0 

139.0 

163.0 

187.0 

212.0 

237 

262 

288 

340 

393 

19 

47.30 

71.50 

96.00 

121.0 

146.0 

171.0 

197.0 

223.0 

249 

276 

303 

357 

412 

20 

49.70 

75.20 

101.00 

127.0 

153.0 

180.0 

207.0 

234.0 

261 

289 

317 

375 

432 

21 

52.20 

78.90 

106.00 

133.0 

161.0 

188.0 

217.0 

245.0 

274 

303 

332 

392 

452 

22 

54.60 

82.60 

111.00 

139.0 

168.0 

196.0 

227.0 

256.0 

286 

316 

347 

409 

471 

23 

57.10 

86.30 

116.00 

145.0 

175.0 

206.0 

236.0 

267.0 

298 

330 

362 

426 

491 

24 

59.60 

89.90 

121.00 

152.0 

183.0 

214.0 

246.0 

278.0 

311 

343 

375 

444 

511 

25 

62.00 

93.60 

126.00 

158.0 

190.0 

223.0 

256.0 

289.0 

323 

357 

391 

461 

531 

26 

64.50 

97.30 

131.00 

164.0 

198.0 

231.0 

266.0 

300.0 

335 

370 

406 

478 

550 

27 

66.90 

101.00 

135.00 

170.0 

205.0 

240.0 

276.0 

311.0 

348 

384 

421 

495 

570 

28 

69.40 

105.00 

140.00 

176.0 

212.0 

249.0 

286.0 

323.0 

360 

397 

436 

512 

590 

29 

71.80 

109.00 

145.00 

182.0 

220.0 

257.0 

295.0 

334.0 

372 

411 

450 

530 

609 

30 

74.20 

112.00 

150.00 

188.0 

227.0 

266.0 

305.0 

345.0 

384 

424 

465 

547 

629 

DIAMETER  AND  NUMBER  OF  WOOD  SCREWS. 


Formulas  for  Wood  Screws. 

No. 

Diameter. 

No. 

Diameter. 

No. 

Diameter. 

N = number 

0 

.056 

11 

.201 

22 

.347 

D = diameter 

1 

.069 

12 

.215 

23 

.361 

n = {NX  .01325)  + .056 

2 

.082 

13 

.228 

24 

.374 

Z)  — .056 

3 

.096 

14 

.241 

25 

.387  • 

.01325 

4 

.109 

15 

.255 

26 

.401 

5 

.122 

16 

.268 

27 

.414 

6 

.135 

17 

.281 

28 

.427 

7 

.149 

18 

.293 

29 

.440 

8 

.162 

19 

.308 

30 

.453 

9 

.175 

20 

.321 

10 

.188 

21 

.334 

114 


WEIGHT  OF  MATERIALS. 


WEIGHT  OF  WROUGHT  IRON. 

The  following  table  is  for  wrought  iron.  Multiply  by  .95  for  weight  of  cast 
iron;  by  1.02  for  steel;  by  1.16  for  copper;  by  1.09  for  brass;  by  1.48  for  lead. 


Thickness 

or 

Diameter. 

Inches. 

Weight 
of  a 

Square  Foot. 
Pounds. 

Weight  of  a 
Square  Bar 
1 Ft.  Long: 
Pounds. 

Weight  of  a 
Round  Bar 

1 Ft.  Long. 
Pounds. 

Thickness 

or 

Diameter. 

Inches. 

Weight 
of  a 

Square  Foot. 
Pounds. 

Weight  of  a 
Square  Bar 

1 Ft.  Long. 
Pounds. 

Weight  of  a 
Round  Bar 
1 Ft.  Long. 
Pounds. 

i 

5.052 

.0526 

.0414 

41 

176.8 

64.47 

50.63 

I 

10.10 

.2105 

.1653 

4| 

181.9 

68.20 

53.57 

f 

15.16 

.4736 

.3720 

41 

186.9 

72.05 

56.59 

20.21 

.8420 

.6613 

4^ 

192.0 

75.99 

59.69 

25.26 

1.316 

1.033 

4| 

197.0 

80.05 

62.87 

30.31 

1.895 

1.488 

5 

202.1 

84.20 

66.13 

35.37 

2.579 

2.025 

. 5i 

212.2 

92.83 

72.91 

1 

40.42 

3.368 

2.645 

5^ 

222.3 

101.9 

80.02 

n 

45.47 

4.263 

3.348 

232.4 

111.4 

87.46 

u 

50.52 

5.263 

4.133 

6 

242.5 

121.3 

95.23 

If 

55.57 

6.368 

5.001 

6i 

252.6 

131.6 

103.3 

u 

60.63 

7.578 

5.952 

6i 

262.7 

142.3 

111.8 

u 

65.68 

8.893 

6.985 

6^ 

272.8 

153.5 

120.5 

u 

70.73 

10.31 

8.101 

7 

282.9 

165.0 

129.6 

u 

75.78 

11.84 

9.300 

7i 

293.0 

177.0 

139.0 

2 

80.83 

13.47 

10.58 

n 

303.1 

189.5 

148.8 

21 

85.89 

15.21 

11.95 

n 

313.2 

202.3 

158.9 

2i 

90.94 

17.05 

13.39 

8 

323.3 

215.6 

169.3 

2f 

95.99 

19.00 

14.92 

333.4 

229.3 

180.1 

21 

101.0 

21.05 

16.53 

8i 

343.5 

243.4 

191.1 

2f 

106.1 

23.21 

18.23 

8f 

353.6 

247.9 

202.5 

21 

111.2 

25.47 

20.01 

9 

363.8 

272.8 

214.3 

21- 

116.2 

27.84 

21.87 

n 

373.9 

288.2 

226.3  ■ 

3 

121.3 

30.31 

23.81 

9i 

384.0 

304.0 

238.7 

31 

126.3 

32.89 

25.83 

9f 

394.1 

320.2 

251.5 

31 

131.4 

35.57 

27.94 

10 

404.2 

336.8 

264.5 

31 

136.4 

38.37 

30.13 

m 

414.3 

353.9 

277.9 

31 

141.5 

41.26 

32.41 

lOi 

424.4 

371.3 

291.6 

31 

146.5 

44.26 

34.76 

10^ 

434.5 

389.2 

305.7 

31 

151.6 

47.37 

37.20 

11 

444.6 

407.5 

320.1 

31 

156.6 

50.57 

39.72 

lU 

454.7 

426.3 

334.8 

4 

161.7 

53.89 

42.33 

Hi 

464.8 

445.4 

349.8 

41 

166.7 

57.31 

45.01 

lU 

474.9 

465.0 

365.2 

41 

171.8 

60.84 

47.78 

12 

485.0 

485.0 

380.9 

Spikes  and  Nails. 


Standard  Steel-Wire  Nails. 

Sfiipl.WirA  Snilrpa 

PnTTiTnnn  Trnn  Vnila 

Sizes. 

Length. 

Common. 

Finishing. 

In. 

Diam. 

In. 

No.  per 
Lb. 

Diam. 

In. 

No.  per 
Lb. 

Length. 

In. 

Diam. 

In. 

No.  per 
Lb. 

Size. 

Length. 

In. 

No.  per 
Lb. 

2d 

1 

.0524 

1,060 

.0453 

1,.558 

3 

.1620 

41 

2d 

1 

800 

3d 

li 

.0588 

640 

.0508 

913 

3i 

.1819 

30 

3d 

li 

400 

4d 

li 

.0720 

380 

.0508 

761 

4 

.2043 

23 

4d 

li 

300 

5d 

u 

.0764 

275 

.0571 

500 

4i 

.2294 

17 

5d 

If 

200 

6d 

2 

.0808 

210 

.0641 

a50 

' 5 

.2576 

13 

6d 

2 

150 

7d 

2i 

.0858 

160 

.0641 

315 

5i 

.2893 

11 

7d 

2i 

120 

8d 

2i 

.0935 

115 

.0720 

214 

6 

.2893 

10 

8d 

2i 

85 

9d 

2f 

.0963 

93 

.0720 

195 

6i 

.2249 

7i 

9d 

2f 

75 

lOd 

3 

.1082 

77 

.0808 

137 

7 

.2249 

7 

lOd 

3 

60 

12d 

3i 

.1144 

60 

.0808 

127 

8 

.3648 

5 

12d 

3i 

50 

16d 

20d 

30d 

40d 

50d 

60d 

3i 

4 

4i 

5 

5i 

6 

.1285 

.1620 

.1819 

.2043 

.2294 

.2576 

48 

31 

22 

17 

13 

11 

.0907 

.1019 

90 

62 

9 

.3&48 

4i 

16d 

20d 

30d 

40d 

50d 

60d 

3i 

4 

4i 

5 

5i' 

6 

40 

20 

16 

14 

11 

8 

WROUGHT  IRON. 


115 


Weight,  in  Pounds,  of  1 Lineal  Foot  of  Wrought  Iron— Flat. 


Multiply  by  .95  for  weight  of  cast  ironi  by  1.02  for  weight  of  steel;  by  1.16 
for  copper;  by  1.09  for  brass;  by  1.48  for  lead. 


Size. 

Inches. 

Weight. 

Pounds. 

Size. 

Inches. 

Weight. 

Pounds. 

Size. 

Inches. 

Weight. 

Pounds. 

1 Xi 

0.85 

5iXf 

6.65 

4 Xf 

8.45 

liXi 

1.06 

5iXf 

6.97 

4iXf 

8.98 

liXi 

» 1.27 

6J  XI 

7.29 

4iXf 

9.51 

UXi 

1.48 

6 Xf 

7.60 

4f  Xf 

10.03 

2 X i 

1.69 

5 Xf 

10.56 

2iXi 

1.90 

1 Xi 

1.69 

5iX  f 

11.09 

2iXi 

2.11 

li  x:i 

2.11 

5i  X f 

11.62 

2f  Xi 

2.32 

UXi 

: 2.53 

5f  Xf 

12.15 

3 Xi 

2.53 

If  Xi 

2.96 

6 Xf 

12.67 

3iXi 

2.75 

2 Xi 

3.38 

3iXi 

2.96 

2iXi 

3.80 

1 Xf 

2.53 

3^Xi 

3.17 

2iXi 

4.22 

liXf 

3.17 

4 Xi 

3.38 

2iXi 

4.65 

liXf 

3.80 

4iXi 

3.59 

3 Xi 

5.07 

If  Xf 

4.44 

4iXi 

3.80 

3iXi 

5.49 

2 Xf 

5.07 

4iXi 

4.01 

3iXi 

5.92 

2iXf 

5.70 

5 Xi 

4.22 

3f  Xi 

6.33 

2iX  f 

6.33 

5iXi 

4.44 

4 Xi 

6.76 

2f  Xf 

6.97 

5iXi 

4.65 

4iXi 

7.18 

3 Xf 

7.60 

5iXi 

4.86 

4iXi 

7.60 

3iX  f 

8.24 

6 Xi 

5.07 

4f  Xi 

8.03 

3iXf  ' 

8.87 

5 Xi 

8.45 

3f  Xf 

9.51 

1 Xi 

1.27 

5iXi 

8.87 

4 Xf 

10.14 

liXf 

1.58 

5iX  i 

9.30 

4iX  f 

10.77 

UXi 

1.90 

5f  Xi 

9.72 

4iXf 

11.41 

liXi 

2.22 

6 Xi 

10.14 

4f  X f 

12.04 

2 Xf 

2.53 

5 X f 

12.67 

2iXf 

2.85 

1 Xf 

2.11 

5iXf 

13.31 

2i  X f 

3.17 

liXf 

2.64 

5iXf 

13.94 

2iXf 

3.49 

UXf 

3.17 

5f  Xf 

14.57 

3 Xi 

3.80 

If  Xf 

3.70 

6 Xf 

15.21 

3iX  f 

4.12 

2 Xf 

4.22 

3iXI 

4.44 

2iXf 

4.75 

liXl 

5.07 

3iXi 

4.75 

2iXf 

5.28 

2 XI 

6.76 

4X1 

5.07 

2f  Xf 

5.81 

3 XI 

10.14 

4iXf 

5.39 

3 Xf 

6.33 

4 XI 

13.52 

4iXI 

5.70 

3iX  f 

6.87 

5 XI 

16.90 

4iXf 

6.02 

3i  X f 

7.39 

6 XI 

20.28 

5 Xf 

6.33 

3f  Xf 

7.92 

7 XI 

23.66 

Strength  of  Metals  in  Pounds  per  Square  Inch. 


Material. 

Ultimate 

Tensile. 

Ultimate 

Compres- 

sion. 

Ultimate 

Shearing. 

Modulus 

of 

Rupture. 

Modulus 

of 

Elasticity. 

Millions. 

Wrought  iron 

50,000 

44,000 

44,000 

48,000 

27 

Shape  iron 

48,000 

26 

Structural  steel | 

60,000 

65,000 

52,000 

52,000 

60,000 

29 

Cast  iron  

18,000 

81,000 

25,000 

45,000 

12 

Steel,  castings 

70,000 

70,000 

60,000 

70,000 

30 

Brass,  cast 

24,000 

♦30,000 

36,000 

20,000 

9 

Bronze,  phosphor 

50,000 

14 

Bronze,  aluminum 

75,000 

120,000 

Aluminum,  commercial 

15,000 

12,000 

12,000 

11 

♦ Unit  stress  producing  10^  reduction  in  original  length. 


116 


WEIGHT  OF  MATERIALS. 


Weight  of  Wrought-Iron  Boltheads,  Nuts,  and  Washers. 


Diameter  of 
Bolt. 
Inches. 

Hexagon  Heads 
and  Nuts. 

Per  Pair. 

Square  Heads 
and  Nuts. 

Per  Pair. 

Round  Washers. 
Per  Pair. 

x 

20  to  a lb. 

16  to  a lb. 

20  to  a lb. 

1 

10  to  a lb. 

8f  to  a lb. 

10  to  a lb. 

1 

5 to  a lb. 

4|  to  a lb. 

5 to  a lb. 

1 

2f  to  a lb. 

2i  to  a lb. 

3 to  a lb. 

f 

2 to  a lb. 

0.56  lb. 

0.63  lb. 

0.77  lb.  . 

0.88  lb. 

0.77  lb. 

l" 

1.251b. 

1.31  lb. 

1.25  lb. 

11 

1.75  lb. 

2.10  lb. 

3.751b. 

11 

2.13  lb. 

2.56  lb. 

2.25  lb. 

If 

3.00  lb. 

3.60  lb. 

3.25  lb. 

If 

3.75  lb. 

4.42  lb. 

4.25  lb. 

If 

4.75  lb. 

5.70  lb. 

5.25  lb. 

If 

5.75  lb. 

7.00  lb. 

6.50  lb. 

If 

7.27  lb. 

8.72  lb. 

8.00  lb. 

2 

8.75  lb. 

10.50  lb. 

9.60  lb. 

Weight  of  100  Bolts  With  Square  Heads  and  Nuts. 
{The  Carnegie  Steel  Co.,  Limited.) 


Diameter  of  Bolts. 


Length 


Head  to 
Point. 

f" 

Lb. 

5 // 

a. 

L 

K 

L 

6/r 

£b. 

ti 

i" 

Lb. 

1" 

Lb. 

If 

4.0 

7.0 

10.5 

15.2 

22.5 

39.5 

63.0 

If 

4.4 

7.5 

11.3 

16.3 

23.8 

41.6 

66.0 

2 

4.8 

8.0 

12.0 

17.4 

25.2 

43.8 

69.0 

109.0 

163 

2i 

5.2 

8.5 

12.8 

18-5 

26.5 

45.8 

72.0 

113.3 

169 

2f 

5.5 

9.0 

13.5 

19.6 

27.8 

48.0 

75.0 

117.5 

174 

2f 

5.8 

9.5 

14.3 

20.7 

29.1 

50.1 

78.0 

121.8 

180 

3 

6.3 

10.0 

15.0 

21.8 

30.5 

52.3 

81.0 

126.0 

185 

3f 

7.0 

11.0 

16.5 

24.0 

33.1 

56.5 

87.0 

134.3 

196 

4 

7.8 

12.0 

18.0 

26.2 

35.8 

60.8 

93.1 

142.5 

207 

4f 

8.5 

13.0 

19.5 

28.4 

38.4 

65.0 

99.1 

151.0 

218 

5 

9.3 

14.0 

21.0 

30.6 

41.1 

69.3 

105.2 

159.6 

229 

5f 

10.0 

15.0 

22.5 

32.8 

43.7 

73.5 

111.3 

168.0 

240 

6 

10.8 

16.0 

24.0 

35.0 

46.4 

77.8 

117.3 

176.6 

251 

6f 

25.5 

37.2 

49.0 

82.0 

123.4 

185.0 

262 

7 

27.0 

39.4 

51.7 

86.3 

129.4 

193.7 

273 

7i 

28.5 

41.6 

54.3 

90.5 

135.0 

202.0 

284 

8 

30.0 

43.8 

59.6 

94.8 

141.5 

210.7 

295 

9 

' 

46.0 

64.9 

103.3 

153.6 

227.8 

317 

10 

48.2 

70.2 

111.8 

165.7 

224.8 

339 

11 

50.4 

75.5 

120.3 

177.8 

261.9 

360 

12 

52.6 

80.8 

128.8 

189.9 

278.9 

382 

13 

86.1 

137.3 

202.0 

296.0 

404 

14 

91.4 

145.8 

214.1 

313.0 

426 

15 

96.7 

154.3 

226.2 

330.1 

448 

16 

102.0 

162.8 

238.3 

347.1 

470 

17 

107.3 

171.0 

250.4 

364.2 

492 

18 

112.6 

179.5 

262.6 

381.2 

514 

19 

117.9 

188.0 

274.7 

398.3 

536 

20 

123.2 

206.5 

286.8 

415.3 

658 

Per  Inch 
Addit’  a1. 

1.4 

2.1 

3.1 

4.2 

5.5 

8.5 

12.3 

16.7 

21.8 

RAILROAD  IRON. 


117 


IRON  REQUIRED  FOR  ONE  MILE  OP  TRACK. 

Tons  of  Iron. 


Rule. — To  find  the  number  of  tons  of  rails  to  the  mile,  divide  the  weightier  ya^rd 
by  7,  and  multiply  by  11.  Thus,  for  56-pound  rail,  divide  56  by  7 equal  8,  multi- 
plied by  11  equal  88  tons,  for  1 mile  of  single  track. 


Weight  of 
Rail  per  Yard. 
Pounds. 

Tons  per  Mile. 

Weight  of 
Rail  per  Yard. 
Pounds. 

Tons  per  Mile. 

Tons. 

Pounds. 

Tons. 

Pounds. 

12 

18 

1,920 

45 

70 

1,600 

14 

22 

48 

75 

960 

16 

25 

320 

50 

78 

1,280 

18 

28 

640 

52 

81 

1,600 

20 

31 

960 

56 

88 

22 

34 

1,280 

57 

89 

1,280 

25 

39 

640 

60 

94 

640 

26 

40 

1,920 

62 

97 

960 

27 

42 

960 

64 

100 

1,280 

28 

44 

65 

102 

320 

30 

47 

320 

68 

106 

1,920 

33 

51 

1,920 

70 

110 

35 

55 

72 

113 

320 

40 

62 

1,920 

76 

119 

960 

Number  of  Rails,  Splices,  and  Bolts  per  Mile  of  Track. 


Length  of 
Rail.  Feet. 

No.  of  Rails 
per  Mile. 

No.  of  Splices. 

No.  of  Bolts, 

4 to  Each 
Joint. 

No.  of  Bolts, 

6 to  Each 
Joint. 

18 

584 

1,168 

2,336 

3,504 

20 

528 

1,056 

2,112 

3,168 

21 

503 

1,006 

2,012 

3,018 

22 

480 

960 

1,920 

2,880 

24 

440 

880 

1,760 

2,640 

25 

422 

844 

1,688 

2,532 

26 

406 

812 

1,624 

2,436 

27 

391 

782 

1,564 

2,346 

28 

377 

754 

1,508 

2,262 

30 

352 

704 

1,408 

2,112 

Railroad  Spikes  per  Mile  of  Track. 


Size  Measured 
Under  Head. 

Average  No. 
per  Keg 
of  200  Lb. 

Ties  2 Ft.  Between  Centers, 
4 Spikes  to  a Tie. 

Rails  Used. 
Pounds  per 

Inches. 

Pounds. 

Kegs. 

Yard. 

X 

375 

5,870 

294 

45  to  70 

5 XA 

400 

5,170 

26 

40  to  56 

5 Xi 

450 

4,660 

234 

35  to  40 

44  XU 

530 

3,960 

20 

28  to  35 

4 X4 

600 

3,520 

17f 

24  to  35 

4 X/s 

■ 680 

720 

3,110 

2,910 

154 

141 

1 20  to  30 

3iX/« 

4 XI 

900 

1,000 

2,350 

2,090 

11 

104 

1 16  to  25 

34  XI 

3 XI 

1,190 

1,240 

1,780 

1,710 

9 

84 

1 16  to  20 

24X1 

1,342 

1,575 

74 

12  to  16 

118 


WIRE  ROPES. 


WIRE  ROPES. 

Wire  ropes  for  mine  use  are  made  of  either  iron  or  steel,  and  are  gener- 
ally round.  Flat  wire  ropes  are  sometimes  used,  but  the  round  rope  is  the 
favorite  for  many  reasons,  and  is  generally  used  in  American  practice, 
excepting  in  some  of  the  deep  metal  mines  having  small  compartment  shafts. 

Taper  ropes  are  sometimes  used,  the  idea  being  to  produce  a rope  of  uni- 
form strength,  that  is,  to  have  it  less  strong  and  of  less  diameter  at  the  cage 
end,  where  the  load  is  least,  and  greater  in  strength  and  diameter  at  the 
drum  end,  where  the  load  is  greatest.  The  theory  is  correct,  and  some 
weight  of  rope  is  saved;  but  practically  there  is  not  much  advantage,  and  it 
is  doubtful  whether  taper  ropes  will  ever  be  generally  used.  The  long- 
established  conviction  that  the  best  of  all  ropes  for  colliery  use  is  a round 
one  made  of  steel  or  iron  has  never  been  overcome  and  probably  never 
will  be. 

Steel  ropes  are  in  most  respects  superior  to  iron  ropes,  and  are  therefore 
gaining  in  favor  every  year.  The  principal  advantage  of  a steel  rope  is  that 
it  has  a greater  strength  than  an  iron  rope  of  equal  diameter;  consequently, 
it  can  be  made  lighter  and  can  pass  around  pulleys  and  drums  with  less 
injury  than  an  iron  rope  of  equal  strength. 

In  fastening  a rope  to  a drum  there  is  often  a grievous  error  made.  Men 
who  w ill  not  think  of  passing  a rope  around  a pulley  of  too  small  diameter 
will  insert  it  in  the  drum  rim  in  such  a way 
as  to  make  a very  sharp  curve,  and  make  a 
weak  point  in  the  rope  that  would  not  other- 
wise exist.  In  the  accompanying  cut  (a) 
shows  the  right  and  {b)  the  wrong  way  of 
passing  the  rope  through  the  drum  rim.*  (a)  (h) 

The  securing  of  the  rope  to  the  drum  or 
the  drum  shaft  by  several  coils  around  each  is  unnecessary.  With  one  coil 
around  either  the  drum  or  the  shaft,  a pull  of  1 lb.  will  resist  a weight  of 
91b.;  if  two  coils,  a pull  of  1 lb.  will  resist  9 X 9,  or  81  lb.;  if  three  coils, 
9 X 9 X 9,  or  729  lb.;  and  so  on,  multiplying  the  former  result  by  9 for  each 
additional  coil. 

No  rope  should  be  subjected  to  a load  greater  than  the  safe  working 
strain.  There  is,  of  course,  in  all  cases,  a wide  margin  between  the  break- 
ing strain  and  the  working  load,  and  on  this  account  it  is  supposed  that  no 
risk  is  run  by  putting  on  a load  considerably  in  excess  of  the  maker’s  safe 
working  strain.  This  is  a mistake;  and  it  is  false  economy.  A rope  over- 
loaded IS  unduly  strained,  and,  although  showing  no  defect  at  the  moment, 
it  will  some  day  give  way  without  warning.  Drums  and  rope  pulleys 
should  have  as  great  diameters  as  the  engines  will  allow.  Ropes  should  be 
regularly  and  properly  greased.  This  can  best  be  done  with  brushes,  but 
brush  greasing  takes  considerable  time.  While  it  pays  in  the  long  run,  it  is 
not  always  convenient  to  use  brushes.  A fairly  good  and  cheap  arrange- 
ment for  greasing  ropes  is  to  make  a wooden  trough,  wide  at  top,  and  small 
enough  at  bottom  to  fit  loosely  around  the  rope.  Make  a mixture  of  1 
barrel  of  coal  tar  or  pitch  tar  to  1 bushel  of  fresh  slaked  lime,  and  boil  it 
well.  Then  fill  the  trough  with  this  mixture  and  run  the  rope  slowly 
through  it. 

A rope  should  not  be  changed  from  a large  drum  to  a small  one,  for  it 
will  not  work  so  well,  neither  will  it  last  as  long.  This  is  also  true,  but  in  a 
lesser  degree,  of  ropes  changed  from  a small  drum  to  a large  one.  After 
having  been  used  for  some  time  on  a drum,  the  rope  adapts  itself  to  that 
diameter  and  resents  a change.  Rope  sheaves  should  be  made  to  fit  the 
rope,  and  should  be  filled  in  with  well-seasoned  blocks  of  oak  or  other  hard 
wood,  set  on  end.  This  will  save  the  rope  and  increase  adhesion. 

Where  great  flexibility  is  required,  such  as  in  hoisting  ropes,  the  strands 
are  usually  made  up  of  19  wires  each,  while  haulage  ropes  have  but  7 wires 
to  the  strand;  yet,  both  kinds  have  6 strands.  A hemp  core  is  generally 
used,  and  in  some  cases  a core  is  also  placed  in  each  strand,  to  further  increase 
the  flexibility  of  the  rope. 

The  lay  of  the  rope  is  the  twist  or  pitch  of  the  wires  in  the  strand,  or  of 
the  strands  in  the  rope.  As  the  lay  of  the  wires  is  less  than  that  of  the 
strands,  each  wire  is  exposed  to  external  wear  for  short  distances  at  intervals 


WIRE  ROPES. 


119 


along  the  rope.  In  the  ordinary  lay,  Fig.  (a),  the  wires  are  twisted  in 
the  opposite  direction  to  the  strands.  This  method  prevents  the  rope  from 
untwisting  when  in  use,  and  the  wires  from  unraveling  when  they  are  worn 
through  or  broken  at  the  surface.  In  the  Lang  lay.  Fig.  (6),  the  wires 
are  twisted  in  the  same  direction  as  the  strands,  thus  giving  each  wire  a 
greater  wearing  surface,  while  the  rope  is  smoother  and  will  wear  longer. 
After  the  wires  begin  to  break,  unraveling  becomes  troublesome*  and  it  is 
more  difficult  to  splice  a Lang  lay  rope  than  an  ordinary  lay  one.  Hoisting 
ropes,  especially  those  used  to  raise  and  lower  men,  should  not  be  spliced. 
The  locked  wire  rope,  a cross-section  of  which  is  shown  in  Fig.  (c),  consists 
of  wires  of  special  cross-section  formed  in  concentric  layers.  The  lay  of 
the  inner  wires  is  opposite  to  that  of  the  outer  ones,  and  somewhat  longer. 
This  prevents  untwisting,  and  brings  the  greater  stress  upon  the  outside 


(a)  {b)  (c) 


layer,  which  is  supposed  to  give  way  first.  The  inside  layer,  although  inac- 
cessible, and  therefore  cannot  be  inspected  or  oiled,  can  be  relied  upon 
until  the  external  portion  of  the  rope  wears  out.  This  form  of  rope  has  a 
smooth  cylindrical  surface,  but  it  is  not  so  flexible  as  the  other  forms,  and  is 
most  suitable  for  haulage  purposes  or  bucket  transportation.  The  life  of  a 
steel  rope  depends  largely  on  the  conditions  to  which  it  is  subjected,  and  the 
care  it  receives.  At  some  mines  the  ropes  must  be  changed  every  six 
months,  while  at  others  the  ropes  last  for  one  year  and  longer.  Where  the 
rope  enters  the  socket  by  which  it  is  attached  to  the  cage  is  perhaps  the 
place  where  signs  of  weakness  will  first  appear.  This  point  should  be  fre- 
quently inspected,  and  a new  connection  made  every  two  or  three  months 
by  cutting  a few  feet  off  the  end  and  paying  it  out  from  the  drum  end. 


WEIGHTS  AND  STRENGTHS  OF  WIRE  ROPES. 

Flat  Ropes. 

{Trenton  Iron  Co.^  Trenton,  N.J.) 


Size.  Inches. 

Approximate 
Weight  per  Foot. 
Pounds. 

Breakin 

(Approximat 

Iron. 

g Stress, 
e.)  Pounds. 

Cast  Steel. 

2 Xf 

1.35 

20,000 

40,000 

2iXf 

1.70 

25,000 

50,000 

3 X% 

2.05 

30,000 

60,000 

31  Xf 

2.40 

35,000 

70,000 

4 Xf 

2.75 

40,000 

80,000 

5 Xf 

3.45 

50,000 

100,000 

6 Xf 

4.15 

60,000 

120,000 

3 Xf 

2.40 

37,500 

75,000 

3fXf 

2.85 

43,750 

87,500 

4 Xf 

3.30 

50,000 

100,000 

5 Xf 

4.20 

62,500 

125,000 

6 Xf 

5.10 

75,000 

150,000 

7 Xf 

6.00 

87,500 

175,000 

8 Xf 

6.90 

100,000 

200,000 

For  safe  working  load  allow  from  one-fifth  to  one-seventh  of  the  break- 
ing stress. 


120 


WIRE  ROPES. 


Composed  of  6 Strands  and  a Hemp  Center,  19  Wires  to  the  Strand. 
{John  A.  Roebling's  Sons  Co.,  Trenton,  N.  J.) 

Swedish  Iron. 


Trade 

Number. 

Diameter. 

Inches. 

Approximate 

Circumfer- 

ence. Inches. 

Weight  per 

Foot. 

Pounds. 

Approximate 

Breaking 

Strain.  Tons 

of  2,000  Lb. 

Allowable 

Working 

Strain.  Tons 

of  2,000  Lb. 

Minimum 

Size  of  Drum 

or  Sheave. 

Feet. 

1 

21 

71 

8.00 

78.0 

15.60 

13 

2 

2 

61 

6.30 

62.0 

12.40 

12 

8 

11 

51 

4.85 

48.0 

9.60 

10 

4 

If 

5 

4.15 

42.0 

8.40 

81 

5 

U 

41 

3.55 

36.0 

7.20 

71 

H 

41 

3.00 

31.0 

6.20 

7 

6 

11 

4 

2.45 

25.0 

6.00 

61 

7 

11 

31 

2.00 

21.0 

4.20 

6 

8 

1 

3 

1.58 

17.0 

3.40 

51 

9 

T 

21 

1.20 

13.0 

2.60 

41 

10 

1 

21 

.89 

9.7 

1.94 

4 

lOi 

% 

2 

.62 

6.8 

1.36 

31 

lOi 

11 

.50 

5.5 

1.10 

21 

10^ 

1 

11 

.39 

4.4 

.88 

21 

10a 

11 

.30 

3.4 

.68 

2 

105 

A 

11 

.22 

2.5 

.50 

H 

10c 

h 

1 

.15 

1.7 

.34 

1 

lOd 

i 

4 

1 

.10 

1.2 

.24 

1 

Cast  Steel. 


1 

21 

7f 

8.00 

156.0 

31.20 

81 

2 

2 

61 

6.30 

124.0 

24.80 

8 

3 

11 

51 

4.85 

96.0 

19.-20 

71 

4 

If 

5 

4.15 

84.0 

16.80 

61 

5 

11 

41 

3.55 

72.0 

14.40 

51 

51 

If 

41 

3.00 

62.0 

12.40 

51 

6 

11 

4 

2.45 

50.0 

10.00 

5 

7 

If 

31 

2.00 

42.0 

8.40 

41 

8 

1 

3 

1.58 

34.0 

6.80 

4 

9 

f 

21 

1.20 

26.0 

5.20 

31 

10 

1 

21 

.89 

19.4 

3.88 

3 

101 

f 

2 

.62 

13.6 

2.72 

21 

101 

11 

.50 

11.0 

2.20 

11 

101 

1 

11 

.39 

8.8 

1.76 

11 

10a 

'h 

11 

.30 

6.8 

1.36 

11 

106 

1 

If 

.22 

5.0 

1.00 

1 

10c 

1 

.15 

3.4 

.68 

1 

lOd 

\ 

4 

1 

.10 

2.4 

.48 

1 

PLOW-STEEL  ROPE. 

Wire  ropes  of  very  high  tensile  strength,  which  are  ordinarily  called 
“plow-steel  ropes,”  are  made  of  a high  grade  of  crucible  steel,  which, 
when  put  in  the  form  of  wire,  will  bear  a stress  of  from  100  to  150  tons  per 
square  inch.  Where  it  is  necessary  to  use  very  long  or  very  heavy  ropes,  a 
reduction  of  the  dead  weight  of  ropes  becomes  a matter  of  serious  consider- 
ation. It  is  advisable  to  reduce  all  bends  to  a minimum,  and  to  use  some- 
what larger  drums  or  sheaves  than  are  suitable  for  an  ordinary  crucible 
rope  having  a strength  of  60  to  80  tons  per  square  inch. 


WIRE  ROPES. 


121 


Plow-Steel  Rope— With  6 Strands  and  a Hemp  Center,  19  Wires  to 
THE  Strand. 


Trade 

Number. 

Diameter. 

Inches. 

Approximate 
Circumfer- 
ence. Inches. 

Weight  per 

Foot. 

Pounds. 

Approximate 

Breaking 

Strain.  Tons 

of  2,000  Lb. 

1 Allowable 

Working 

Strain.  Tons 

of  2,000  Lb. 

Minimum 

Size  of  Drum 

or  Sheave. 

Feet. 

21 

11.95 

305.00 

61.00 

11 

21 

71 

9.85 

254.00 

50.80 

10 

1 

21 

71 

8.00 

208.00 

41.60 

9 

2 

2 

61 

6.30 

165.00 

33.00 

8 

3 

If 

51 

4.85 

128.00 

25.60 

7i 

4 

If 

5 

4.15 

111.00 

22.20 

6 

5 

11 

4f 

3.55 

96.00 

19.20 

5f 

61 

If 

41 

3.00 

82.00 

16.40 

5i 

6 

11 

4 

2.45 

67.00 

13.40 

5 

7 

If 

31 

2.00 

56.00 

11.20 

8 

1 

3 

1.58 

44.00 

8.80 

4i 

9 

1 

2f 

1.20 

34.00 

6.80 

3f 

10 

f 

21 

.89 

25.00 

5.00 

3i 

101 

1 

2 

.62 

18.00 

3.60 

3 

lOi 

If 

.50 

14.50 

2.90 

2i 

m 

1 

11 

.39 

11.40 

2.28 

2 

lOa 

11 

.30 

8.85 

1.77 

la 

10b 

2. 

If 

.22 

6.55 

1.31 

1 

10c 

1 

.15 

4.50 

.90 

7 

8 

lOd 

4 

f 

.10 

3.00 

.60 

1 

TRANSMISSION  OR  HAULAGE  ROPE. 

Plow-Steel  Rope— With  7 Wires  to  the  Strand. 


11 

U 

4f 

3.55 

91.00 

18.20 

8i 

12 

If 

4i 

3.00 

78.00 

15.60 

8 

13 

If 

4 

2.45 

64.00 

12.80 

7i 

14 

H 

2.00 

53.00 

10.60 

6f 

15 

1 

3 

1.58 

42.00 

8.40 

6f 

16 

7 

J 

2f 

1.20 

32.00 

6.40 

5 

17 

f 

2i 

.89 

24.00 

4.80 

4 

18 

2i 

.75 

21.00 

4.20 

3f 

19 

f 

2 

.62 

17.00 

3.40 

3 

20 

* 

If 

.50 

14.00 

2.80 

2f 

21 

h 

If 

.39 

11.00 

2.20 

2f 

22 

If 

.30 

8.55 

1.71 

2 

23 

1 

If 

.22 

6.35 

1.27 

If 

24 

TJI 

1 

.15 

4.35 

.87 

If 

25 

y 

.125 

3.65 

.73 

1 

122 


WIRE  ROPES. 


TRANSMISSION  OR  HAULAGE  ROPE. 

Composed  of  6 Strands  and  a Hemp  Center,  7 Wires  to  the  Strand. 
Swedish  Iron. 


Trade 

Number. 

Diameter. 

Inches. 

Approximate 

Circumfer- 

ence. Inches. 

Weight  per 

Foot. 

Pounds. 

Approximate 

Breaking 

Strain.  Tons 

of  2,000  Lb. 

Allowable 

Working 

Strain.  Tons 

of  2,000  Lb. 

Minimum 

Size  of  Drum 

or  Sheave. 

Feet. 

11 

4f 

3.550 

34.00 

6.80 

13 

12 

If 

4i 

3.000 

29.00 

5.80 

12 

13 

li 

4 

2.450 

24.00 

4.80 

lOf 

14 

If 

2.000 

20.00 

4.00 

9i 

15 

1 

3 

1.580 

16.00 

3.20 

8i 

16 

8* 

1.200 

12.00 

2.40 

7i 

17 

.890 

9.30 

1.86 

6f 

18 

fi 

2? 

.750 

7.90 

1.58 

6 

19 

f 

2 

.620 

6.60 

1.32 

5i 

20 

If 

.500 

5.30 

1.06 

4i 

21 

9 

If 

.390 

4.20 

.84 

4 

22 

li 

.300 

3.30 

.66 

3i 

23 

f 

If 

.220 

2.40 

.48 

2f 

24 

1^ 

.150 

1.70 

.34 

2i 

25 

f 

.125 

1.40 

.28 

2i 

Cast  Steel. 


11 

If 

4f 

3.55 

68.00 

13.60 

8f 

12 

If 

4i 

3.00 

58.00 

11.60 

8 

13 

li 

4 

2.45 

48.00 

9.60 

7i 

14 

If 

3f 

2.00 

40.00 

8.00 

6i 

15 

1 

3 

1.58 

32.00 

6.40 

5f 

16 

1 

•2f 

1.20 

24.00 

4.80 

5 

17 

f 

2i 

.89 

18.60 

3.72 

4f 

18 

if 

2f 

.75 

15.80 

3.16 

4 

19 

8 

2 

.62 

13.20 

2.64 

3f 

20 

tV 

If 

.50 

10.60 

2.12 

3 

21 

i 

If 

.39 

8.40 

1.68 

2f 

22 

li 

.30 

6.60 

1.32 

2i 

23 

3. 

If 

.22 

4.80 

.96 

2 

24 

A 

1 

.15 

3.40 

.68 

If 

25 

37 

¥ 

.125 

2.80 

.56 

If 

The  rope  usually  employed  for  transmission  of  power  is  a seven-wire  iron 
rope.  Ropes  of  twelve  and  also  of  nineteen  wires  to  the  strand  are  frequently 
substituted,  where  it  is  impracticable  to  use  the  larger  sheaves  which  seven- 
wire  ropes  require.  The  driving  sheaves  should  always  be  lined  with  some 
flexible  material,  such  as  a packing  of  rubber  and  leather. 

The  shortest  practicable  span  is  found  by  experience  to  be  about  50  feet. 
The  following  table  gives  the  proper  deflections  at  center  of  span  to  secure 
the  most  economical  results: 

Table  of  Deflections. 


Span  in  feet 

50 

100 

150 

200 

250 

300 

350 

400 

450 

Deflection  in  feet 

0.17 

0.69 

1.56 

2.78 

4.34 

6.25 

8.52 

11.12 

14.07 

It  is  frequently  convenient  to  use  sheaves  of  different  sizes,  in  order  to 
obtain  the  requisite  speed  in  the  driven  mechanism.  In  such  cases  the 
power  transmitted  will  be  the  same  as  if  both  were  of  the  diameter  of  the 
smaller  sheave. 


WIRE  ROPES. 


122a 


HERCULES  WIRE  ROPE. 

{From  A.  Leschen  <Sc  Sons  Rope  Co.,  St.  Louis,  Mo.) 

Hercules  wire  rope  is  made  from  wire  specially  drawn  from  a patent 
tempered  steel  made  solely  for  this  brand  of  rope.  The  manufacturers  claim 
for  it  a combination  of  strength,  toughness,  pliability,  and  perfect  elastic 
properties.  It  can  be  used  over  the  same  drums  and  sheaves  as  ordinary 
wire  rope,  thus  making  unnecessary  any  change  in  plant. 


HERCULES  HOISTING  ROPE. 

(Round  Strands.) 

Made  of  6 Strands  of  19  Wires  Each,  Laid  Around  a Hemp  Center. 


Diameter  in 
Inches. 

Approximate 
Breaking 
Strain  in  Tons 
of  2,000  lb. 

Average  Weight 
Per  Foot. 

Diameter  in 
Inches. 

Approximate 
Breaking 
Strain  in  Tons 
of  2,000  lb. 

Average  Weight 
Per  Foot. 

3. 

8 

7 

0.22 

li 

77 

2.50 

i 

m 

0.39 

If 

96 

3.00 

20 

0.62 

u 

113 

3.65 

f 

29 

0.89 

u 

157 

5.00 

i 

36 

1.20 

2 

191 

6.30 

1 

50 

1.58 

2i 

238 

8.00 

60 

2.00 

2^ 

266 

11.00 

HERCULES  HAULAGE  AND  TRANSMISSION  ROPE. 

(Round  Strands.) 

Made  of  6 Strands  of  7 Wires  Each,  Laid  Around  a Hemp  Center. 


Diameter  in 
Inches. 

Approximate 
Breaking 
Strain  in  Tons 
of  2,0001b. 

Average  Weight 
Per  Foot. 

Diameter  in 
Inches. 

Approximate 
Breaking 
Strain  in  Tons 
of  2,0001b. 

AverageWeight 
Per  Foot. 

lU 

0.39 

1 

47 

1.50 

1 

18k 

0.62 

H 

53 

1.82 

3 

T 

25k 

0.88 

U 

74 

2.28 

J 

88k 

1.12 

HERCULES  PATENT  FLATTEN  ED-STRAN  D WIRE  ROPE. 

These  ropes,  instead  of  being  made  up  of  strands  of  circular  form,  are  con- 
structed of  strands,  each  of  which  has  one  or  more  flattened  surfaces,  so  that 
one  flattened  surface  is  exposed  on  the  outside  of  the  full  length  of  the  rope. 
This  results  in  a plurality  of  wires  in  each  strand  taking  the  wear  instead  of 


Fig.  1.  Fig.  2.  Fig.  3.  Fig.  4. 


only  one  external  wire  of  each  strand  as  in  ordinary  ropes,  when  new.  The 
manufacturers  claim  for  these  ropes,  longer  life,  more  uniform  wear,  greater 
flexibility,  less  liability  of  wires  becoming  brittle,  and  freedom  from  all  ten- 
dency to  spin  or  kink'.  It  is  also  claimed  that  the  smoother  surface  effects 
considerable  saving  in  the  wear  of  pulleys  and  sheaves.  Cross-sections  of 
the  flattened  strand  ropes  are  shown  in  Figs.  1,  2,  3,  and  4. 


122b 


WIRE  ROPES. 


HBROULKS  HOISTING  ROPE. 

(Patent  Flattened  Strand.) 


Diameter  in 
Inches. 

Approximate 
Breaking 
Strain  in  Tons 
of  2,000  lb. 

Average  Weight 
Per  Foot. 

Diameter  in 
Inches. 

Approximate 
Breaking 
Strain  in  Tons 
of  2,000  lb. 

Average  Weight 
Per  Foot. 

i 

m 

0.44 

u 

84 

2.50 

22i 

0.67 

H 

124 

3.71 

32 

0.96 

U 

168 

5.00 

7 

8* 

40i 

1.25 

2 

211 

6.50 

1 

56 

1.70 

2i 

260 

8.50 

li 

67 

2.15 

HERCULES  HAULAGE  AND  TRANSMISSION  ROPE. 

(Patent  Flattened  Strand.) 


Diameter  in 
Inches. 

Approximate 
Breaking 
Strain  in  Tons 
of  2,000  lb. 

Average  Weight 
Per  Foot. 

Diameter  in 
Inches. 

Approximate 
Breaking 
Strain  in  Tons 
of  2,000  lb. 

Average  Weight 
Per  Foot. 

13 

0.40 

1 

53 

1.64 

1 

21 

0.68 

H 

64 

2.00 

f 

30 

0.93 

H 

80 

2.40 

¥ 

38 

1.20 

CRUCIBLE  CAST'STEEL  HOISTING  ROPE. 


(Patent  Flattened  Strand.) 


Diameter 
in  Inches. 

Approxi- 
mate 
Breaking 
Strain  in 
Tons  of 
2,000  lb. 

Average 
Weight 
Per  Foot. 

Minimum 
Size  of 
Drums  or 
Sheaves 
in  Feet. 

Diameter 
in  Inches. 

Approxi- 
mate 
Breaking 
Strain  in 
Tons  of 
2,000  lb. 

Average 
Weight 
Per  Foot. 

Minimum 
Size  of 
Drums  or 
Sheaves 
in  Feet. 

i 

9i 

0.44 

li 

1| 

69 

3.17 

5i 

1 

15 

0.67 

2 

li 

81 

3.71 

5^ 

f 

21 

0.96 

3 

H 

94 

4.33 

6i 

T 

29 

1.25 

ai 

li 

109 

5.00 

7i 

1 

38 

1.70 

4 

2 

140 

6.50 

8 

li 

47 

2.15 

4i 

2i 

176 

8.50 

9 

li 

56 

2.50 

5 

CRUCIBLE  OAST-STEEL  HAULAGE  AND  TRANSMISSION  ROPE. 


(Patent  Flattened  Strand.) 


Diameter  in 
Inches. 

Average  Weight 

Per  Foot. 

Diameter  in 
Inches. 

Average  Weight 

Per  Foot. 

1 

0.25 

7 

1 

1.20 

L 

0.40 

1 

1.64 

\ 

0.68 

2.00 

1 

0.93 

l| 

2.40 

WIRE  ROPES. 


122c 


8WKDCS  IRON  HOISTING  ROPK. 

(Patent  Flattened  Strand.) 


Diameter 
in  Inches. 

Approxi- 
mate 
Breaking 
Strain  in 
Tons  of 
2,000  lb. 

Average 
Weight 
of  Rope 
Per  Foot. 

Minimum 
Size  of 
Drums  or 
Sheaves 
in  Feet. 

Diameter 
in  Inches. 

Approxi- 
mate 
Breaking 
Strain  in 
Tons  of 
2,000  lb. 

Average 
Weight 
of  Rope 
Per  Foot. 

Minimum 
Size  of 
Drums  or 
Sheaves 
in  Feet. 

I 

i 

4 

0.44 

u 

34 

3.17 

6 

i 

6 

0.67 

2i 

li 

40 

3.71 

6i 

f 

9 

0.96 

3 

u 

45 

4.33 

7 

T 

13 

1.25 

3i 

u 

54 

5.00 

7i 

1 

17 

1.70 

4 

2 

66 

6.50 

9 

H 

21 

2.15 

4i 

2i 

75 

8.50 

10 

U 

28 

2.50 

5 

SWEDES  IRON  HAULAGE  AND  TRANSMISSION  ROPE. 

(Patent  Flattened  Strand.) 


Diameter  in 
Inches. 

Average  Weight 

Per  Foot. 

Diameter  in 
Inches. 

Average  Weight 

Per  Foot. 

i 

0.40 

n 

1.64 

1 

0.68 

H 

2.00 

f 

0.93 

u 

2.40 

1.20 

EXTRA  STRAIN  ON  A HOISTING  ROPE  WITH  A FEW  INCHES 
OF  SLACK  CHAIN. 


Dynamometer  Tests. 

Tons. 

Cwts. 

Eirst  Test. 

Empty  cage  lifted  gently  

1 

16 

Empty  cage  with  24  inches  slack  chain  

2 

10 

Empty  cage  with  6 inches  slack  chain  

4 

0 

Empty  cage  with  12  inches  slack  chain  

5 

10 

Second  Test. 

Cage  and  four  empty  cars  weighed  by  machine 

2 

17 

Cage  and  four  empty  cars  lifted  gently 

3 

0 

Cage  and  four  empty  cars  with  3 inches  slack  chain 

5 

0 

Cage  and  four  empty  cars  with  6 inches  slack  chain 

5 

10 

Cage  and  four  empty  cars  with  12  inches  slack  chain 

7 

0 

Third  Test. 

Cage  and  full  cars  weighed  by  machine 

5 

1 

No.  1,  lifted  gently  

5 

1 

No.  2,  lifted  gently  

5 

3 

No.  1,  with  3 inches  slack  chain 

8 

10 

No.  2,  with  3 inches  slack  chain 

8 

10 

No.  1,  with  6 inches  slack  chain 

10 

10 

No.  2,  with  6 inches  slack  chain 

11 

10 

No.  1,  with  9 inches  slack  chain 

12 

10 

No.  2,  with  9 inches  slack  chain 

11 

10 

122d 


WIRE  AND  SHEET-METAL  GAUGES. 


TABLE  OF  WIRE  AND  SHEET-METAL  GAUGES. 


Number 

of 

Gauge. 

u.  s. 

Standard 
Gauge 
for  Sheet 
and  Plate 
Iron  and 
Steel. 
(Legal 
Standard.) 
Inch. 

British 
Imperial 
Standard 
Wire 
Gauge. 
(Legal 
Standard 
in  Great 
Britain.) 
Millim. 

Birsning- 

ham 

Gauge. 

Inch. 

American 
or  Brown 
and 
Sharpe 
Gauge. 
Inch. 

Roebling’.s 

Gauge. 

Inch. 

Trenton 

Iron 

Co.’s 

;Wire 

Gauge. 

Inch. 

English 

Legal 

Standard. 

Inch. 

Number 
• of 
Gauge. 

0000000 

.5 

12.7 

.49 

.500 

0000000 

000000 

.469 

11.78 

.46 

.464 

000000 

00000 

.438 

10.97 

.43 

.45 

.432 

00000 

0000 

.406 

10.16 

.454 

.46 

.393 

.40 

.4 

0000 

000 

.375 

9.45 

.425 

.40964 

.362 

.36 

.372 

000 

00 

.344 

8.84 

.38 

.3648 

.331 

.33 

.348 

00 

0 

.313 

8.23 

.34 

.32486 

.307 

.305 

.324 

0 

1 

.281 

7.62 

.3 

.2893 

.283 

.285 

.3 

1 

2 

.266 

7.01 

.284 

.25763 

.263 

.265 

.276 

2 

3 

.25 

6.4 

.259 

.22942 

.244 

.245 

.252 

3 

4 

.234 

5.89 

.238 

.20431 

.225 

.225 

.232 

4 

5 

.219 

5.38 

.22 

.18194 

.207 

.205 

.212 

5 

6 

.203 

4.88 

.203 

.16202 

.192 

.19 

.192 

6 

7 

.188 

4.47 

.18  ' 

.14428 

.177 

.175 

.176 

7 

8 

.172 

4.06 

.165 

.12849 

.162 

.16 

.16 

8 

9 

.156 

3.66 

.148 

.11443 

.148 

.145 

.144 

9 

10 

.141 

3.26 

.134 

.10189 

.135 

.13 

.128 

10 

11 

.125 

2.95 

.12 

.09074 

.12 

.1175 

.116 

11 

12 

.109 

2.64 

.109 

.08081 

.105 

.105 

.104 

12 

13 

.094 

2.34 

.095 

.07196 

.092 

.0925 

.092 

13 

14 

.078 

2.03 

.083 

.06408 

.08 

.08 

.08 

14 

15 

.07 

1.83 

.072 

.05707 

.072 

.07 

.072 

15 

16 

.0625 

1.63 

.065 

.05082 

.063 

.061 

.064 

16 

17 

.0563 

1.42 

.058 

.04526 

.054 

.0525 

.056 

17 

18 

.05 

1.22 

.049 

.0403 

.047 

.045 

.048, 

18 

19 

.0438 

1.01 

.042 

.03589 

.041 

.04 

.04 

19 

20 

.0375 

.91 

.035 

.03196 

.035 

.035 

.036 

20 

21 

.0344 

.81 

.032 

.02846 

.032 

.031 

.032 

21 

22 

.0313 

.71 

.028 

.02535 

.028 

.028 

.028 

22 

23 

.0281 

.61 

.025 

.02257 

.025 

.025 

.024 

23 

24 

.025 

.56 

.022 

.0201 

.023 

.0225 

.022 

24 

25 

.0219 

.51 

.02 

.0179 

.02 

.02 

.02 

25 

26 

.0188 

.45 

.018 

.01594 

.018 

.018 

.018 

26 

27 

.0172 

.42 

.016 

.01419 

.017 

.017 

.0164 

27 

28 

.0156 

.38 

.014 

.01264 

.016 

.016 

.0148 

28 

29 

.0141 

.35 

.013 

.01126 

.015 

.015 

.0136 

29 

30 

.0125 

.31 

.012 

.01002 

.014 

.014 

.0124 

30 

31 

.0109 

.29 

.01 

.00893 

.0135 

.013 

.0116 

31 

32 

.0101 

.27 

.009 

.00795 

.013 

.012 

.0108 

32 

33 

.0094 

.25 

.008 

.00708 

.011 

.011 

.01 

33 

34 

.0086 

.23 

.007 

.0063 

.01 

.01 

.0092 

34 

35 

.0078 

.21 

.005 

.00561 

.0095 

.0095 

.0084 

35 

36 

.007 

.19 

.004 

.005 

.009 

.009 

.0076 

36 

37 

.0066 

.17 

.00445 

.0085 

.0085 

.0068 

37 

38 

.0063 

.15 

.00396 

.008 

.008 

.006 

39 

.13 

.00353 

.0075 

.0075 

.0052 

39 

40 

.12 

.00314 

.007 

.007 

.0048 

40 

41 

.11 

.0044 

41 

42 

.10 

.004 

42 

43 

.09 

.0036 

43 

44 

.08 

.0032 

44 

45 

.07 

.0028 

45 

46 

.06 

.0024 

46 

47 

.05 

.002 

47 

■48 

.04 

.0016 

43 

49 

.03 

.0012 

49 

50 

.025 

.001 

5i) 

WIRE  ROPEf^. 


123 


STRESS  IN  HOISTING  ROPES  ON  INCLINED  PLANES  OF  VARIOUS 
DEGREES. 

{From Wire-Rope  Transportation,’'  published  by  Trenton  Iron  Co.) 

The  following  table  is  based  upon  an  allowance  of  40  lb.  per  ton  for 
rolling  friction,  but  there  will  be  an  additional  stress  due  to  the  weight  of 
the  rope  and  inclination  of  the  plane. 


Rise  per 
100  Ft. 
Horizontal. 
Ft. 

Angle 

of 

Inclination. 

Stress  in  Lb. 

per  Ton 
of  2,000  Lb. 

Rise  per 
100  Ft. 
Horizontal. 
Ft. 

Angle 

of 

Inclination. 

Stress  in  Lb. 

per  Ton 
of  2,000  Lb. 

5 

2° 

52' 

140 

105 

46° 

24' 

1,484 

10 

5° 

43' 

240 

110 

47° 

44' 

1,516 

15 

8° 

32' 

336 

115 

49° 

00' 

1,535 

20 

11° 

10' 

432 

120 

50° 

12' 

1,573 

25 

140 

03' 

527 

125 

51° 

21' 

1,597 

30 

16° 

42' 

613 

130 

52° 

26' 

1,620 

35 

19° 

18' 

700 

135 

53° 

29' 

1,642 

40 

21° 

49' 

782 

140 

54° 

28' 

1,663 

45 

24° 

14' 

860 

145 

55° 

25' 

1,682 

50 

26° 

34' 

933 

150 

56° 

19' 

1,699 

55 

28° 

49'- 

1,003 

155 

57° 

11' 

1,715 

60 

30° 

58' 

1,067 

160 

58° 

00' 

1,730 

65 

33° 

02' 

1,128 

165 

58° 

47' 

1,744 

70 

35° 

00' 

1,185 

170 

59° 

33' 

1,758 

75 

,36° 

53' 

1,238 

175 

60° 

16' 

1,771 

80 

38° 

40' 

1,287 

180 

60° 

57' 

1,782 

85 

40° 

22' 

1,332 

185 

61° 

37' 

1,794 

90 

42° 

00' 

1,375 

190 

62° 

15' 

1,804 

95 

43° 

32' 

1,415 

195 

62° 

52' 

1,813 

100 

45° 

00' 

1,450 

200 

63° 

27' 

1,822 

RELATIVE  EFFECTS  OF  VARIOUS  SIZED  SHEAVES  OR  DRUMS  ON 
THE  LIFE  OF  WIRE  ROPES. 

Mine  ofiftcials  and  other  users  of  wire  ropes  have  often  felt  the  want  of  a 
table  or  set  of  tables  that  would  enable  them  to  determine  at  a glance  what 
effect  the  use  of  various  sized  sheaves  would  have  on  various  sized  ropes. 
The  following  tables  have  been  specially  prepared  for  the  Coal  and  Metal 
Miner’s  Pocketbook  by  Mr.  Thomas  E.  Hughes,  of  Pittsburg,  Pa. 

CAST-STEEL  ROPES  FOR  INCLINES. 

Made  of  6 Strands  of  7 Wires  Each,  Laid  Around  a Hemp  Core. 


Diameters  of  Sheaves  or  Drums  in  Feet,  Showing  Percentages 
of  Life  for  Various  Diameters. 


Rope. 

Inches. 

lOOfc 

90/. 

80/ 

75/ 

60/ 

50/ 

25/ 

n 

16.00 

14.00 

12.00 

11.00 

9.00 

7.00 

4.75 

If 

14.00 

12.00 

10.00 

8.50 

7.00 

6.00 

4.50 

n 

12.00 

10.00 

8.00 

7.25 

6.00 

5.50 

4.25 

H 

10.00 

8.50 

7.75 

7.00 

6.00 

5.00 

4.00 

1 

8.50 

7.75 

6.75 

6.00 

5.00 

4.50 

3.75 

f 

e 

7.75 

7.00 

6.25 

5.75 

4.50 

3.75 

3.25 

i 

7.00 

6.25 

5.50 

5.00 

4.25 

3.50 

2.75 

I 

6.00 

5.25 

4.50 

4.00 

3.25 

3.00 

2.50 

5.00 

4.50 

4.00 

3.50 

2.75 

2.25 

1.75 

Note.— We  do  not  publish  a table  of  iron  ropes  for  inclines,  as  the  use  of 
iron  ropes  for  this  purpose  has  been  generally  abandoned,  steel  ropes  being 
far  more  satisfactory  and  economical. 


124 


WIRE  ROPES. 


CAST-STKEL  HOISTING  ROPES. 

Made  of  6 Strands  of  19  Wires  Each,  Laid  Around  a Hemp  Core. 


Diameters  of  Sheaves  or  Drums  in  Feet,  Showing  Percentages 
of  Life  for  Various  Diameters. 


Rope. 

Inches, 

lOOf. 

90^ 

80^ 

75/. 

60/ 

50/ 

25/ 

H 

14.00 

12.00 

10.00 

8.50 

7.00 

6.00 

4.50 

If 

12.00 

10.00 

8.00 

7.00 

6.00 

5.25 

4.25 

If 

10.00 

8.50 

7.50 

6.75 

5.50 

5.00 

4.00 

If 

9.00 

7.50 

6.50 

5.50 

5.00 

4.50 

3.75 

1 

8.00 

7.00 

6.00 

5.50 

4.50 

4.00 

3.50 

7.50 

6.75 

5.75 

5.00 

4.25 

3.50 

3.00 

f 

5.50 

4.50 

4.00 

3.75 

3.25 

3.00 

2.25 

1 

4.50 

4.00 

3.75 

3.25 

3.00 

2.50 

2.00 

i 

4.00 

3.00 

3.00 

2.75 

2.25 

2.00 

1.50 

i 

8 

3.00 

2.00 

1.50 

IRON  HOISTING  ROPES. 

Made  of  6 Strands  of  19  Wires  Each,  Laid  Around  a Hemp  Core. 


Diameter 

of 


Diameters  of  Sheaves  or  Drums  in  Feet,  Showing  Percentages 
of  Life  for  Various  Diameters. 


Rope. 

Inches. 

100/ 

90/ 

80/ 

75/ 

60/ 

50/ 

25/ 

If 

12.00 

11.00 

9.00 

7.50 

6.00 

5.00 

3.00 

If 

10.00 

9.00 

7.50 

7.00 

5.25 

4.75 

4.00 

If 

9.00 

7.75 

6.50 

5.75 

4.50 

4.00 

3.50 

If 

8.00 

6.75 

5.50 

5.00 

4.25 

3.50 

3.00 

1 

6.75 

6.00 

5.00 

4.75 

4.00 

3.25 

2.75 

7 

6 

6.75 

6.00 

5.00 

4.50 

4.00 

3.00 

2.50 

f 

5.00 

4.75 

4.00 

3.75 

3.00 

2.75 

2.00 

1 

4.50 

3.75 

3.25 

3.00 

2.75 

2.25 

1.75 

i 

3.50 

3.25 

3.00 

2.75 

2.00 

1.50 

1.00 

f 

3.00 

2.00 

1.25 

1.00 

Wire  rope  is  as  pliable  as  new  hemp  rope  of  the  same  strength;  the  former 
will  therefore  run  on  the  same  sized  sheaves  and  pulleys  as  the  latter.  But 
the  greater  the  diameter  of  the  sheaves,  pulleys,  and  drums,  the  longer  wire 
rope  will  last.  In  the  construction  of  machinery  for  wire  rope,  it  will  be 
found  good  economy  to  make  the  drums  and  sheaves  as  large  as  possible. 

The  tables  of  wire-rope  manufacturers  give  “ proper  diameters  of  drum  or 
sheave  ” at  from  50  to  65  times  the  rope  diameter;  but  the  expression  would 
more  properly  be  the  “minimum  admissible  diameter.”  For  ordinary  ser- 
vice, by  using  sheaves  and  drums  from  75  to  100  times  the  diameter  of  the 
rope,  the  average  life  of  hoisting  ropes  would  be  materially  lengthened. 
For  rapid  hoisting,  during  which  abnormal  strains  are  most  likely  to  occur, 
or  where  a low  factor  of  safety  is  employed,  a sheave  diameter  of  150  times 
that  of  the  rope  is  to  be  recommended. 

Experience  has  demonstrated  that  the  wear  increases  with  the  speed.  It 
is  therefore  better  to  increase  the  load  than  the  speed.  Wire  rope  is  manu- 
factured either  with  a wire  or  a hemp  center.  The  latter  is  more  pliable 
than  the  former,  and  will  wear  better  where  there  is  short  bending. 

Wire  rope  must  not  he  coiled  or  uncoiled  like  hemp  rope.  When  mounted  on 
a reel,  the  latter  should  be  mounted  on  a spindle  or  flat  turntable  to  pay  off 
the  rope.  When  forwarded  in  a small  coil,  without  reel,  roll  it  over  the 
ground  like  a wheel,  and  run  off  the  rope  in  that  way.  All  untwisting  or 
kinking  must  be  avoided. 


WIRE  ROPES. 


125 


PROPER  WORKING  LOAD 

For  steel  hoisting  ropes,  made  with  19  wires  to  the  strand,  when  used  on 
drums  of  different  diameters.  Total  strain  of  wire  rope,  including  bending 
strain  and  the  strain  due  to  load,  assumed  at  50,000  lb.  per  sq.  in.  of  actual 
steel  section,  d = diameter  of  rope  in  in.;  D = diameter  of  drum  in  in.; 
S = strain  per  sq.  in.  due  to  bending;  L = proper  working  load  in  pounds. 

S = 1,894,000  X L = 20,000  - 757,600  X 


{^By  permission  of  E.  T.  Sederholm,  Chief  Engr.,  Fraser  & Chalmers,  Chicago.) 


126 


WIRE  ROPES. 


Starting  Strain  on  Hoisting  Rope.— In  selecting  a hoisting  rope,  due  allow- 
ance must  be  made  for  the  shock  and  extra  strain  imposed  on  the  rope  when 
the  load  is  started  from  rest.  Experiments  made  by  placing  a dynamometer 
between  the  rope  and  the  cage  have  shown  that  starting  stress  may  be  from 
two  to  three  times  the  actual  load. 


Experiment  1. 


Strain  in  Rope. 
Pounds. 


Empty  cage,  lifted  gently 

Empty  cage,  started  with  2k  in.  of  slack  rope 
Empty  cage,  started  with  6 in.  of  slack  rope  .. 
Empty  cage,  started  with  12  in.  of  slack  rope 


4,030 

5,600 

8,950 

12,300 


Experiment  2. 


Strain  in  Rope. 
Pounds. 


Cage  and  loaded  cars,  as  weighed 

Cage  and  loaded  cars,  lifted  slowly  and  gently  

Cage  and  loaded  cars,  started  with  3 in.  of  slack  rope 
Cage  and  loaded  cars,  started  with  6 in.  of  slack  rope 
Cage  and  loaded  cars,  started  with  9 in.  of  slack  rope 


11,300 

11,525 

19,025 

24,625 

26,850 


Horsepower  of  Manila  Ropes. 
{Link- Belt  Engineering  Co.) 


Diam.  of 
Rope. 

Weight  per 
Foot. 

Breaking 

Strain. 

Working 

Strain. 

1,000  Ft. 
per  Min. 

2,000  Ft. 
per  Min. 

3,000  Ft. 
per  Min. 

4,000  Ft. 
per  Min. 

5,000  Ft. 
per  Min. 

H.P. 

Tens. 

Wt. 

H.P. 

Tens. 

Wt. 

H.P. 

Tens. 

Wt. 

H.P. 

Tens. 

Wt. 

H.P. 

Tens. 

Wt. 

1 

0.15 

4,000 

121 

90 

4i 

90 

6i 

80 

7i 

80 

8i 

70 

j 

0.18 

5,000 

151 

2} 

110 

5i 

110 

71 

100 

9f 

100 

m 

90 

0.27 

7,500 

227 

4i 

170 

8i 

170 

lU 

160 

14i 

150 

16 

130 

1* 

0.33 

9,000 

272 

5 

200 

10 

200 

14 

180 

m 

170 

19 

150 

I? 

0.45 

12,250 

371 

7 

280 

13i 

270 

19 

250 

23i 

230 

26 

210 

li 

0.50 

14,000 

424 

8 

320 

15i 

310 

22 

290 

27 

270 

29i 

240 

If 

0.65 

18,062 

547 

lOi 

410 

20 

400 

28i 

370 

34f 

350 

38i 

310 

u 

0.73 

20,250 

613 

Hi 

460 

22 

440 

31i 

420 

39 

390 

43i 

350 

ll 

0.82 

25,000 

760 

14i 

570 

27^ 

550 

m 

520 

49 

490 

55^ 

448 

u 

1.08 

30,250 

916 

17 

680 

33i 

660 

47i 

630 

58i 

580 

64| 

520 

2 

1.27 

36,000 

1,000 

20i 

810 

40 

1 

790 

56i 

740 

69i 

670 

77k 

620 

WIRE-ROPE  FASTENINGS. 

Thimble  spliced,  in  ordinary  style,  is  shown  in  Fig.  1 (a).  In  this  method, 
the  wires,  after  being  frayed  out  at  the  end  and  the  rope  bent  around  the 
thimble,  are  laid  snugly  about  the  main  portion  of  the  rope  and  securely 
fastened  by  wrapping  with  stout  wire,  the  extreme  ends  that  project  below 
this  wrapping  being  folded  back,  as  shown. 

Another  style  of  thimble  splicing  is  shown  in  Fig.  1 (5).  In  this  case  the 
strands  are  interlocked  as  in  splicing,  and  the  joint  is  wrapped  with  wire  as 
in  the  former  method.  The  socket  fastening  is  shown  in  Fig.  1 (c).  The  hole 
in  which  the  rope  end  is  fastened  is  conical  in  shape.  The  rope  is  generally 
secured  by  fraying  out  the  wires  at  the  end,  the  interstices  being  filled  up 
with  spikes  driven  in  tightly.  The  whole  is  finally  cemented  by  pouring  in 
molten  Babbitt  metal.  This  makes  a much  neater  fastening  than  either 
of  those  shown  in  (a)  and  (6),  but  it  does  not  possess  anything  like  as 
much  strength.  The  thimble  possesses  a serious  disadvantage;  it  is 
usually  made  of  a piece  of  curved  metal  bent  around  into  an  oval  shape, 


WIRE-ROPE  SPLICING. 


127 


as  shown  in  (a)  and  (6),  with  the  groove,  in  which  the  rope  lies,  outside, 
the  ends  coming  together  in  a sharp  point.  When  weight  is  placed  on  the 
rope,  the  strain  on  the  thimble  is  apt  to  cause  one  end  to  wedge  itself 
beyond  or  past  the  other,  and  with  its  sharp  edge 
it  cuts  the  strands  in  the  splice.  Mr.  William 
Hewitt,  of  Trenton,  N.  J.,  while  testing  the 
strength  of  wire  ropes,  discovered  this  tendency, 
and  experimented  with  sockets  with  the  idea 
of  devising  some  method  of  fastening  the  rope 
securely  in  the  socket.  He  found  that  by  adopt- 
ing the  following  plan  he  secured  good  results: 

The  wires,  after  being  frayed  out  at  the  end, 
were  bent  upon  themselves  in  hook  fashion,  the 
prongs  of  some  being  longer  than  others,  so  that 
the  bunch  would  conform  to  the  conical  aperture 
of  the  socket,  and  the  melted  Babbitt  metal  was 
finally  run  in  as  usual.  The  rope  was  subjected 
to  a strain  of  over  129,000  lb.,  and  the  wires  in 
the  socket  were  unaffected.  The  simplicity  of  this  method  commends 
itself  to  practical  men. 


Fig.  1. 


RAPID  METHOD  OF  SPLICING  A WIRE  ROPE.* 

The  only  tools  needed  are  a cold  cutter  and  hammer  for  cutting  and 
trimming  the  strands,  and  two  needles  12  in.  long,  made  of  good  steel  and 
tapered  ovally  to  a point.  Cut  off  the  ends  of  the  ropes  to  be  spliced  and 
unlay  three  adjacent  strands  of  each  back  15  ft.;  cut  out  the  hemp 
center  to  this  point  and  relay  the  strands  for  7 ft.  and  cut  them  off*.  Pull 
the  ropes  by  each  other  until  they  have  the  position  shown  in  Fig.  2 (a), 
cut  off  a and  d',  b and  c'.  Fig.  2 (5),  making  their  lengths  approximately  10 
and  12i  ft.,  respectively,  measured  from  the  point  where  the  hemp  centers 
were  cut.  Place  the  ropes  together,  Fig.  2 (5);  unlay  e,d,c,  Fig.  2 (a), 

keeping  the  strands  to- 
gether, and  follow  with  e', 
d',  c'.  Fig.  2 (5).  Similarly, 
unlay  /,  a',  b',  Fig.  2 (5), 
and  follow  with  /,  a, b, 
until  the  rope  appears  as  in 
Fig.  2 (c).  Next  run  the 
strands  into  the  middle  of 
the  rope.  To  do  this,  cut 


(cj 

Fig.  2. 


off  the  end  of  the  strand  e'.  Fig.  2 (c),  so  that  when  it  is  put  in  place  it  will  just 
reach  to  the  end  x of  the  hemp  core,  and  then  push  the  needle  A,  Fig.  2 (c), 
through  the  rope  from  the  under  side,  leaving  two  strands  at  the  front  of  the 
needle,  as  shown.  Push  the  needle  B through  from  the  upper  side  and  as 
close  to  the  needle  A as  possible,  leaving  the  strands  e and  e'  between  them; 
place  the  needle  A on  the  knee  and  turn  the  needle  B around  with  the  coil  of 
the  rope,  and  force  the  strand  e'  into  the  center  of  the  rope.  Repeat  this 


*W.  H.  Morris,  " Mines  and  Minerals,”  September,  1898. 


WIRE  ROPES. 


WIRE-ROPE  SPLICING. 


129 


operation  with  the  other  ends  and  cut  them  off  so  that  the  ends  coming 
together  in  the  center  of  the  rope  will  butt  against  each  other  as  nearly  as 
possible.  


ORDINARY  LONG  SPLICE. 

Tools  Required.— One  pair  wire  nippers,  for  cutting  oif  strands;  one  pair 
pliers,  for  pulling  through  and  straightening  ends  of  strands;  two  marline- 
spikes,  one  round  and  one  oval,  for  opening  strands;  one  knife  to  cut  hemp 
center;  two  clamps,  to  untwist  rope  to  insert  ends  of  strands,  or,  in  place  of 
them,  two  short  hemp-rope  slings,  with  a stick  for  each  as  a lever;  a wooden 
mallet  and  some  rope  twine.  Also,  a bench  and  vise  are  handy. 

The  length  of  the  splice  depends  on  the  size  of  the  rope.  The  larger  ropes 
require  the  longer  splices.  The  splice  of  ropes  from  | in.  to  ^ in.  in  diameter 
should  not  be  less  than  20  ft.;  from  | in.  to  1^  in.,  30  ft.;  and  from  in. 
up,  40  ft. 

To  splice  a rope,  tie  each  end  with  a piece  of  cord  at  a distance  equal  to 
one-half  the  length  of  the  splice,  or  10  ft.  back  from  the  end,  for  a rope,  after 
which  unlay  each  end  as  far  as  the  cord.  Then  cut  out  the  hemp  center, 
and  bring  the  two  ends  together  as  close  as  possible,  placing  the  strands  of 
the  one  end  between  those  of  the  other,  as  shown  in  Fig.  3 (o).  Now  remove 
the  cord  k from  the  end  M of  the  rope,  and  unlay  any  strand,  as  a,  and  follow  it 
up  with  the  strand  of  the  other  end  M'  of  the  rope  that  corresponds  to  it,  as 
a',  Fig.  3 (a).  About  6 in.  of  a are  left  out,  and  a is  cut  off  about  6 in.  from  the 
rope,  thus  leaving  two  short  ends,  as  shown  at  P in  Fig.  3(6),  which  must  be 
tied  for  the  present  by  cords  as  shown.  The  cord  k should  again  be  wound 
around  the  end  M of  the  rope.  Fig.  3 (a),  to  prevent  the  unraveling  of  the 
strands;  after  which  remove  the  cord  k'  on  the  other  or  M'  end  of  the  rope, 
and  unlay  the  strand  6;  follow  it  up,  as  above,  with  the  strand  6',  leaving 
the  ends  out,  and  tying  them  down  for  the  present,  as  before  described  in 
the  case  of  strands  a and  a',  see  Q,  Fig.  3 (6) ; also,  replace  the  cord  k'  for  the 
same  purpose  as  stated  above.  Now,  again  remove  the  cord  k and  unlay  the 
next  strand,  as  c,  Fig.  3 (a),  and  follow  it  up  with  c',  stopping,  however,  this 
time  within  4 ft.  of  the  first  set.  Continue  this  operation  with  the  remaining 
6 strands,  stopping  4 ft.  short  of  the  preceding  set  each  time.  The  strands 
are  now  in  their  proper  places,  with  the  ends  passing  each  other  at  intervals 
of  4 ft.,  as  shown  in  Fig.  3(c).  To  dispose  of  the  loose  ends,  clamp  the  rope  in  a 
vise  at  the  left  of  the  strands  a and  a'.  Fig.  3(c),  and  fasten  a clamp  to  the  rope 
at  the  right  of  these  strands;  then  remove  the  cords  tied  around  the  rope 
that  hold  these  two  strands  down;  after  which  turn  the  clamp  in  the  oppo- 
site direction  to  which  the  rope  is  twisted,  thereby  untwisting  the  rope,  as 
shown  in  Fig.  3(d).  The  rope  should  be  untwisted  enough  to  allow  its  hemp 
core  to  be  pulled  out  with  a pair  of  nippers.  Cut  off  24  in.  of  the  hemp  core, 
12  in.  at  each  side  from  the  point  of  intersection  of  the  strands  a and  a',  and 
push  the  ends  of  the  strands  in  their  place,  as  shown  in  Fig.  3 (d).  Then 
allow  the  rope  to  twist  up  to  its  natural  shape,  and  remove  the  clamps. 
After  the  rope  has  been  allowed  to  twist  up,  the  strands  tucked  in  generally 
bulge  out  somewhat.  This  bulging  may  be  reduced  by  lightly  tapping  the 
bulged  part  of  the  strands  with  a wooden  mallet,  which  will  force  their  ends 
farther  into  the  rope.  Proceed  in  the  same  manner  to  tuck  in  the  other  ends 
of  the  strands. 


CHAINS. 

The  links  of  iron  chains  are  usually  made  as  short  as  is  consistent  with 
easy  play,  so  as  to  make  them  less  liable  to  kink,  and  also  to  prevent  bending 
when  wound  around  drums,  sheaves,  etc. 

The  weight  of  close-link  chain  is  about  three  times  the  weight  of  bar  from 
which  it  is  made,  for  equal  lengths. 

Karl  von  Ott,  comparing  weight,  cost,  and  strength  of  three  materials, 
hemp,  iron  wire,  and  chain  iron,  concludes  that  the  proportion  between  cost 
of  hemp  rope,  wire  rope,  and  chain  is  as  2 : 1 ; 3,  and  that,  therefore,  for 
equal  resistances,  wire  rope  is  only  half  the  cost  of  hemp  rope,  and  a third 
of  cost  of  chains. 

Chains  of  warranted  superior  iron  will  stand  25^  more  strain  before 
breaking.  The  report  of  the  U.  S.  Test  Board,  1881,  shows  that  the  ultimate 
strength  of  chains  may  be  taken  at  1.6  that  of  the  iron  from  which  the  links 
are  made. 


130 


HYDROSTA  TICS. 


The  strength  of  chains  varies,  owing  to  the  nature  of  the  iron  from  which 
they  are  made,  and  their  mechanical  construction.  The  following  table  is 
approximately  correct  for  ordinary  iron  chains: 

Table  of  Weight  and  Strength  of  Chains. 


Diameter  of 
Rod  of 
Which  the 
Links  Are 
Made. 
Inches. 

Weight  of 
Chain 
per 

Running 

Foot. 

Pounds. 

Working 

Strength. 

Tons. 

Breaking 

Strain. 

Tons. 

Diameter  of 
Rod  of 
Which  the 
Links  Are 
Made. 
Inches. 

Weight  of 
Chain 
per 

Running 

Foot. 

Pounds. 

Working 

Strength. 

Tons. 

Breaking 

Strain. 

Tons. 

.325 

.19 

.773 

7 

7.10 

4.40 

16.80 

.579 

.36  • 

1.37 

If 

8.14 

5.00 

19.32 

A 

.904 

.45 

2.14 

1 

9.26 

5.71 

22.00 

1 

1..30 

.85 

3.09 

H 

11.70 

7.23 

26.44 

1.78 

1.09 

4.20 

U 

14.50 

9.00 

32.64 

h 

2.31 

1.43 

5.50 

li 

17.50 

10.80 

39.42 

2.93 

1.80 

6.96 

20.80 

13.00 

47.00 

1 

3.62 

2.23 

8.58 

24.40 

15.24 

55.14 

T5 

4.38 

2.70 

10.39 

28.40 

17.65 

63.97 

3 

5.21 

3.21 

12.36 

32.60 

20.27 

73.44 

13 

16 

6.11 

3.80 

14.42 

2 

37.00 

23.10 

83.55 

HYDROSTATICS. 

Hydrostatics  treats  of  the  equilibrium  of  liquids,  and  of  their  pressures  on 
the  walls  of  vessels  containing  them;  the  science  depends  on  the  way  in 
which  the  molecules  of  a liquid  form  a mass  under  the  action  of  gravity 
and  molecular  attraction,  the  latter  of  which  is  so  modified  in  liquids  as  to 
give  them  their  state  of  liquidity.  While  the  particles  of  a liquid  cohere, 
they  are  free  to  slide  upon  one  another  without  the  least  apparent  friction; 
and  it  is  this  perfect  mobility  that  gives  them  the  mechanical  properties 
considered  in  hydrostatics. 

The  fundamental  property  may  be  thus  stated:  When  a pressure  is  exerted 
on  any  part  of  the  surface  of  a liquid,  that  pressure  is  transmitted  undiminished 
to  all  parts  of  the  mass,  and  in  all  directions.  This  is  a physical  axiom,  and  on 
it  are  based  nearly  all  the  principles  of  hydrostatics. 

Equilibrium  of  Liquids. — This  is  a property  of  liquids  that  can  be  easily 
demonstrated,  and  examples  are  frequently  seen.  Thus,  if  two  barrels  are 
connected  at  the  bottom  with  a pipe,  and  water  is  poured  in  one  until  it 
reaches  within  a foot  of  the  top,  the  water  in  the  other  will  be  found  to  have 
attained  the  same  height. 

Pressure  of  Liquids  on  Surfaces.— The  general  proposition  on  this  point  is  as 
follows:  The  pressure  of  a liquid  on  any  surface  immersed  in  it  is  equal  to  the 
weight  of  a column  of  the  liquid  whose  base  is  the  surface  pressed,  and  whose 
height  is  the  perpendicular  depth  of  the  center  of  gravity  of  the  surface  below  the 
surface  of  the  liquid.  The  pressure  thus  exerted  is  independent  of  the  shape 
or  size  of  the  vessel  or  cavity  containing  the  liquid. 

The  pressure  of  a liquid  against  any  point  of  any  surface,  either  curved 
or  plane,  is  always  perpendicular  to  the  surface  at  that  point. 

At  any  ^ven  depth  the  pressure  of  a liquid  is  equal  in  every  direction, 
and  is  in  direct  proportion  to  the  vertical  depth  below  the  surface. 

The  weight  of  a cubic  foot  of  fresh  water,  at  ordinary  temperature  of  the 
atmosphere,  that  is,  from  32°  F.  to  80°  F.,  is  usually  assumed  at  62.5  lb.  This 
is  a trifle  more  than  the  actual  weight,  but  is  sufficiently  close  for  purposes 
of  calculation. 

To  Find  the  Pressure  Exerted  by  Quiet  Water  Against  the  Side  of  a Gangway  or 
Heading. — Multiply  the  area  of  the  side  in  square  feet  by  the  perpendicular 
distance  from  the  surface  of  the  water  to  a point  equidistant  between  the 
top  and  bottom  of  the  submerged  heading  or  gangway,  and  multiply  the 
product  by  62.5.  The  result  will  be  the  pressure  in  pounds,  exclusive  of 
atmospheric  pressure.  This  latter  need  not  be  considered  in  ordinary 
mining  work. 


HYDROSTATICS. 


131 


Example.— If  an  abandoned  colliery,  opened  by  a slope  on  a pitch  of  25° 
and  100  yd.  long,  is  allowed  to  fill  with  water,  what  is  the  average  pressure 
exerted  on  each  square  foot  of  the  lower  rib  of  the  gangway,  assuming 
that  the  gangways  were  driven  dead  level,  and  that  the  length  of  the  slope 
was  measured  to  a point  on  the  lower  rib  equidistant  between  top  and 
bottom  of  gangway. 

We  here  have  a perpendicular  height  of  water  = 300  X sine  of  25° 
= 126.78  ft.  Then,  the  pressure  on  each  square  foot  of  the  lower  rib  of 
gangway  = 126.78  X 62.5  lb.,  or  the  weight  of  1 cu.  ft.,  or  a pressure  on  each 
square  foot  of  surface  of  7,923.75  lb.,  or  over  3i  gross  tons.  The  total  pressure 
exerted  along  the  gangway  may  readily  be  found  by  multiplying  the 
7,923.75  lb.  by  the  number  of  square  feet  of  the  lower  rib  against  which 
it  rests. 

To  find  the  total  pressure  of  quiet  water  against  and  perpendicular  to  any 
surface  whatever,  as  a dam,  embankment,  or  the  bottom,  side  or  top  of  any 
(Containing  vessel,  water  pipe,  etc.,  no  matter  whether  said  surface  be 
vertical,  horizontal,  or  inclined;  or  whether  it  be  flat  or  curved;  or  whether 
it  reach  to  the  surface  of  the  water  or  be  entirely  below  it: 

Multiply  the  area,  in  square  feet,  of  the  surface  pressed,  by  the  vertical  depth  in 
feet  of  its  center  of  gravity  below  the  surface  of  the  water,  and  this  product  by  62.5. 
The  result  will  be  the  pressure  in  pounds. 

Thus,  assuming  that  in  the  annexed  three  figures  the  depth  of  water  in 
(each  dam  is  12  ft.,  and  the  wall  or  embankment  is  50  ft.  long,  then  in 
Eig.  1 the  total  pressure  will  equaL12  X 50  X 6 X 62.5  = 225,000  lb. 

In  Figs.  2 and  3 the  walls  or  embankments,  being  inclined,  expose  a 
greater  surface  to  pressure,  say  18  ft.  from  A to  B.  Then  the  total  pressure 
.equals  18  X 50  X 6 X 62.5  = 337,500  lb. 

Now,  the  results  obtained  are  the  total  pressures  without  regard  to  direction. 

In  Fig.  1 the  total 
pressure  calculated, 
or  225,000  lb.,  is  hori- 
zontal,  tending 
either  to  overturn 
the  wall  or  make  it 
slide  on  its  base. 
The  center  of  pres- 


Fig.  1. 


Fig.  2. 


Fig.  3. 


sure  is  at  C,  or  one-third  of  the  vertical  depth  from  the  bottom. 

In  Fig.  2 the  pressure  is  exerted  in  two  directions;  one  pressure,  acting 
horizontally,  tends  to  overthrow  or  slide  the  wall,  while  the  other,  acting 
vertically,  tends  to  hold  it  in  place. 

In  Fig.  3 the  pressure  is  also  exerted  in  two  directions;  one  pressure, 
acting  horizontally,  tends  to  overthrow  or  slide  the  wall,  while  the  other 
tends  to  lift. 

So  long  as  the  vertical  depth  of  water  remains  the  same,  the  horizontal 
pressure  remains  the  same,  no  matter  what  inclination  is  given  the  wall. 
Thus,  in  Figs.  2 and  3,  the  horizontal  pressure  is  the  same  as  in  Fig.  1, 
or  225,000  lb. 

The  total  pressure  of  the  water  is  distributed  over  the  entire  depth  of  the 
submerged  part  of  the  back  of  the  wall,  and  is  least  at  the  top,  gradually 
increasing  toward  the  bottom.  But  so  far  as  regards  the  united  action  of 
every  portion  of  it,  in  tending  to  overthrow  the  wall,  considered  as  a single 
mass  of  masonry,  incapable  of  being  bent  or  broken,  it  may  all  be  assumed 
to  be  applied  at  C,  which  is  one-third  of  the  vertical  depth  from  the  bottom 
in  Fig.  1,  or,  what  is  the  same  thing,  one-third  of  the 
slope  distance  from  the  bottom  in  Figs.  2 and  3. 

No  matter  how  much  water  is  in  a dam  or  vessel, 
the  pressure  remains  the  same,  so  long  as  the  area 
pressed  and  the  vertical  depth  of  its  center  of  gravity 
below  the  level  surface  of  the  water  remains  un- 
changed. Thus,  if  the  water  in  dam  shown  in  Fig.  1 
extended  back  1 mile,  it  would  exert  no  more  pressure 
against  the  wall  than  if  it  extended  back  only  1 ft. 

In  any  two  vessels  having  the  same  base,  and  con- 
taining the  same  depth  of  water,  no  matter  what 
quantity,  the  pressures  on  the  bases  are  equal.  Thus, 
if  Figs.  4 and  5 have  the  same  base  and  be  filled  with 
water  to  the  same  depth,  the  pressure  on  the  bases 
will  be  equal.  This  fact,  that  the  pressure  on  a given  surface,  at  a given 


Fig.  4. 


Fig.  5. 


132 


HYDROSTATICS. 


depth,  is  independent  of  the  quantity  of  water,  is  called  the  hydrostatic 
paradox. 

As  the  pressure  of  water  against  any  point  is  at  right  angles  to  the  surface 
at  that  point,  it  follows  that  props  or  other  strengthening  material  for  the 
strengthening  of  such  structures  as  a sloping  dam,  should  be  so  placed  as  to 
offer  the  greatest  resistance  in  a line  at  right  angles  to  the  sloping  surface, 
and  these  supports  should  be  strongest  and  closest  together  at  the  bottom. 
For  the  same  reason,  the  hoops  on  a circular  tank  should  be  strongest  and 
closest  at  the  bottom. 

Transmission  of  Pressure  Through  Water.— Water,  in  common  with  other 
liquids,  possesses  the  important  property  of  transmitting  pressure  equally  in 
all  directions.  Thus,  if  a vessel  is  constructed  with  two 
cylinders,  the  area  of  one  being  10  sq.  in.,  and  that  of  the 
other  100  sq.  in.,  and  the  vessel  is  filled  with  water  (Fig.  6), 
and  pistons  fitted  to  the  cylinders,  a pressure  of  100  lb. 
applied  at  the  smaller  will  balance  1,000  lb.  at  the  larger. 
This  is  the  principle  of  the  hydrostatic  press.  Air  and  other 
gaseous  fluids  transmit  pressure  equally  in  all  directions, 
like  liquids,  but  not  as  rapidly. 

To  Find  the  Pressure  on  a Plane  Surface  at  Any  Given  Depth 
of  Water.— For  pounds  per  square  inch,  multiply  depth  in 
feet  by  .434.  For  pounds  per  square  foot,  multiply  depth 
in  feet  by  62.5.  For  tons  per  square  foot,  multiply  depth 
in  feet  by  .0279.  The  pressure  per  square  foot  at  different 
depths  increases  directly  as  the  depths.  The  total  pressure 
against  a plane  1 ft.  wide  at  different  depths  increases  as  the  square  of  the 
depths. 


Fig.  6. 


Pressure  in  Pounds  per  Sq.  Ft.  at  Different  Vertical  Depths,  and 
ALSO  THE  Total  Pressure  Against  a Plane  1 Ft.  Wide  Extending 
Vertically  From  the  Surface  of  the  Water  to  the  Same  Depths. 


Depth. 

Feet. 

Pressure. 
Pounds 
per  Sq.  Ft. 

Total 

Pressure. 

Pounds. 

Depth. 

Feet. 

Pressure. 

Pounds 
per  Sq.  Ft. 

Total 

Pressure. 

Pounds. 

Depth. 

Feet. 

Pressure. 
Pounds 
per  Sq.  Ft. 

Total 

Pressure. 

Pounds. 

1 

62.5 

31 

27 

1,687 

22,781 

65 

4,062 

132,025 

2 

125 

125 

28 

1,750 

24,500 

70 

4,375 

153,124 

3 

187 

281 

29 

1,812 

26,281 

75 

4,687 

175,779 

4 

250 

500 

30 

1,875 

28,125 

80 

5,000 

200,000 

5 

312 

781 

31 

1,937 

30,031 

85 

5,312 

225,775 

6 

375 

1,125 

32 

2,000 

32,000 

90 

5,625 

253,124 

7 

437 

1,531 

33 

2,062 

34,031 

95 

5,937 

282,025 

8 

500 

2,000 

34 

2,125 

36,125 

100 

6,250 

312.500 

9 

562 

2,531 

35 

2,187 

38,281 

110 

6,875 

378,124 

10 

625 

3,125 

36 

2,250 

40,500 

120 

7,500 

450,000 

11 

687 

3,781 

37 

2,312 

42,781 

130 

8,125 

528,100 

12 

750 

4,500 

38 

2,375 

45,125 

140 

8,750 

612,496 

13 

812 

5,281 

39 

2,437 

47,531 

150 

9,375 

703,116 

14 

875 

6,125 

40 

2,500 

50,000 

160 

10,000 

800,000 

15 

937 

7,031 

41 

2,562 

52,531 

170 

10,625 

903,100 

16 

1,000 

8,000 

42 

2,625 

55,125 

180 

11,250 

1,012,496 

17 

1,062 

9,031 

43 

2,687 

57,781 

190 

11,875 

1,128,100 

18 

1,125 

10,125 

44 

2,750 

60,500 

200 

12,500 

1,250,000 

19 

1,187 

11,281 

45 

2,812 

63,281 

225 

14,062 

1,582,025 

20 

1,250 

12,500 

46 

2,875 

66,125 

250 

15,625 

1,953,100 

21 

1,312 

13,781 

47 

2,937 

69,031 

275 

17,187 

2,363,275 

22 

1,375 

15,125 

48 

3,000 

72,000 

300 

18,750 

2,812,500 

23 

1,437 

16,531 

49 

3,062 

75,031 

350 

21,875 

3,828,100 

24 

1,500 

18,000 

50 

3,125 

78,125 

400 

25,000 

5,000,000 

25 

1,562 

19,531 

55 

3,437 

94,531 

450 

28,120 

6,328,100 

26 

1,625 

21,125 

60 

3,750 

112,500 

500 

31,250 

7,812,500 

Pressure  of  Water  in  Pipes.— As  water  exerts  a pre.ssure  equallv  in  all 
directions,  it  is  important  that  in  pipe  lines  the  j)ipe  should  be  sufficiently 
thick  to  assure  strength  enough  to  resist  a bursting  pressure.  In  ordinary 


HYDROSTATICS. 


133 


practice,  the  thickness  of  cast-iron  water  pipes  of  different  bores  is  calculated 
by  Mr.  J.  T.  Fanning’s  formula,  given  in  his  Hydraulic  Engineering,  which 
is  as  follows: 


Thickness  in  inches 


(pressure  in  lb.  per  sq.  in.  -f  100)  X hore  in  in. 
.4  X ultimate  tensile  strength 


+ .333 


(■ 


hore  in  in.  \ 

loo  /■ 


This  formula,  worked  out  for  different  heads  and  diflTerent  sizes  of  bore, 
yields  the  following  results: 


Thickness  of  Pipe  for  Different  Heads  and  Pressures. 


Head  in  Ft 

50 

100 

200 

300 

500 

1,000 

Pressure  in  Lb. 
per  Sq.  In. 

21.7 

43.4 

86.8 

130 

217 

434 

Bore.  Inches. 

Thickness  of  Pipe.  Inches. 

2 

.36 

.37 

.38 

.39 

.42 

.48 

3 

.37 

.38 

.40 

.42 

.45 

.54 

4 

.39 

.40 

.42 

.45 

.50 

.61 

6 

.41 

.43 

.47 

.50 

.57 

.75 

8 

.45 

.47 

.52 

.57 

.66 

.90 

10 

.47 

.50 

.56 

.62 

.74 

1.04 

12 

.49 

.53 

.60 

.67 

.82 

1.18 

16 

.55 

.60 

.70 

.79 

.98 

1.46 

18 

.57 

.63 

.74 

.85 

1.06 

1.60 

20 

.61 

.67 

.79 

.91 

1.15 

1.75 

24 

.66 

.73 

.87 

1.02  ' 

1.30 

2.03 

30 

.74 

.83 

1.01 

1.19 

1.55 

2.46 

36 

.82 

.93 

1.15 

1.36 

1.80 

2.88 

48 

.98 

1.13 

1.42 

1.70 

2,28 

3.73 

In  the  above  table,  the  ultimate  tensile  strength  of  cast  iron  is  taken  at 
18,000  lb.  per  sq.  in.  The  addition  of  100  lb.  to  the  pressure  is  made  to  allow 
for  water  ram.  The  valves  of  water  pipes  should  he  closed  slowly,  and  the 
necessity  of  this  increases  as  the  pipes  increase  in  diameter.  If  this  rule  is 
not  observed,  the  momentum  of  the  running  water  is  arrested  suddenly,  and 
a great  pressure  is  created  against  the  pipes  in  all  directions,  and  through- 
out the  entire  length  of  the  line  above  the  valve,  even  if  it  be  many  miles, 
and  there  is  danger  of  their  bursting  at  any  point.  For  this  reason,  stop- 
gates  are  shut  by  screws,  because  they  prevent  any  very  sudden  closing;  but 
in  pipes  of  large  diameters,  even  the  screws  must  be  worked  very  slowly  to 
prevent  bursting. 

Compressibility  of  Liquids.— Liquids  are  not  entirely  incompressible,  but 
they  , are  so  nearly  so,  that  for  most  purposes  they  may  be  considered  as 
incompressible.  The  bulk  of  water  is  diminished  about  by  a pressure  of 
324  lb.  per  sq.  in.,  or  22  atmospheres;  varying  slightly  with  its  temperature. 
It  is  perfectly  elastic,  regaining  its  original  bulk  when  the  pressure  is 
removed. 

Construction  of  Dams  in  Mines.— Dams  may  be  constructed  in  mines,  either 
to  isolate  a portion  of  the  workings  so  that  they  can  be  flooded  to  extinguish 
fires,  or,  in  cases  where  an  extremely  wet  formation  has  been  penetrated,  it 
is  sometimes  expedient  to  construct  a dam  so  as  to  prevent  the  water  from 
flowing  into  the  workings.  Mine  dams  should  be  of  sufficient  strength  to 
resist  any  column  of  water  that  will  be  likely  to  come  against  them.  The 
dam  should  be  arched  toward  the  direction  from  which  the  pressure  comes, 
and  should  be  given  a good  firm  bearing  in  both  walls  and  in  the  floor  and 
roof.  Fig.  7 illustrates  a brick  dam  that  was  constructed  in  Kehley’s  Run 
Colliery,  at  Shenandoah,  Pa.,  to  isolate  a portion  of  the  seam  so  that  it  might 


184 


HYDROSTATICS. 


be  flooded  to  extinguish  a mine  fire.  This  is  one  of  the  largest  mine  dams 
that  has  ever  been  constructed.  It  is  composed  of  three  brick  arches,  each 
having  a thickness  of  5 ft.,  that  are  placed  one  against  the  other  so  that  they 
act  as  one  solid  structure.  The  gangway  at  this  point  is  about  20  ft.  wide, 
and  the  distance  to  the  next  upper  level  is  about  119  ft.  It  was  intended 
that  this  should  be  the  maximum  head  of  water  that  the  dams  would  ever 
have  to  resist,  though  they  were  made  sufliciently  strong  to  resist  a head  of 
water  reaching  to  the  surface.  The  separate  walls  were  constructed  one  at 
a time,  and  the  cement  allowed  to  set  before  the  next  wall  was  placed.  The 
back  wall  was  carried  to  a greater  depth  and  height  than  the  others,  so  as  to 
make  sure  of  the  fact  that  all  slips  or  partings  had  been  closed.  The  total 
pressure  upon  the  dam  when  the  water  was  in  the  mine  was  about  70,000  lb. 
per  sq.  ft. 

Dams  constructed  to  permit  the  flooding  of  a mine  usually  require  no 
passages  through  them,  but  where  dams  are  constructed  to  confine  the 
water  to  certain  parts  of  the  workings,  and  so  reduce  pumping  charges,  it 
may  be  necessary  to  provide  both  manways  and  drain  pipes  through  the 


Fig.  7. 


dams.  Fig.  8 illustrates  a plan  and  cross-section  of  a dam  in  the  Curry 
Mine,  at  Norway,  Mich.  (“Mines  and  Minerals,”  Vol.  18,  page  177;  Trans. 
A.  I.  M.  E.,  XXVII,  402),  constructed  to  keep  the  water  that  came  from  some 
exploring  drifts  out  of  the  mine  workings.  As  originally  constructed,  it 
consisted  of  a sandstone  dam  10  ft.  thick  and  arched  on  the  back  face 
with  a radius  of  6 ft.  A piece  of  20"  pipe  provided  a manway  through  the 
masonry  and  was  held  in  place  by  three  sets  of  clamps  and  bolts  passing 
through  the  stonework.  A 5"  drain  pipe  was  also  carried  through  the  dam 
and  secured  by  clamps.  When  the  pressure  came  upon  the  dam  it  w'as 
found  to  leak,  so  the  water  was  drained  off  and  a 22"  brick  wall  built 
2 ft.  4 in.  back  of  the  dam,  the  space  between  being  filled  with  concrete,  and 
the  manway  and  drain  pipe  extended  through  the  brick  w'all.  Before  closing 
the  drain  pipe,  horse  manure  was  fastened  against  the  face  of  the  brick  wall 
by  means  of  a plank  partition.  After  this  the  manway  and  drain  pipe  were 
closed,  and  when  the  pressure  came  on,  the  dam  was  found  to  le^  a small 


HYDRAULICS. 


135 


amount,  but  this  soon  practically  ceased,  showing  that  the  manure  had 
closed  the  leaks.  A gauge  in  the  head  of  the  manway  on  this  dam  showed  a 
pressure  of  211  lb.,  which  corresponded  to  a static  head  of  640  ft.  of  water. 
The  total  pressure  against  the  dam  was  something  over  800  tons,  which  it 
successfully  resisted. 


HYDRAULICS. 

Hydraulics  treats  of  liquids  in  motion,  and  in  this,  as  in  hydrostatics, 
water  is  taken  as  the  type.  In  theory  its  principles  are  the  same  as  those  of 
falling  bodies,  but  in  practice  they  are  so  modified  by  various  causes  that 
they  cannot  be  relied  on  except  as  verified  by  experiment.  The  discrepancy 
arises  from  changes  of  temperature  that  vary  the  fluidity  of  the  liquid,  from 
friction,  the  shape  of  the  orifice,  etc.  As  we  shall  deal  with  water  only,  the 
first  cause  may  be  thrown  aside  as  of  little  account. 

In  theory  the  velocity  of  a jet  is  the  same  as  that  of  a body  falling  from  the 
surface  of  the  water. 

To  Find  the  Theoretical  Velocity  of  a Jet  of  Water.— Let  v = the  velocity, 
g = the  acceleration  of  gravity  (32.16  ft.),  and  d = the  distance  of  the  orifice 
below  the  surface  of  the  water. 

Then,  '&=i/2g'd,  orv  = the  square  root  of  twice  the  product  of  g X d. 

Example.— The  depth  of  water  above  the  orifice  is  64  ft.;  what  is  the 
velocity  ? ^ 

Substituting  64  for  d,  and  32.16  for  g,  we  have,  v = 4/2  X 32.16  X 64,  or 
64.16.  

To  Find  the  Theoretical  Quantity  of  Water  Discharged  in  a Given  Time.— Multi- 
ply the  area  of  the  orifice  by  the  velocity  of  the  water,  and  that  product  by 
the  number  of  seconds. 

Example.— What  quantity  of  water  will  be  discharged. in  5 seconds  from 
an  orifice  having  an  area  of  2 sq.  ft.,  at  a depth  of  16  ft.? 

|/  2 X 32.16  X 16  X 2 = 64.16  cu.  ft,,  or  the  amount  discharged  in  1 
second,  and  in  5 seconds  the  amount  will  be  5 X 64.16  = 320.8  cu.  ft. 

The  above  rules  are  only  theoretical,  and  are  only  useful  as  foundations 
on  which  to  build  practical  formulas. 

Flow  of  Water  Through  Orifices. — The  standard  orifice,  or  an  orifice  so 
arranged  that  the  water  in  flowipg  from  it  touches  only  a line,  as  would  be 
the  case  in  flowing  through  a hole  in  a very  thin  plate,  is  used  for  the 
measurement  of  water.  The  contraction  of  the  jet,  which  always  occurs 
when  water  issues  from  a standard  orifice,  is  due  to  the  circumstance  that 
the  particles  of  water  as  they  approach  the  orifice  move  in  converging 
directions,  and  that  these  directions  continue  to  converge  for  a short  distance 
beyond  the  plane  of  the  orifice.  This  contraction  causes  only  the  inner 
corner  of  the  orifice  to  be  touched  by  the  escaping  water,  and  takes  place 
in  orifices  of  any  shape,  its  cross-section  being  similar  to  the  orifice  until 
the  place  of  greatest  contraction  is  passed.  Owing  to  this  contraction, 
the  actual  discharge  from  an  orifice  is  always  less  than  the  theoretical 
discharge. 

The  Coefficient  of  Contraction. — The  coefficient  of  contraction  is  the  number 
by  which  the  area  of  the  orifice  is  to  be  multiplied  in  order  to  find  the  area 
of  the  least  cross-section  of  the  jet.  In  this  way  by  experiment  this  coeffi- 
cient has  been  found  to  be  about  .62  (Merriman’s  “Hydraulics”);  or,  in 
other  words,  the  minimum  cross-section  of  the  jet  is  62^  of  the  cross-section 
of  the  orifice. 

The  Coefficient  of  Velocity.— The  coefficient  of  velocity  is  the  number  by 
which  the  theoretical  velocity  of  flow  from  the  orifice  is  to  be  multiplied  in 
order  to  find  the  actual  velocity  at  the  least  cross-section  of  the  jet.  This 
may  be  taken  for  practical  work  as  .98;  or,  in  other  words,  the  actual  flow 
at  the  contracted  section  is  98^  of  the  theoretical  velocity. 

The  Coefficient  of  Discharge.— The  coefficient  of  discharge  is  the  number  by 
which  the  theoretical  discharge  is  to  be  multiplied  in  order  to  obtain  the 
actual  discharge.  This  has  been  found  by  thousands  of  experiments  to  be 
equal  to  the  product  of  the  coefficients  of  contraction  and  velocity,  and  for 
practical  work  it  may  be  taken  as  .61;  or,  the  actual  discharge  from  standard 
orifices  is  61^  of  the  theoretic  discharge. 


136 


HYDRAULICS. 


Note.— While  the  coefficients  for  standard  orifices  with  sharp  edges  have 
been  determined  fairly  close,  those  for  the  more  complicated  cases  of  weirs, 
and  especially  for  the  fiow  of  water  through  long  pipes,  are  simply  the 
nearest  approximation  to  the  truth  that  it  has  been  possible  to  obtain.  In 
all  cases,  the  coefficient  should  be  one  that  has  been  determined  under  con- 
ditions similar  to  those  in  the  problem  in  hand.  For  instance,  it  is  not  prac- 
ticable to  use  the  coefficient  for  small  pipes  in  solving  problems  relating  to 
large  ones,  or  for  short  pipes  in  solving  problems  relating  to  long  ones. 

Suppression  of  the  Contraction.— When  a vertical  orifice  has  its  lower  edge 
at  the  bottom  of  a reservoir,  the  particles  of  water  flowing  through  its  lower 
portion  move  in  lines  nearly  perpendicular  to  the  plane  of  the  orifice,  and 
the  contraction  of  the  jet  does  not  form  on  the  lower  side.  The  same  thing 
occurs  in  a lesser  degree  when  the  lower  edge  of  the  orifice  is  within  a dis- 
tance of  three  times  its  least  diameter  from  the  bottom.  The  suppression  of 
contraction  will  occur  on  the  side  if  it  is  placed  within  a distance  of  three 
times  its  least  diameter  from  the  side  of  a reservoir,  the  suppression  of 
contraction  being  the  greater  the  nearer  the  orifice  is  to  the  side.  By  round- 
ing the  edge  of  the  orifice  sufficiently,  the  contraction  can  be  completely 
suppressed,  and  the  discharge  can  be  increased.  As  stated  before,  the  value 
of  the  coefficient  of  contraction  for  a standard  square-edged  orifice  is  .62,  but 
with  a rounded  orifice  it  may  have  any  value  between  .62  and  1.00,  depend- 
ing on  the  degree  of  rounding.  The  coefficient  of  discharge  for  square- 
edged  orifices  has  a mean  value  of  .61;  this  is  increased  with  rounded  edges 
and  may  have  any  value  between  .61  and  1.00,  although  it  is  not  probable 
that  values  greater  than  .95  can  be  obtained  except  by  the  most  careful 
adjustment  of  the  rounded  edges  to  the  exact  curve  of  a completely  con- 
tracted jet.  A rounded  interior  orifice  is  therefore  always  a source  of  error 
when  the  object  of  the  orifice  is  the  measurement  of  the  discharge. 


GAUGING  WATER. 

Water  is  sold  by  two  methods;  i.  e.,  the  flowing  unit  and  the  capacity 
unit.  The  flowing  unit  is  a cubic  foot  per  second.  In  the  western  part  of 
North  America  the  miners''  inch  has  come  into  use  quite  largely,  while  in 
Australia  and  New  Zealand  the  cubic  foot  per  second  is  the  common  measure, 
1 cu.  ft.  per  second  being  1 “ head,”  and  10  heads  of  water  would  be  10  cu.  ft. 
per  second,  regardless  of  the  actual  hydrostatic  head  under  which  the  water 
was  delivered.  Water  is  sometimes  sold  for  irrigation  bj^  the  capacity  unit, 
that  is,  so  much  land  covered  to  a certain  depth,  as,  for  instance,  the  “acre- 
foot,”  which  means  that  1 acre  has  been  covered  to  a depth  of  1 foot,  or  that 
an  amount  of  43,560  cu.  ft.  of  water  has  been  furnished. 

Miners’  Inch.— The  miners’  inch  may  be  roughly  defined  as  the  quantity  of 
water  that  will  flow  in  1 minute  through  a vertical  standard  orifice  having  a 
section  of  1 sq.  in.  and  a head  of  6i  in.  above  the  center  of  the  orifice.  This 
quantity  equals  1.53  cu.  ft.,  and  the  mean  quantity  may  be  taken  at,  approxi- 
mately, 1.5  cu.  ft.  per  minute.  The  laws  or  customs  defining  the  miners’ 
inch  in  different  districts  vary  so  that  the  amount  of  water  actually  delivered 
varies  from  1.2  to  1.76  cu.  ft.  per  minute,  the  principal  reasons  for  these  varia- 
tions being  the  method  adopted  for  measuring  the  water  where  large  quan- 
tities are  used;  as,  for  instance,  at  Smartsville,  in  California,  an  opening  4 in. 
deep,  250  in.  long,  with  a head  of  7 in.  above  the  top  edge,  is  said  to  furnish 
1,000  miners’  inches,  while  it  would  actually  furnish  considerably  over  1,^X)0. 
In  other  places,  the  size  of  the  opening  for  measuring  the  amounts  is 
restricted,  and  may  actually  furnish  less  than  the  rated  amount.  In  Montana 
the  common  method  of  measurement  was  formerly  through  a vertical  rect- 
angle 1 in.  high,  with  a head  on  the  center  of  the  orifice  of  4 in.  The  num- 
ber of  miners’  inches  discharged  was  considered  to  be  the  same  as  the 
number  of  linear  inches  in  the  length  of  the  orifice;  thus,  under  the  given 
head,  an  orifice  1 in.  deep  and  60  in.  long  could  discharge  60  miners’  inches. 

The  State  Legislature  of  Montana  has  now  passed  a law  defining  the 
miners’  inch  as  the  number  of  gallons  of  water  discharged  in  a given  time, 
regardless  of  the  character  of  the  openings  or  methods  of  measurement. 
The  statement  is  as  follows:  “Where  water  rights,  expressed  in  miners’ 
inches,  have  been  granted,  100  miners’  inches  shall  be  considered  equivalent 
to  a flow  of  2^  cu.  ft.  (18.7  gal.)  per  second,  and  this  proportion  shall  be 
observed  in  determining  the  equivalent  flow  representea  by  any  number  of 
miners’  inches.” 


MINERS’  INCH. 


137 


If  this  amount  is  reduced  to  cubic  feet  per  minute,  it  will  be  found  to 
be  equal  to  a flow  of  1.5  cu.  ft.  per  minute,  which  is  the  value  given  above 
for  the  miners’  inch. 

Duty  or  Work  Performed  by  a Miners’  Inch  of  Water.— Few  tests  have  been 
made  in  regard  to  the  duty  of  a miners’  inch  of  water,  but  the  North 
Bloomfleld  mine  and  the  La  Grange  mine,  in  California,  have  carried  on 
a series  of  experiments  extending  over  several  years.  At  the  La  Grange 
mine  the  observations  were  carried  on  simultaneously  upon  several  differ- 
ent claims,  hence  parallel  dates  appear.  The  accompanying  tables  give 
the  results  of  these  experiments.  In  general  it  is  governed  by  the  size, 
capacity,  character  of  pavement,  and  grade  of  sluices,  together  with  the 
supply  of  water.  A heavy  grade  will  compensate  for  a limited  supply. 
With  an  abundant  supply  of  water  and  material,  the  capacity  of  the  sluices 
will  depend  on:  First,  the  character  of  the  material  washed;  second,  the 
size  and  minimum  grade  of  the  sluices;  third,  the  character  of  the  riffles  used. 


Duty  of  Miners’  Inch. 

{Risdon  Iron  Works,  Evans’s  Elevator  Catalogue.) 
North  Bloomfield  Mine. 


Years. 

Cubic  Yards  of  Gravel 
Washed. 

Miners’  24-Hour 
Inches. 

Grades. 

Cubic  Yards  Washed 
per  Miners’  Inch. 

Cubic  Feet  of  Water  Used 
per  Cubic  Feet 
of  Gravel  Moved. 

Height  of  Bank. 

Remarks. 

1870-74 

1875 

1876 

1877 

3.250.000 

1.858.000 
2,919,700 
2,993,930 

710,987 

386,972 

700.000 

595.000 

614  in.  to  12  ft. 

in.  to  12  ft. 
634  in. to  12  ft. 
6J4  in.  to  12  ft. 

4.60 

4.80 

4.17 

3.86 

18 

17 

20 

21 

100  ft. 

100  ft. 

200  ft. 

265  ft. 

Sluices  6 ft.  wide, 
32  in.  deep. 

RiflBes  principally 
blocks  (wood), but 
rock  riflBes  in  tail 
sluices. 

The  larger  portion 
of  the  material 
moved  was  top 
gravel. 

Totals 

11,021,630 

2,392,959 

4.60 

18- 

La  Grange  Mine. 


1874- 76 

1875- 76 

1874- 76 

1875- 78 

1880-81 

676,968 

683,244 

284,932 

459,570 

329,120 

624.745 

375,155 

207,010 

302,960 

203,325 

4 in.  to  16  ft. 

4 in.  to  16  ft. 

4 in.  to  16  ft. 

4 in.  to  16  ft. 

4 in.  to  16  ft. 

1.08 

1.82 

1.37 

1.52 

1.57 

74.0 

43.9 

58.0 

52.0 

50.0 

10  to  48  ft. 

6 ft. 

50  to  80  ft. 

40  to  50  ft. 

10  to  80  ft. 

Sluices  4 ft.  wide 
and  30  in.  deep, 
paved  with 
blocks. 

Totals 

2,433,834 

1,713,195 

1.42 

56.0 

The  right-angled  V notch  is  frequently  used  for  gauging  the  flow  of  compara- 
tively small  streams.  The  notch  is  usually  fitted  into  a box  provided  with 
baffle  boards.  Fig.  9,  or  where  this  is  not  practicable  the  water  should  be 
so  impounded  above  the  notch  as  to  remove  all  possibility  of  surface  cur- 
rents producing  a perceptible  velocity  of  approach.  The  distance  a of  the 
surface  of  the  water  below  the  top  of  the  box  is  taken  at  a point  some  dis- 
tance back  from  the  notch  (at  least  18  to  20  in.),  where  the  surface  of  the 
water  is  unaffected  by  the  flow  through  the  notch.  The  distance  a,  sub- 
tracted from  the  total  depth  of  the  notch  H,  gives  the  head  h of  the  water 
passing  over  the  notch.  The  discharge  in  cubic  feet  per  second  may  be 
found  by  the  formula  _ _ 

Q = .306t//i5  = .mh^v^h, 

in  which  Q equals  the  quantity  in  cubic  feet  per  minute  and  h equals  the 


138 


HYDRAVLICS. 


head  in  inches.  The  accompanying  table  gives  the  discharge  in  cubic  feet 
per  minute  through  a right-angled  V notch,  as  shown  in  Fig.  9,  for  heads 
varying  from  1.05  in.  to  12  in. 


TABLE  I. 

Discharge  of  Water  Through  a Right-Angled  V Notch. 


h 

Head. 

Inches. 

Q 

Quantity 
per  Min. 
Cu.  Ft. 

n 

Head. 

Inches. 

Quantity 
per  Min. 
Cu.  Ft. 

n 

Head. 

Inches. 

Q 

Quantity 
per  Min. 
Cu.  Ft. 

h 

Head. 

Inches. 

Q 

Quantity 
per  Min. 
Cu.  Ft. 

Ti 

Head. 

Inches. 

Q 

Quantity 
per  Min. 
Cu.  Ft. 

1.05 

.3457 

3.25 

5.827 

5.45 

21.22 

7.65 

49.53 

9.85 

93.18 

1.10 

.3884 

3.30 

6.054 

5.50 

21.71 

7.70 

50.34 

9.90 

94.37 

1.15 

.4340 

3.35 

6.285 

5.55 

22.20 

7.75 

51.16 

9.95 

95.56 

1.20 

.4827 

3.40 

6.523 

5.60 

22.70 

7.80 

51.99 

10.00 

96.77 

1.25 

.5345 

3.45 

6.765 

5.65 

23.22 

7.85 

52.83 

10.05 

97.98 

1.30 

.5896 

3.50 

7.012 

5.70 

23.74 

7.90 

53.67 

10.10 

99.20 

1.35 

.6480 

3.55 

7.266 

5.75 

24.26 

7.95 

54.53 

10.15 

100.43 

1.40 

.7096 

3.60 

7.524 

5.80 

24.79 

8.00 

55.39 

10.20 

101.67 

1.45 

.7747 

3.65 

7.788 

5.85 

25.33 

8.05 

56.26 

10.25 

102.92 

1.50 

.8432 

3.70 

8.058 

5.90 

25.87 

8.10 

57.14 

10.30 

104.18 

1.55 

.9153 

3.75 

8.332 

5.95 

26.42 

8.15 

58.03 

10.35 

105.45 

1.60 

.9909 

3.80 

8.613 

6.00 

26.98 

8.20 

58.92 

10.40 

106.73 

1.65 

1.0700 

3.85 

8.899 

6.05 

27.55 

8.25 

59.82 

10.45 

108.02 

1.70 

1.1530 

3.90 

9.191 

6.10 

28.12 

8.30 

60.73 

10.50 

109.31 

1.75 

1.2400 

3.95 

9.489 

6.15 

28.70 

8.35 

61.65 

10.55 

110.62 

1.80 

1.3300 

4.00 

9.792 

6.20 

29.28 

8.40 

62.58 

10.60 

111.94 

1.85 

1.4240 

4.05 

10.100 

6.25 

29.88 

8.45 

63.51 

10.65 

113.26 

1.90 

1.5220 

4.10 

10.410 

6.30 

30.48 

8.50 

64.45 

10.70 

114.60 

1.95 

1.6250 

4.15 

10.730 

6.35 

31.09 

8.55 

65.41 

10.75 

115.94 

2.00 

1.7310 

4.20 

11.060 

6.40 

31.71 

8.60 

66.37 

10.80 

117.29 

2.05 

1.8410 

4.25 

11.390 

6.45 

32.33 

8.65 

67.34 

10.85 

118.65 

2.10 

1.9550 

4.30 

11.730 

6.50 

32.96 

8.70 

68.32 

10.90 

120.02 

2.15 

2.0740 

4.35 

12.070 

6.55 

33.60 

8.75 

69.30 

10.95 

121.41 

2.20 

2.1960 

4.40 

12.420 

6.60 

34.24 

8.80 

70.30 

11.00 

122.81 

2.25 

2.3230 

4.45 

12.780 

6.65 

34.89 

8.85 

71.30 

11.05 

124.21 

2.30 

2.4550 

4.50 

13.140 

6.70 

35.56 

8.90 

72.31 

11.10 

125.61 

2.35 

2.5900 

4.55 

13.510 

6.75 

36.23 

8.95 

73.33 

11.15 

127.03 

2.40 

2.7300 

4.60 

13.890 

6.80 

36.89 

9.00 

74.36 

11.20 

128.45 

2.45 

2.8750 

4.65 

14.270 

6.85 

37.58 

9.05 

75.40 

11.25 

129.90 

2.50 

3.0240 

4.70 

14.650 

6.90 

38.27 

9.10 

76.44 

11.30 

131.35 

2.55 

3.1770 

4.75 

15.040 

6.95 

38.96 

9.15 

77.49 

11.35 

132.81 

2.60 

3.3350 

4.80 

15.440 

7.00 

39.67 

9.20 

78.55 

11.40 

134.27 

2.65 

3.4980 

4.85 

15.850 

7.05 

40.38 

9.25 

79.63 

11.45 

135.75 

2.70 

3.6660 

4.90 

16.260 

7.10 

41.10 

9.30 

80.71 

11.50 

137.23 

2.75 

3.8380 

4.95 

16.680 

7.15 

41.83 

9.35 

81.80 

11.55 

138.73 

2.80 

4.0140 

5.00 

17.110 

7.20 

42.56 

9.40 

, 82.90 

11.60 

140.23 

2.85 

4.1960 

5.05 

17.540 

7.25 

43.30 

9.45 

84.01 

11.65 

141.75 

2.90 

4.3820 

5.10 

17.970 

7.30 

44.06 

9.50 

85.12 

11.70 

143.28^ 

2.95 

4.5740 

5.15 

18.420 

7.35 

44.82 

9.55 

86.24 

11.75 

144.82 

3.00 

4.7700 

5.20 

18.870 

7.40 

45.58 

9.60 

87.37 

11.80 

146.36 

3.05 

4.9710 

5.25 

19.320 

7.45 

46.36 

9.65 

88.52 

11.85 

147.91 

3.10 

5.1780 

5.30 

19.790 

7.50 

47.14 

9.70 

89.67 

11.90 

149.48 

3.15 

5.3880 

5.35 

20.260 

7.55 

47.92 

9.75 

90.83 

11.95 

151.05 

3.20 

5.6050 

5.40 

20.730 

7.60 

48.72 

9.80 

92.00 

12.00 

152.64 

1 cu.  ft.  contains  7.48  U.  S.  gallons;  1 U.  S.  gallon  weighs  8.34  lb. 

Gauging  by  Weirs.— A weir  is  an  obstruction  placed  across  a stream  for  the 
purpose  of  divermng  the  water  so  as  to  make  it  flow  through  a desired  chan- 
nel, which  may  be  a notch  or  opening  in  the  weir  itself.  The  term  usually 
applies  to  rectangular  notches  in  which  the  water  touches  only  the  bottom 
and  ends,  the  opening  being  a notch  without  any  upper  edge.  Weirs  are  of 
two  general  classes:  weirs  with  end  contractions^  Kg.  10  (a),  and  weirs  without 


GAUGING  BY  WEIRS. 


139 


Fig.  9. 


Let  I 
H : 


h = 1 


end  contractions,  Fig.  10  (&).  The  crest  and  edges  of  the  weir  with  end  con- 
tractions should  be  sharp,  as,  shown  at  a,  Fig.  10  (c)  and  {d  ).  The  head 
of  water  H producing  the  flow  over  the  weir  should  be  measured  at  a suffi- 
cient distance  from  the  crest  to  avoid  the  effects  of  the  curve  of  the  surface 
as  it  flows  over  the  crest.  The 
water  above  the  weir  should 
be  motionless,  or  if  it  has  any 
perceptible  current  toward 
the  weir,  this  should  be  deter- 
mined and  taken  into  account 
in  the  formula.  Fig.  11  illus- 
trates a weir  constructed  across 
a small  stream  for  measuring 
its  flo  w.  The  head  is  measured 
from  the  stake  F^some  distance 
back  of  the  weir,  the  top  of  the  stake  being  level  with  the  crest  of  the  weir 
B.  The  discharge  over  the  weir  may  be  calculated  from  the  following 
formula: 

= length  of  weir  in  feet; 
head  in  feet; 

velocity  with  which  the  water  approaches  the  weir  in  feet; 
a head  equivalent  to  the  velocity  with  which  the  water 
approaches  the  weir; 
c = coefficient  of  discharge; 

Q = theoretic  discharge  in  cubic  feet  per  second; 

Q'  = actual  discharge  in  cubic  feet  per  second. 

For  weirs  with  end  contractions  and  a velocity  of  approach,  the  actual 

discharge  is 

Q = 5.347  c?i/(Lr-|- 1.4 /i)3. 

Where  the  water  has  no 

velocity  of  approach, 

Q = 5.347  cZ 

For  weirs  without  end  con- 
tractions, but  with  a velocity 
of  approach,  the  actual  dis- 
charge is 

Q = 5.347  c;i/(iT+i/i)3. 
Where  the  water  has  no 

velocity  of  approach, 

q = 5.347CZ  VW. 

The  velocity  with  which 
the  water  approaches  the  weir 
may  be  found  by  determining 
the  approximate  discharge 
from  the  stream  without  any  allowance  for  velocity  of  approach,  and  then 
dividing  this  discharge  in  cubic  feet  per  second  by  the  area  of  the  stream  in 
square  feet  where  it  approaches  the  weir,  which  will  give  the  velocity  of 
approach  in  feet  per 


second.  Having  ob- 
tained the  value  ofv, 
the  equivalent  head  h 
may  be  found  by  the 
formula 

h = 0.01555  ^2. 

Since  v is  small  in 
a properly  constructed 
weir,  it  is  usually  neg- 
lected unless  great 
accuracy  is  required. 

The  values  of  coeffi- 
cients of  discharge,  as 
determined  from  ex- 
periments for  weirs 
with  end  contractions, 
are  given  in  Table  II, 
and  for  weirs  without  end  contractions  in  Table  III.  The  values  of  the 
coefficients  in  Tables  II  and  III  are  given  in  feet  and  tenths.  Frequently 


Fig.  11. 


140 


HYDRA  ULICS, 


in  measuring  water  where  only  a close  approximation  is  required,  it  is 
desired  to  take  all  of  the  measurement  in  feet  and  inches.  See  Table  IV. 


TABLE  II. 

Values  of  the  Coefficient  of  Discharge  for  Weirs  With 
End  Contractions. 


Length  of  Weir.  Feet. 


Effective  Head. 


Feet. 

.66 

1 

2 

3 

5 

10 

19 

.10 

.632 

.639 

.646 

.652 

.653 

.655 

.656 

.15 

.619 

.625 

.634 

.638 

.640 

.641 

.642 

.20 

.611 

.618 

.626 

.630 

.631 

.633 

.634 

.25 

.605 

.612 

.621 

.624 

.626 

.628 

.629 

.30 

.601 

.608 

.616 

.619 

.621 

.624 

.625 

.40 

.595 

.601 

.609 

.613 

.615 

.618 

.620 

.50 

.590 

.596 

.605 

.608 

.611 

.615 

.617 

.60 

,587 

.593 

.601 

.605 

.608 

.613 

.615 

.70 

.590 

.598 

.603 

.606 

.612 

.614 

.80 

.595 

.600 

.604 

.611 

.613 

.90 

.592 

.598 

.603 

.609 

.612 

1.00 

.590 

.595 

.601 

.608 

.611 

1.20 

.585 

.591 

.597 

.605 

.610 

1.40 

.580 

.587 

.594 

.602 

.609 

1.60 

.582 

.591 

.600 

.607 

TABLE  III. 

Values  of  the  Coefficient  of  Discharge  for  Weirs  Without 
End  Contractions. 


Length  of  Weir.  Feet. 


Effective  Head. 


Feet. 

19 

10 

7 

5 

4 

3 

2 

.10 

.657 

.658 

.658 

.659 

.15 

.643 

.644 

.645 

.645 

.647 

.649 

.652 

.20 

.635 

.637 

.637 

.638 

.641 

.642 

.645 

.25 

.630 

.632 

.633 

.634 

.636 

.638 

.641 

.30 

.626 

.628 

.629 

.631 

.633 

.636 

.639 

.40 

.621 

.623 

.625 

.628 

.630 

.633 

.636 

.50 

.619 

.621 

.624 

.627 

.630 

.633 

.637 

.60 

.618 

.620 

.623 

.627 

.f)30 

.634 

.638 

.70 

.618 

.620 

.624 

.628 

.631 

.635 

.640 

.80 

.618 

.621 

.625 

.629 

.633 

.637 

.643 

.90 

.619 

.622 

.627 

.631 

.635 

.639 

.645 

1.00 

.619 

.624 

.628 

.633 

.637 

.641 

.648 

1.20 

.620 

.626 

.632 

.636 

.641 

.646 

1.40 

.622 

.629 

.634 

.640 

.644 

1.60 

.623 

.631 

.637 

.642 

.647 

CONVERSION  FACTORS. 


141 


TABLE  IV. 

Weir  Table  Giving  Cubic  Feet  Discharged  per  Minute  for  Each  Inch 
IN  Length  of  Weir  for  Depths  From  i In.  to  25  In. 

This  table  should  not  be  used  unless  the  length  of  the  crest  is  at  least 
3 or  4 times  the  depth  of  water  passing  over  the  weir,  for  if  this  is  not  the 
case,  there  will  be  serious  errors  caused  by  end  contractions. 


Inches. 

0 

8 

3. 

8 

a 

1 

7 

8 

0 

.01 

.05 

.09 

.14 

.20 

.26 

.33 

1 

.40 

.47 

.55 

.65 

.74 

.83 

.93 

1.03 

2 

1.14 

1.24 

1.36 

1.47 

1.59 

1.71 

1.83 

1.96 

3 

2.09 

2.23 

2.36 

2.50 

2.63 

2.78 

2.92 

3.07 

4 

3.22 

3.37 

3.52 

3.68 

3.83 

3.99 

4.16 

4.32 

5 

4.50 

4.67 

4.84 

5.01 

5.18 

5.36 

5.54 

5.72 

6 

5.90 

6.09 

6.28 

6.47 

6.65 

6.85 

7.05 

7.25 

7 

7.44 

7.64 

7.84 

8.05 

8.25 

8.45 

8.66 

8.86 

8 

9.10 

9.31 

9.52 

9.74 

9.96 

10.18 

10.40 

10.62 

9 

10.86 

11.08 

11.31 

11.54 

11.77 

12.00 

12.23 

12.47 

10 

12.71 

13.95 

13.19 

13.43 

13.67 

13.93 

14.16 

14.42 

11 

14.67 

14.92 

15.18 

15.43 

15.67 

15.96 

16.20 

16.46 

12 

16.73 

16.99 

17.26 

17.52 

17.78 

18.05 

18.32 

18.58 

13 

18.87 

19.14 

19.42 

19.69 

19.97 

20.24 

20.52 

20.80 

14 

21.09 

21.37 

21.65 

21.94 

22.22 

22.51 

22.79 

23.08 

15 

23.38 

23.67 

23.97 

24.26 

24.56 

24.86 

25.16 

25.46 

16 

25.76 

26.06 

26.36 

26.66 

26.97 

27.27 

27.58 

27.89 

17 

28.20 

28.51 

28.82 

29.14 

29.45 

29.76 

30.08 

30.39 

18 

30.70 

31.02 

31.34 

31.66 

31.98 

32.31 

32.63 

32.96 

19 

33.29 

33.61 

33.94 

34.27 

34.60 

34.94 

35.27 

35.60 

20 

35.94 

36.27 

36.60 

36.94 

37.28 

37.62 

37.96 

38.31 

21 

38.65 

39.00 

39.34 

39.69 

40.04 

40.39 

40.73 

41.09 

22 

41.43 

41.78 

42.13 

42.49 

42.84 

43.20 

43.56 

43.92 

23 

44.28 

44.64 

45.00 

45.38 

45.71 

46.08 

46.43 

46.81 

24 

47.18 

47.55 

47.91 

48.28 

48.65 

49.02 

49.39 

49.76 

CONVERSION  FACTORS. 

Cubic  Feet  Into  Gallons: 

1 723 

1 cu.  ft.  = 1,728  cu.  in.  = gal.  = 7,4805194  gal. 


Gallons  Into  Cubic  Feet: 

231 

1 United  States  liquid  gal.  = 231  cu.  in.  = ——  cu.  ft.  = .133680555  cu.  ft. 

x^lZo 

Feet  per  Second  Into  Miles  per  Hour: 

3 600  15 

1 ft.  per  sec.  = 3,600  ft.  per  hr.  ==  or  ~ miles  per  hour. 

JoU  22 

Miles  per  Hour  Into  Feet  per  Second: 

5 280  22 

1 mi.  per  hr.  ==  5,280  ft.  per  hr.  = or  — ft.  per  sec. 

OjDUO  lo 

Second'Feet  per  Day  Into  Gallons: 

1 second-foot,  or  7.4805194  gal.  per  sec.  for  1 day,  or  86,400  sec.  = 646,316.87616  gal. 

Millions  of  Gallons  Into  Second-Feet  per  Day:J 

231  000  000 

1,000,000  gal.  per  24  hr.  = cu.  ft.  per  sec.,  or  1.5472286  second-feet. 

l,72o  X oO,4Uu 

Second-Feet  per  Day  Into  Acre-Feet: 

1 second-foot  flow  for  1 day  = 86,400  cu.  ft.  = , or  1.983471  acre-feet. 


142 


HYDRA  ULICS. 


Acre-Feet  into  Second'Feet  Flow  for  24  Hours: 

One  acre-foot  each  24  hr.  = 43,560  cu.  ft.  each  86,400  sec. 

43,560  121  ^ ^ o.  V. 

= . or  — second-foot  flow  for  24  hr. 

86,400  240 


Acre-Feet  Into  Gallons: 

1 acre-foot  = 43,560  cu.  ft. 


43,560  X 1,728  75,271,680 


231 


231 


, or  325,851.428  gal. 


Millions  of  Gallons  Into  Acre-Feet: 

1,000,000  United  States  liquid  gal.,  or  231,000,000  cu.  in.  = 133,680.555  cu.  ft., 
133,680 


43,560 


= 3.0688832  acre-feet. 


Second-Feet  Into  Minute  Gallons: 

Factors:  1 cu.  ft.  contains  1,728  cu.  in.;  1 gal.  has  a capacity  of  231  cu.  in.; 
1 second-foot  equals  [(1,728  -r-  231)  X 60]  gal.  per  min.,  or  448.831164  minute- 
gallons. 


Minute-Gallons  Into  Second-Feet: 

Factors:  1 gal.  contains  231  cu.  in.;  1 cu.  ft.  contains  1,728  cu.  in.;  1 gal. 
per  min.  equals  [(231  1,728)  60]  second-feet,  or  .0022280092  second-foot. 


FLOW  OF  WATER  IN  OPEN  CHANNELS. 


Ditches.— In  the  case  of  hydraulic  mining  and  irrigation,  water  is  usually 
conveyed  through  ditches.  The  ditch  line  should  be  carefully  surveyed  and 
all  brush  and  trees  removed,  and  the  underbrush  cut  away  and  burned, 
before  beginning  to  excavate  the  ditch. 

The  follovung  letters  will  be  used  in  the  formulas  for  determining  the 
various  factors  relating  to  ditches: 

h = difference  in  level  between  ends  of  canal  or  ditch,  or  between  two 
points  under  consideration; 

I ^ horizontal  length  of  portion  of  canal  or  ditch  under  consideration; 

s = slope  = ratio  y = sin  of  slope; 

a = area  of  water  cross-section  in  square  feet; 

p = wet  perimeter  =a'  portion  of  outline  of  cross-section  of  stream  in 
contact  with  channel,  in  feet; 


c'  = 


v'  = 
% = 
X = 

Q = 


hydraulic  radius,  or  hydraulic  mean  depth  = ratio 

coefficient,  depending  on  nature  of  surface  of  the  ditch; 
coefficient  depending  on  nature  of  surface  of  ditch,  as  determined  by 
Kutter’s  formula; 

mean  velocity  of  flow  in  feet  per  second; 
surface  velocity  of  a stream; 
bottom  velocity  of  a stream; 

bottom  or  one  side  of  a section,  the  form  of  which  is  half  a regular 
hexagon,  in  feet; 

quantity  of  water  flowing,  in  cubic  feet  per  second; 
coefficient  of  roughness  in  Kutter’s  formula. 


The  form  of  ditch  and  its  grade  will  depend  largely  on  the  amount  of 
water  to  be  conveyed  and  the  character  of  the  soil  in  the  section  under 
consideration.  As  a general  rule,  the  average  flow  of  water  in  a ditch 
should  not  be  less  than  2 ft.  per  second,  and  under  most  circumstances 
should  not  exceed  4 ft.,  though  in  rare  cases  where  the  formation  is  suitable, 
mean  velocities  of  5 ft.  per  second  are  employed.  Sand  will  deposit  from  a 
current  flowing  at  the  rate  of  li  ft.  per  second,  and  if  the  current  does  not 
have  a velocity  of  at  least  2 ft.  per  second,  vegetation  is  liable  to  block  the 
ditch  line. 


Safe  Bottom  Velocity.— The  bottom  velocity  of  a stream  may  be  ob^ined 
from  the  average  velocity  by  the  following  formula:  Vf,  = v — 10.87  rs. 

The  following  table  gives  values  of  safe  bottom  and  mean  velocities,  cor- 
responding with  certain  materials,  as  given  by  Ganguillet  and  Kutter: 


FLOW  OF  WATER  IN  CHANNELS. 


143 


Material  of  Channel. 

Safe  BottomVelocityVfi. 
Feet  per  Second. 

Mean  Velocity  v. 
Feet  per  Second. 

Soft  brown  earth 

.249 

.328 

Soft  loam  

.499 

.656 

Sand 

1.000 

1.312 

Gravel 

1.998 

2.625 

Pebbles  

2.999 

3.938 

Broken  stone,  flint 

4.003 

5.579 

Conglomerate,  soft  slate 

4.988 

6.564 

Stratified  rock 

6.006 

8.204 

Hard  rock 

10.009 

13.127 

Resistance  of  Soils  to  Erosion  by  Water.— W.  A.  Burr,  “ Engineering  News/’ 
February  8, 1894,  gives  a diagram  showing  the  resistance  of  various  soils  to 
erosion  % water.  The  following  values  have  been  selected  from  Mr.  Burr’s 
work  for  different  kinds  of  soil: 


Pure  sand  resists  erosion  by  flow  of 1.10  ft.  per  sec. 

Sandy  soil,  15/o  clay 1.20  ft.  per  sec. 

Sandy  loam,  40^  clay 1.80  ft.  per  sec. 

Loamy  soil,  65^  clay  3.00  ft.  per  sec. 

Clay  loam,  85^  clay 4.80  ft.  per  sec. 

Agricultural  clay,  95^  clay 6.20  ft.  per  sec. 

Clay  7.35  ft.  per  sec. 


Carrying  Capacity  of  Ditches.— Ditches  should  never  be  run  full,  but  should 
be  constructed  large  enough  so  that  they  will  carry  the  desired  amount  of 
water  when  from  ^ to  I full.  For  any  given  cross-section,  the  greatest  flow 
will  be  attained  when  the  hydraulic  radius  or  hydraulic  mean  depth  is  equal 
to  one-half  of  the  actual  depth  of  the  channel.  The  cross-section  of  a ditch 
or  conduit  that  has  the  greatest  possible  carrying  capacity  is  a half  circle, 
and  the  nearest  practical  approach  to  this  is  a half  hexagon.  Knowing 
the  cross-section  of  a ditch,  its  dimensions  may  be  found  by  the  formula: 

/ 2a  ' 

^ y 2.598 

As  the  obtuse  angle  between  the  side  and  bottom  of  the  ditch  is  120°,  the 
form  can  be  easily  laid  off.  The  carrying  capacity  of  ditches  generally 
increases  after  they  have  been  in  use  some  time,  as  the  ditch  becomes  lined 
with  a fine  scum  that  closes  the  pores  in  the  soil  and  prevents  leakage.  This 
may  increase  the  amount  to  as  much  as  10^. 

Grade.— The  grade  of  the  ditch  must  be  sufficient  to  create  the  desired 
velocity  of  flow,  and  depends  largely  on  the  character  of  the  material  com- 
posing the  surfaces  of  the  ditch.  If  the  surface  is  smooth,  as,  for  instance, 
where  the  ditch  is  cut  through  clay  or  is  lined  with  masonry,  the  grade  can 
be  considerably  less  than  where  the  surface  is  rough,  or  when  cut  through 
coarse  gravel  or  when  lined  with  rough  stone.  In  mountainous  countries, 
where  the  ground  is  hard,  deep  narrow  ditches  with  steep  grades  are  gener- 
ally preferred  to  larger  channels  with  gentle  slopes,  as  the  cost  of  excavation 
is  considerably  less;  but  steep  grades  and  narrow  ditches  are  suitable  only 
when  the  banks  can  resist  the  rapid  flow.  In  California,  grades  of  from  16  to 
20  ft.  per  mile  are  used,  and  10  ft.  per  mile  is  quite  common.  Water  channels 
of  a uniform  cross-section  should  have  a uniform  grade,  otherwise,  the  flow 
will  be  checked  in  places,  which  will  result  in  deposits  of  sand  or  silt  in 
some  portions  of  the  ditch,  which  are  liable  to  cause  the  banks  to  be  over- 
flowed and  the  ditch  to  be  ultimately  destroyed.  In  designing  any  given 
ditch,  the  grade  is  generally  assumed  to  correspond  to  the  formation  of  the 
country  and  the  velocity  figured  from  the  grade.  In  case  v is  found  to  be  so 
great  that  it  would  cut  the  banks,  it  will  be  necessary  either  to  reduce  the 
grade  or  to  change  the  form  of  the  ditch  so  as  to  reduce  the  velocity. 

Ditch  banks,  when  possible,  should  be  composed  of  solid  material,  but 
frequently  it  is  necessary  to  use  excavated  material.  Where  this  is  the  case, 
care  must  be  taken  to  see  that  the  material  is  so  placed  as  to  avoid  settling 


144 


HYDRA  ULICS. 


and  cracking  as  much  as  possible.  All  stumps,  roots,  etc.  should  be  separated 
from  the  material  to  be  used  for  embankments.  If  artificial  banks  are  neces- 
sary, it  is  best  to  build  them  of  masonry,  provided  the  expense  is  not  too 
great;  or,  the  water  may  be  carried  across  depressions  in  pipes  or  flumes. 
When  the  character  of  the  material  through  which  the  ditch  is  constructed 
is  not  sufficiently  firm  to  resist  the  desired  current  velocity,  it  becomes  neces- 
sary to  line  the  ditch.  In  some  locations  the  ditches  are  simply  smoothed 
on  the  inside  and  lined  with  from  | in.  to  1 in.  of  cement  mortar,  made  up 
of  Portland  cement  and  sharp  sand.  In  other  cases  they  are  lined  with  dry 
stonework  laid  up  in  order  and  carefully  bonded  together.  Sometimes  the 
stonework  is  pointed  with  cement  or  mortar  on  the  inside,  so  as  to  present  a 
more  uniform  surface  to  the  flow.  In  other  cases,  the  sides  are  simply 
revetted  with  stone. 

influence  of  Depth  on  Ditch.— The  depth  of  the  flow  in  a ditch  has  consider- 
able influence  on  the  scouring  or  eroding  of  the  bottom  and  the  banks, 
owing  to  the  fact  that  a much  greater  average  velocity  can  be  attained  in  a 
deep  stream  than  in  a shallow  stream,  without  causing  an  excessive  velocity 
of  the  water  in  contact  with  the  wet  perimeter.  For  this  reason,  in  cases 
where  banks  will  stand  it,  it  is  best  to  use  narrow  deep  ditches  rather  than 
wide  fiat  ditches,  though  each  location  has  to  be  treated  in  accordance  with 
its  own  special  conditions,  and  no  general  rule  can  be  laid  down. 

Measuring  the  Flow  of  Water  in  Channels.— The  laws  for  the  resistance  to  the 
fiow  may  be  expressed  by  the  relation  (see  page  142  for  significance  of  letters) : 

ha  = c'lpv^  or,  D = X f = V"?  X s X r. 


If  c = formula  becomes  v = c i/  rs. 

The  coefficient  c is  usually  found  by  means  of  Kutter’s  formula,  one  form 
of  which  is  as  follows: 

23  + 1 + ■ 

.5521  + (23  + --5^) -7^’ 

\ ^ ^ j/  r 

The  values  for  n,  the  coefficient  of  roughness,  under  various  conditions, 
are  as  follows: 


Character  of  Channel. 


Value  of  n. 


Clean,  well-planed  timber 

Clean,  smooth,  glazed  iron,  and  stoneware  pipes 

Masonry,  smoothly  plastered  with  cement,  and  for  very  clean, 

smooth,  cast-iron  pipe 

Unplaned  timber,  ordinary  cast-iron  pipe,  and  selected  pipe 

sewers,  well  laid  and  thoroughly  flushed...! 

Rough  iron  pipes  and  ordinary  sewer  pipes,  laid  under  the 

usual  conditions 

Dressed  masonry  and  well-laid  brickwork  

Good  rubble  masonry  and  ordinary  rough  or  fouled  brickwork 

Coarse  rubble  masonry  and  firm,  compact  gravel 

Well-made  earth  canals  in  good  alinement 

Rivers  and  canals  in  moderately  good  order  and  i>erfectly  free 

from  stones  and  weeds 

Rivers  and  canals  in  rather  bad  condition  and  somewhat 

obstructed  by  stones  and  weeds 

Rivers  and  canals  in  bad  condition,  overgrown  with  vegeta- 
tion and  strewn  with  stones  and  other  detritus,  according  to 
condition  


.009 

.010 

.011 


.013 

.015 

.017 

.020 

.0225 

.025 

.030 


.035  to  .050 


FLUMES. 


145 


As  it  is  quite  diflQcult  to  obtain  the  value  of  c by  Kutter’s  formula,  the  fol- 
lowing three  approximate  formulas  for  v are  given: 


For  canals  with  earthen  banks, 

If  the  ditch  is  lined  with  dry  stonework, 


/100,000r2s 
^ ~ \ 9 r + 35  ‘ 

;ioo,ooor^ 


If  the  ditch  is  lined  with  rubble  masonry,  v 


1100,000  r2s 
\ 7.3r  + 6 ’ 


To  find  the  quantity  Q of  water  fiowing  through  any  channel  in  a given 
time,  multiply  the  velocity  by  the  area,  or  Q = av. 

Flow  in  Brooks  and  Rivers.— When  a stream  is  so  large  that  it  becomes 
impracticable  to  employ  a weir  for  measuring  its  flow,  fairly  accurate 
results  may  be  arrived  at  by  determining  the  velocity  of  the  current  at 
various  points  in  a carefully  surveyed  cross-section  of  the  stream,  thus 
determining  both  v and  a.  The  greatest  velocity  of  current  occurs  at  a point 
some  distance  below  the  surface,  in  the  deepest  part  of  the  channel.  When 
determining  the  current  velocities  in  the  different  portions  of  a stream,  it  is 
frequently  advantageous  to  divide  the  stream  into  divisions.  This  may  be 
accomplished  by  stretching  a wire  across  and  tying  strings  or  rags  about  the 
wire  at  various  points.  The  mean  velocity  of  the  current  between  these 
points  can  be  determined  by  current  meters,  or  by  floats.  The  points  for 
observation  should  be  chosen  where  the  channel  is  comparatively  straight 
an^  the  current  uniform.  Surface  floats  may  be  used,  in  which  case  the 
mean  velocity  of  the  point  where  the  float  is  used  may  be  found  as  follows: 
If  v'  equals  the  observed  velocity,  then  the  mean  velocity  will  be  v = .9  v'. 

By  taking  observations  of  the  velocity  of  the  current  in  each  section  of 
a stream,  the  amount  of  water  flowing  may  be  determined  for  each  separate 
section.  The  total  amount  of  water  flowing  in  the  stream  will  be  the  sum 
of  the  amounts  in  each  section.  The  average  velocity  of  the  entire  stream 
may  be  found  by  dividing  the  total  amount  of  water  flowing  by  total  area  of 
the  cross-section  of  the  stream.  The  correction  necessary  to  reduce  surface 
velocity  to  mean  velocity  may  be  made  as  follows:  Measure  off  of  the 
ordinary  distance,  and  figure  the  time  as  though  for  the  full  distance.  For 
instance,  if  only  90  ft.  were  employed,  the  time  would  be  taken  and  the 
problem  figured  as  though  it  were  100  ft.,  on  account  of  the  fact  that  the 
mean  velocity  is  only  of  the  surface  velocity. 


FLUMES. 

Flumes  are  used  for  conveying  water  when  a ditch  line  would  be 
abnormally  long,  or  when  the  material  to  be  excavated  is  very  hard.  They 
may  be  constructed  of  timber  or  of  metal,  but  metal  flumes  are  compara- 
tively rare,  as  piping  can  be  used  instead.  The  line  of  the  proposed  flume 
should  be  carefully  cleared  of  all  standing  timber,  and  the  brush  burned  for 
at  least  20  ft.  each  side  of  the  flume  line  to  prevent  danger  from  fire.  The 
life  of  an  ordinary  flume,  which  is  supported  on  or  constructed  of  timber,  is 
always  short,  varying,  as  a rule,  from  10  to  20  years,  depending  on  whether 
the  flume  is  allowed  to  run  dry  a portion  of  the  year  or  is  always  full  of 
water,  the  care  with  which  it  was  originally  constructed,  and  the  attention 
paid  to  repairs. 

Grade  of  Flumes.— Flumes  are  usually  set  on  a much  steeper  grade  than  is 
possible  in  ditches,  the  grade  frequently  being  as  much  as  25  to  30  ft.  per 
mile,  and  in  special  cases  even  more.  The  result  of  this  is  that  the  carrying 
capacity  of  flumes  is  much  greater  than  that  of  ditches  of  the  same  size. 

The  form  of  flume  depends  largely  on  the  material  of  which  it  is  constructed. 
Metal  flumes  may  have  a semicircular  form,  while  wooden  flumes  are  either 
rectangular  or  V-shaped.  The  former  is  used  almost  exclusively  for  con- 
veying water,  and  the  latter  quite  extensively  for  fluming  timber  or 
cord  wood  from  the  mountains  to  the  shipping  point  in  the  valley. 

Timber  flumes  should  be  so  constructed  that  the  water  will  meet  with  but 
small  resistance,  and  the  bottom  and  side  should  be  enclosed  in  a frame  of 
timbers  so  braced  or  secured  that  there  is  no  possible  chance  of  the  sides 
spreading  or  lifting  from  the  bottom,  and  thus  cause  leakage.  As  a rule,  all 
mortised  and  tenoned  joints  should  be  avoided  in  flume  construction. 


116 


HYDRAVLICS. 


Fig.  12  shows  a timber  flume  in  which  no  joints  are  cut,  the  bottoms  of  the 
posts  being  kept  in  place  by  stringers  spixed  on  the  sills,  and  the  tops  tied 
together  by  pieces  bolted  on.  Fig.  13  shows  a construction  in  which  the  posts 
are  let  into  the  sills  and  supported  by  diagonarbraces.  The  ties  across  the  top 
of  the  posts  are  also  notched  to  receive  the  upper  ends  of  the  posts.  As  a 

rule,  in  such  a construction 
these  ties  are  only  placed  on 
every  third  or  fourth  frame, 
the  diagonal  braces  being 
depended  on  to  hold  the 
other  posts  in  place.  The 
joints  between  the  planking 
may  be  battened  on  the  in- 
side with  strips  of  i"  lumber, 
4 or  5 in.  wide,  or  the  edges 
of  the  planking  may  be 
dressed  and  painted  before 
they  are  put  together,  so  as 
to  form  a tight  joint. 

Connection  With  Ditches. 
Where  flumes  connect  with 
ditches  or  dams,  the  posts 
for  several  boxes  should  be  made  longer,  so  that  they  may  receive  another 
sideboard  to  prevent  the  water  from  splashing  over  the  sides.  The  flume 
should  also  be  widened  out  or  flared,  both  at  its  entry  and  discharge  ends. 
Where  the  flume  passes  through  a bank  of  earth,  an  outer  siding  may  be 
nailed  on  the  outside  of  the  posts,  to  protect  the  flume  from  rotting. 

Trestles.— Where  flumes  are  carried  on  trestles,  the  individual  frames 
supporting  the  flume  are  usually  placed  on  heavy  stringers,  which  in  turn 
are  supported  upon  trestle  bents  from  12  to  16  ft.  apart,  the  frames  supporting 
the  flume  being  placed  about  4 ft.  apart. 

Curves.— Where  flumes  are  laid  around  curves,  the  outer  edge  of  the  flume 
should  be  elevated  so  as  to  prevent  splashing  and  to  cause  the  flowing  water 
to  have  a uniform  depth  across  the  width  of  the  flume.  It  is  impossible  to 
give  any  deflnite  rule  as  to  the.  amount  that  the  outer  edge  of  the  flume 
should  be  raised,  but  this  is  usually  accomplished  by  judging  the  amount 
when  the  flume  is  first  constructed,  and  correcting  this  by  wedging  up  after 
the  water  is  flowing.  The  individual  boxes  of  the  flume  may  have  to  be 
cut  into  2 or  3 portions  on  curves,  and  at  times  the  side  planks  are  sawed 
partially  through,  so  as  to  enable  them  to  be  bent  to  the  desired  curve. 

Waste  gates  should  be  placed  every  half  mile,  to  empty  the  flume  for 
repairs,  or  in  case  of  accident.  They  are  also  useful  for  flushing  snow  out  of 
a flume.  In  snow  regions,  flumes  are  frequently  protected  by  sheds  over 
their  exposed  portions. 

Flow  of  Water  Through  Flumes.— As  smooth  wooden  surfaces  offer  consider- 
ably less  resistance  to  the  flow  of  water  than  earth  or  stone  canals,  the 
coefficients  must  necessarily  be  somewhat  reduced,  and  the  following 
formula  is  useful  in  giving  the  flow  of  water  through  flumes: 


1 100,000  r2  S 

\ 6.6  r + 0.46’ 


That  flumes  may  have  their  full  carrying  capacity,  they  have  to  be  of 
sufficient  length  to  get  the  water  in  motion,  or,  as  it  is  technically  expressed, 
“ to  put  the  water  in  train.”  It  is  largely  on  this  account  that  flumes  have 
to  be  made  of  a larger  cross-section  at  both  the  entrance  and  the  exit.  In 
.cold  countries  it  may  be  best  to  construct  the  flume  narrower  than  it  is  deep, 
as  in  cold  weather  the  ice  in  the  narrow  flume  freezes  a crust  entirely  across 
the  surface,  thus  protecting  the  water  from  further  action  of  the  elements 
and  frequently  prolonging  the  flow  through  the  flume  for  several  weeks, 
while  wide  shallow  flumes  will  not  freeze  on  the  surface  so  quickly,  but  will 
freeze  in  from  the  bottom  and  sides  until  they  are  practically  a solid  mass  of 
ice.  When  a flume  is  laid  on  the  ground  along  a bank,  it  should  be  laid  as 
close  to  the  bank  as  possible,  so  as  to  protect  it  from  snow  or  landslides,  and 
so  that  in  the  winter  the  snow  will  drift  in  under  and  behind  it,  thus 
preventing  the  circulation  of  the  air  about  the  flume.  This  will  protect  the 
flume,  and  may  prolong  the  flow  for  some  time  after  cold  weather  sets  in. 


TUNNELS. 


147 


TUNNELS. 

Tunnels  are  sometimes  used  for  conveying  water,  in  connection  with 
flume  or  ditch  lines.  Where  a tunnel  is  unlined,  it  is  best  to  give  the  roof 
the  shape  of  the  Gothic  arch,  owing  to  the  fact  that  this  stands  better  and 
resists  scaling  to  a greater  extent  than  the  round  arch,  which  usually  scales 
off  until  it  has  the  form  of  the  Gothic  arch.  If  tunnels  are  to  be  used  as 
water  conduits,  without  lining,  care  should  be  taken  to  make  the  inside  of 
the  tunnel  as  smooth  as  possible.  In  some  cases,  in  order  to  increase  the 
carrying  capacity  of  the  tunnel,  they  have  been  lined  with  wooden-stave 
pipe,  backed  with  concrete,  the  pipe  requiring  no  metal  bands,  but  depend- 
ing on  the  concrete  to  keep  it  in  place.  When  such  linings  are  employed,  it 
is  not  practicable  to  have  them  exposed  to  the  alternate  action  of  the  water 
and  the  atmosphere,  hence  the  tunnel  should  be  kept  continually  full  of 
water.  To  accomplish  this,  the  tunnel  may  be  dropped  below  the  grade  of 
the  ditch  or  flume  line,  so  that  it  is  always  under  a slight  hydrostatic 
pressure,  and  even  if  the  water  were  turned  off  from  the  line,  the  tunnel 
would  remain  full  of  water,  the  same  as  an  inverted  siphon.  Sometimes 
tunnels  are  lined  with  cement,  being  given  either  a circular  or  oval  form, 
or  they  may  have  a flat  bottom,  with  flat  sides  and  an  arched  roof.  The 
cement  may  be  placed  directly  on  the  country  rock  composing  the  walls  of 
the  tunnel,  or  the  tunnel  may  be  lined  with  brick  or  stone,  and  then 
cemented  on  the  inside. 

Flow  Through  Tunnels.— The  flow  of  water  through  tunnels,  when  they  are 
only  partially  filled,  is  calculated  by  the  formulas  for  flow  in  open  channels, 
while  in  the  case  of  lined  tunnels  that  are  run  full,  the  flow  is  calculated  by 
formulas  for  calculating  the  flow  through  pipes. 


FLOWTHROUGH  PIPES. 

Hydraulic  Gradient.— If  a pipe  of  uniform  cross-section  be  connected  with 
a reservoir,  and  water  allowed  to  discharge  through  its  open  end,  it  has  been 
found  that  the  pressure  on  the  pipe  at  any  point  is  equal  to  the  vertical  dis- 
tance from  the  center  of  the  pipe  at  that  point  to  an  imaginary  line,  called 
the  hydraulic  gradient  or  hydraulic  grade  line.  This  is  a line  drawn  from  a 
point  slightly  below  the 
surface  of  the  water  in  the 
reservoir  to  the  outlet  of 
the  pipe,  as  ab.  Fig.  14. 

The  distance  from  the  sur- 
face of  the  water  to  the 
point  a is  equal  to  the  head 
lost  in  overcoming  the  fric- 
tion at  the  entrance  to  the 
pipe,  and  is  rarely  over  1 ft. 

If  the  pipe  were  laid  along 
the  line  a b,  it  would  carry 
exactly  the  same  amount 
of  water  as  when  laid  hori- 
zontally, as  shown,  but 
there  would  be  practically 
no  pressure  tending  to 
burst  the  pipe  at  any  point 
along  this  line;  while  if  it 
were  laid  along  the  line  from  the  point  a'  (the  reservoir  being  made 
deeper),  it  would  still  deliver  exactly  the  same  amount  of  water,  but  the 
pressure  tending  to  burst  the  pipe  would  be  greatly  increased.  In  order 
that  a pipe  may  have  a maximum  discharge,  no  point  in  the  line  must  rise 
above  the  hydraulic  gradient,  and  it  makes  no  difference  in  the  discharge 
how  far  below  the  gradient  it  may  fall. 

In  Fig.  15,  the  pipe  rises  above  the  hydraulic  gradient  a c,  and  in  this  case 
a new  hydraulic  gradient  ah  would  have  to  be  established,  and  the  flow 
calculated  for  this  head,  the  pipe  b c simply  acting  to  carry  off  the  water 
delivered  to  it  at  b.  If  the  upper  side  of  the  pipe  were  open  at  the  point  b, 
the  water  would  have  no  tendency  to  escape,  but,  on  the  contrary,  air  would 
probably  enter,  and  the  pipe  flow  only  partially  full  from  b to  c. 

Flow  in  Pipes.— Darcy,  a French  engineer,  made  a series  of  experiments  on 
different  diameters  of  cast-iron  pipe,  with  different  degrees  of  internal 


148 


HYDRA  TJLICS. 


roughness,  from  which  he  calculated  a series  of  formulas.  The  following 
are  some  of  these  formulas,  as  arranged  by  Mr.  E.  Sherman  Gould,  C.  E.,  E.  M., 
one  of  the  most  experienced  hydraulic  engineers  in  America.  Darcy  found 

that  the  character  of  the  inside 
surface  of  the  pipe  played  a 
very  important  part  in  its  dis- 
charge, and  he  deduced  a 
formula  and  determined  a 
series  of  coefficients  for  it,  but 
Mr.  Gould  calls  attention  to  the 
fact  that  the  coefficients  for 
pipes  from  8"  to  48"  in  diam- 
eter practically  cancel  the 
numerical  factor  employed  in 
Darcy’s  formula,  and  that  a 
slightly  different  factor  applies  to  pipes  from  3 to  8 in.,  so  that  we  may  have 
the  following  simple  formulas,  in  which  the  factors  given  apply: 

Q = amount  of  water  in  cubic  feet  per  second; 
q = Y.S.  gallons  per  minute; 

D = diameter  of  pipe  in  feet; 
d = diameter  of  pipe  in  inches; 

H = total  head  in  feet; 
h = head  per  1,000  ft.; 

V = velocity  in  feet  per  second. 

Pipes  above  8 in.  in  diameter,  rough  inside  surface, 

Q = \/Wh  = V = i.onV^- 

For  diameter  in  inches,  Q = 

Pipes  between  3 and  8 in.  in  diameter,  rough  inside  surface, 
q 0.89 = 0.89  D'^VWfi)  V = 1.13i/dA. 

Large  pipes,  smooth  inside  surface, 

q = = 1.4  ir-\/'Dh]  V = 1.78i/;M. 

Small  pipes,  smooth  inside  surface, 


q = = 1.25  D^\/Dh\  V = l.e/DA 

As  a rule,  it  is  best  to  calculate  any  pipe  line  by  the  formula  for  pipes 
having  a rough  internal  surface,  for  if  this  is  not  done  the  results  are  liable 
to  be  disappointing,  since  all  pipes  become  more  or  less  rough  with  use. 


Eytelwein’s  Formula  for  the  Delivery  of  Water  in  Pipes: 

D = diameter  of  pipe  in  inches; 

H = head  of  water  in  feet; 

L = length  of  pipe  in  feet; 

W = cubic  feet  of  water  discharged  per  minute 


W = 4.71 


H 


D = .538 


5 LX 


'A/ 


H 


Hawksley’s  Formula: 

G = number  of  gallons  delivered  per  hour; 
L = length  of  pipe  in  yards; 

H = head  of  water  in  ffiet; 

D = diameter  of  pipe  in  inches. 


Neville’s  General  Formula: 

V = velocity  in  feet  per  second; 
r = hydraulic  mean  depth  in  feet; 

s = sine  of  inclination,  or  total  fall  divided  by  total  length. 

V = 140  r s — 11  ^ r s. 

In  cylindrical  pipes,  v multiplied  by  47.124^2  gives  the  discharge  per 
minute  in  cubic  feet,  or  v multiplied  by  293.7286  d2  gives  the  discharge  per 
minute  in  gallons,  d being  the  diameter  of  the  pipe  in  feet. 


COMPARISOy  OF  FORMULAS, 


149 


COMPARISON  OF  FORMULAS. 

R = mean  hydraulic  depth  in  feet  *=  area  wet  perimeter 
circular  section  of  pipe; 

J£ 

S = sine  of  slope  = j-  ; 

V — velocity  in  feet  per  second; 
d = diameter  of  pipe  in  feet; 

L = length  of  pipe  in  feet; 


H = head  of  water  in  feet. 

Prony,  v 

= 97.05 1/ RS—  .08;  or,  v = 99.88i/i2  5—  .154. 

Eytelwein, 

V = 50-^1 

1 dH 

L + 50  d' 

Eytelwein, 

V = 108/i2S-  .13. 

Hawksley, 

V = 48^ 

1 dH 

L + 54  d' 

Neville, 

V = 140i/RS-llfRS. 

Darcy, 

V = C|/ R S]  for  value  of  C,  see  following  Table. 

= - for 
4 


Diameter  of  pipe  (inches) 

k 

1 

2 

3 

4 

5 

6 

1 

7 

i 

8 

Value  oi  C. 

65 

80 

93 

99 

102 

103 

105 

106 

107 

Diameter  of  pipe  (inches) 

9 

10 

12 

14 

16 

18 

20 

22 

24 

Value  of  C 

108 

109 

109.5 

110 

110.5 

110.7 

111 

111.5 

111.5 

Maximum  value  of  C for  very  large  pipes,  113.3. 


Kutter, 


where 


V = Cy  RS, 


181  + 


.00281 


(7  = 


.00281  \ 

~) 


Weisbach, 


h 


L 

r 


2}/’ 


where  h = head  necessary  to  overcome  the  friction  in  a pipe;  r — the  mean 
radius  of  the  pipe  in  feet;  and  g = gravity  = 32.2. 


Darcy, 


d V^12d' 


Siphons.— When  any  part  of  the  pipe  line  rises  above  the  source  of  supply, 
such  a line  is  called  a siphon.  If  this  rise  is  greater  than  the  height  of  tlie 
water  barometer  (34  ft.  at  sea  level),  water  will  not  flow  through  the  siphon. 
The  flow  through  the  siphon  will  oe  the  same  as  that  through  any  pipe  line 
so  long  as  there  is  no  accumulation  of  air  at  the  highest  point  of  the  line; 
but  such  an  accumulation  will  decrease  or  entirely  stop  the  flow.  All 
siphons  should  be  provided  at  their  highest  points  with  valves  for  discharging 
the  air  and  introducing  water  to  fill  the  siphon,  and  it  is  usually  best  to  trap 
the  lower  end  of  the  pipe  so  that  air  cannot  enter  it,  and  to  enlarge  the 
upper  end  so  as  to  reduce  the  loss  of  the  stream  in  entering.  For  a siphon 
to  work  well,  the  fall  between  the  intake  and  the  discharge  end  should  be 
considerable,  if  the  rise  amounts  to  much. 


150 


HYDRA  ULICS. 


B 

S 

g 

5 

s 

I 


I 


imMmmmmmmmimmm 

r^-rH'-r^-cic^'-C^'c^’-COCOCOiO^^^^ 


imrnimmmMmmMmmi 

" issiigg 


SSHSSS5SgEJg|S3||g|a||["'“'_ 

awsiEw^isiigimiffliilif 

-djilrl 


"co  cb  ib'o.  I-  CN  ^ ^ CO  ^ rH  o'i>  cn'co  ar 

T-l  r-(  r-l  I-H  I-H  tH  rH 


co':ot^Tj<Qoocoa5i>'!^<cocoiiCi>(MT-ii:bi^ 


cain<MoorH-)-u:.<c<o<cmi>ovoo>coinocJOto>nrHm^cD 

-®--saa3ssssssi:«sss^|S|S|gs| 

O<D000>0>t-.tDC0rtt>Tl-t0>o'iS<5‘l:-^00(M<»r4«S!^5  M^(N 


3S35!S3S!S2;Sa3aS?S"SgSiilI 

SS3SSSSSSS^??^^^^9mm»9» 


T-'OCOCD00  0 04rt.oV^-(NrHOiOCOO^O^OO  . 

■rHrHr-5T--loic4oiC4c4Tl?iOOcbl>Qb05a5  0;^'» 


il-sis 


rHrHr-l,-l(M04(M04(MTfii0OC01>Q005a5O^C0;;H^ga;rHC0^ 

«??'«««33S53Sgi«Sia!!!!l 


.s  .s  .s  .s  .s  .s  .s  .s  .g  .g  .g  .g  .g  .g  .g  .g  .g  .g  .g  .g  .g  .g  .g  .S  .g  .g  .g  .S 

rlOICOTriO'Ol-XOitrHOlCOrfiCy^l^OOasrH'MCOTf^tOOl-OOaiO 


The  quantities  above  are  American  gallons  per  minute.  For  cubic  feet,  divide  by  7.5. 


FRICTION  IN  PIPES. 


151 


LOSS  OF  HEAD  IN  PIPE  BY  FRICTION 

In  each  100  ft.  in  length  of  different  diameters,  when  discharging  the  follow- 
ing quantities  of  water  per  minute,  as  given  by  Pel  ton  Water  Wheel  Co. 

Inside  Diameter  of  Pipe.  Inches. 


Velocity. 

Ft.  per  Sec. 

1. 

2 

3 

4 

5 

6 

Loss  of. 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 
Head.  Ft. 

Cu.  Ft. 
per  Min. 

Loss  of 

Head.  Ft. 

Cu.  Ft. 

per  Min. 

Loss  of 

Head.  Ft. 

Cu.  Ft. 

per  Min. 

Loss  of 

Head.  Ft. 

Cu.  Ft. 

per  Min. 

Loss  of 

Head.  Ft. 

Cu.  Ft. 

per  Min. 

2.0 

2.37 

.65 

1.185 

2.62 

.791 

5.89 

.593 

10.4 

.474 

16.3 

.395 

23.5 

2.2 

2.80 

.73 

1.404 

2.88 

.936 

6.48 

.702 

11.5 

.561 

18.0 

.468 

25.9 

2.4 

3.27 

.79 

1.639 

3.14 

1.093 

7.07 

.819 

12.5 

.650 

19.6 

.547 

28.2 

2.6 

3.78 

.86 

1.891 

3.40 

1.260 

7.65 

.945 

13.6 

.757 

21.3 

.631 

30.6 

2.8 

4.32 

.92 

2.160 

3.66 

1.440 

8.24 

1.080 

14.6 

.864 

22.9 

.720 

32.9 

3.0 

4.89 

.99 

2.440 

3.92 

1.620 

8.83 

1.220 

15.7 

.978 

24.5 

.815 

35.3 

3.2 

5.47 

1.06 

2.730 

4.18 

1.820 

9.42 

1.370 

16.7 

1.098 

26.2 

.915 

37.7 

3.4 

6.09 

1.12 

3.050 

4.45 

2.040 

10.00 

1.520 

17.8 

1.220 

27.8 

1.021 

40.0 

3.6 

6.76 

1.19 

3.380 

4.71 

2.260 

10.60 

1.690 

18.8 

1..350 

29.4 

1.131 

42.4 

3.8 

7.48 

1.26 

3.740 

4.97 

2.490 

11.20 

1.870 

19.9 

1.490 

31.0 

1.250 

44.7 

4.0 

8.20 

1.32 

4.100 

5.23 

2.730 

11.80 

2.050 

20.9 

1.640 

32.7 

1.370 

47.1 

4.2 

8.97 

1.39 

4.490 

5.49 

2.980 

12.30 

2.240 

22.0 

1.790 

34.3 

1.490 

49.5 

4.4 

9.77 

1.45 

4.890 

5.76 

3.250 

12.90 

2.4.30 

23.0 

1.950 

36.0 

1.620 

51.8 

4.6 

10.60 

1.52 

5.300 

6.02 

3.530 

13.50 

2.640 

24.0 

2.110 

37.6 

1.760 

54.1 

4.8 

11.45 

1.58 

5.720 

6.28 

3.810 

14.10 

2.850 

25.1 

2.270 

39.2 

1.900 

. 56.5 

5.0 

12.33 

1.65 

6.170 

6.54 

4.110 

14.70 

3.080 

26.2 

2.460 

40.9 

2.050 

58.9 

5.2 

13.24 

1.72 

6.620 

6.80 

4.410 

15.30 

3.310 

27.2 

2.650 

42.5 

2.210 

61.2 

5.4 

14.20 

1.78 

7.100 

7.06 

4.730 

15.90 

3.550 

28.2 

2.840 

44.2 

2.370 

63.6 

5.6 

15.16 

1.85 

7.580 

7.32 

5.060 

16.50 

3.790 

29.3 

3.030 

45.8 

2.530 

65.9 

5.8 

16.17 

1.91 

8.090 

7.58 

5.400 

17.10 

4.040 

30.3 

3.240 

47.4 

2.700 

68.3 

6.0 

17.23 

1.98 

8.610 

7.85 

5.740 

17.70 

4.310 

31.4 

3.450 

49.1 

2.870 

70.7 

7.0 

22.89 

2.31 

11.450 

9.16 

7.620 

20.60 

5.720 

36.6 

4.570 

57.2 

3.810 

82.4 

Inside  Diameter  of  Pipe.  Inches. 


7 

8 

9 

10 

11 

12 

-2  p, 

> 

d 

^ fl" 

s ir 

£.3 
.S 
s 1, 

o 

d 

a «H 

C3  Jh 

ij  s 
w 

pH 

» ft 

tJ  a> 

PC 

o S 

PP 

o S. 

PP 

o S, 

2.0 

.338 

32.0 

.296 

41.9 

.264 

53.0 

.237 

65.4 

.216 

79.2 

.198 

a 94.2 

2.2 

.401 

35.3 

.351 

46.1 

.312 

58.3 

.281 

72.0 

.255 

87.1 

.234 

,103.0 

2.4 

.468 

38.5 

.410 

50.2 

.365 

63.6 

.327 

78.5 

.297 

95.0 

.273 

113.0 

2.6 

.540 

41.7 

.473 

54.4 

.420 

68.9 

.378 

85.1 

.344 

103.0 

.315, 

122.0 

2.8 

.617 

44.9 

.540 

58.6 

.480 

74.2 

.432 

91.6 

.392 

111.0 

.360 

132.0 

3.0 

.698 

48.1 

.611 

62.8 

.544 

79.5 

.488 

98.2 

444 

119.0 

.407 

141.0 

3.2 

.785 

51.3 

.686 

67.0 

.609 

84.8 

.549 

105.0 

.499 

127.0 

.457 

151.0 

3.4 

.875 

54.5 

.765 

71.2 

.680 

90.1 

.612 

111.0 

.557 

134.0 

.510 

160.0 

3.6 

.969 

57.7 

.848 

75.4 

.755 

95.4 

.679 

118.0 

.617 

142.0 

.566 

169.0 

3.8 

1.070 

60.9 

.936 

79.6 

.831 

101.0 

.749 

124.0 

.680 

150.0 

.624 

179.0 

4.0 

1.175 

64.1 

1.027 

83.7 

.913 

106.0 

.822 

131.0 

.747 

158.0 

.685 

188.0  ‘ 

4.2 

1.280 

67.3 

1.122 

87.9 

.998 

111.0 

.897 

137.0 

.81 6 

166,0 

.749 

198.0 

4.4 

1.390 

70.5 

1.220 

92.1 

1.086 

116.0 

.977 

144.0 

.888 

174.0 

.815 

207.0 

4.6 

1.510 

73.7 

1.320 

96.3 

1.177 

122.0 

1.059 

150.0 

.963 

182.0 

.883, 

217.0 

4.8 

1.630 

76.9 

1.430 

100.0 

1.270 

127.0 

1.145 

157.0 

1.040 

190.0 

.954 

226.0 

5.0 

1.760 

80.2 

1.540 

105.0 

1.370 

132.0 

1.230 

163.0 

1.122 

198.0 

1.02g 

235.0 

5.2 

1.890 

83.3 

1.650 

109.0 

1.470 

138.0 

1.320 

170.0 

1.200 

206. 0 

1.104 

245.0 

5.4 

2.030 

86.6 

1.770 

113.0 

1.570 

143.0 

1.410 

177.0 

1.280 

214.0 

L183 

254.0 

5.6 

2.170 

89.8 

1.890 

117.0 

1.680 

148.0 

1.510 

183.0 

1.370 

222.0 

1.260 

264.0 

5.8 

2.310 

93.0 

2.010 

121.0 

1.800 

154.0 

1.610 

190.0 

1.460 

229.0 

1.340 

273.0 

6.0 

2.460 

96.2 

2.150 

125.0 

1.920 

159.0 

1.710 

196.0 

1.560 

237.0 

1.430 

283.0  ; 

7.0 

3.260 

112.0 

2.850 

146.0 

2.520 

185.0 

2.280 

229.0 

2.070 

277.0 

1.910 

330.0 

Example.— Have  200  ft.  head  and  600  ft.  of  11"  pipe,  carrying  119  cu.  ft.  of^ 
water  per  minute.  To  find  effective  head:  In  right-hand  column,  under  11" j 
pipe,  find  119  cu.  ft.  Opposite  this  will  be  found  the  coefficient  of  friction  for" 
this  amount  of  water,  which  is  .444.  Multiply  this  by  the  number  of  hun- 
dred feet  of  pipe,  which  is  6,  and  you  will  have  2.66  ft.,  which  is  the  loss  of 
head.  Therefore,  the  effective  head  is  200  — 2.66  = 197.34. 


152 


HYDRA  ULICS. 


LOSS  OF  HEAD  IN  PIPE  BY  FRICTION 

In  each  100  ft.  in  length  of  different  diameters,  when  discharging  the  follow- 
ing quantities  of  water  per  minute,  as  given  by  Pelton  Water  Wheel  Co. 

Inside  Diameter  of  Pipe.  Inches. 


13 

14 

15 

16 

18 

20 

£-1 

"n 

u.  Ft. 
r Min. 

Ft. 

Min. 

o 

Ft. 

Min. 

o 

Ft. 

Min. 

<4-  ^ 

o 

a 

o 

o’ 

o 

O 

o "g 

p u 

o 'g 

p ^ 

i 

S 

H 

ij  « 

O. 

n 

O K 

^ e, 

w 

Q « 

P* 

K 

o « 
o< 

1-3  V 

w 

O. 

2.0 

.183 

110 

.169 

128 

.158 

147 

.147 

167 

.132 

212 

.119 

262 

2.2 

.216 

121 

.200 

141 

.187 

162 

.175 

184 

.156 

233 

.140 

288 

2.4 

.252 

133 

.234 

154 

.218 

176 

.205 

201 

.182 

254 

.164 

314 

2.€ 

.290 

144 

.270 

167 

.252 

191 

.236 

218 

.210 

275 

.189 

340 

2.S 

.332 

156 

.308 

179 

.288 

206 

.270 

234 

.240 

297 

.216 

366 

3.0 

.375 

166 

.349 

192 

.325 

221 

.306 

251 

.271 

318 

.245 

393 

3.2 

.422 

177 

.392 

205 

.366 

235 

.343 

268 

.305 

339 

.275 

419 

3.4 

.471 

188 

.438 

218 

.408 

250 

.383 

284 

.339 

360 

.306 

445 

3.3 

.522 

199 

.485 

231 

.452 

265 

.425 

301 

.377 

382 

.339 

471 

3.8 

.576 

210 

.535 

243 

.499 

280 

.468 

318 

.416 

403 

.374 

497 

4.0 

.632 

221 

.587 

256 

.548 

294 

.513 

335 

.456 

424 

.410 

523 

4.2 

.691 

232 

.641 

269 

.598 

309 

.561 

352 

.499 

445 

.449 

550 

4.4 

.751 

243 

.698 

282 

.651 

324 

.611 

368 

.542 

466 

.488 

576 

4.8 

.815 

254 

.757 

295 

.707 

339 

.662 

385 

.588 

488 

.529 

602 

4.1 

.881 

265 

.818 

308 

.763 

353 

.715 

402 

.636 

509 

.572 

628 

6.0 

.949 

276 

.881 

321 

.822 

368 

.770 

419 

.685 

530 

.617 

654 

5.2 

1.020 

287 

.947 

333 

.883 

383 

.828 

435 

.736 

551 

.662 

680 

5.4 

1.092 

298 

1.014 

346 

.947 

397 

.888 

452 

.788 

572 

.710 

707 

5.6 

1.167 

309 

1.083 

359 

1.011 

412 

.949 

469 

.843 

594 

.758 

733 

5.3 

1.245 

321 

1.155 

372 

1.078 

427 

1.011 

486 

.899 

615 

.809 

759 

6.0 

1.325 

332 

1.229 

385 

1.148 

442 

1.076 

502 

.957 

636 

.861 

785 

7.0 

1.750 

387 

1.630 

449 

1.520 

515 

1.430 

586 

1.270 

742 

1.143 

916 

Inside  Diameter  of  Pipe.  Inches. 


22 

24 

26 

28 

30 

36 

w § 

o 

QB  • 

- a 

o 

o 

© 

-J  o 

k,  £ 

o 

o 

■k>'  a 

J- 

1-9  4) 

te 

s •- 

o s, 

Los 

Head 

s, 

Los 

Head 

Los 

Head 

p ki 

OS. 

Los 

Head 

9 t- 

O g, 

Losi 

Head 

og, 

2.0 

.108 

316 

.098 

377 

.091 

442 

.084 

513 

.079 

589 

.066 

848 

2.2 

.127 

348 

.116 

414 

.108 

486 

.099 

564 

.093 

648 

.078 

933 

2.4 

.149 

380 

.136 

452 

.126 

531 

.116 

616 

.109 

707 

.091 

1,018 

2.« 

.171 

412 

.157 

490 

.145 

575 

.134 

667 

.126 

766 

.104 

1,100 

2.8 

.195 

443 

.180 

528 

.165 

619 

.153 

718 

.144 

824 

.119 

1,188 

8.0 

.222 

475 

.204 

565 

.188 

663 

.174 

770 

.163 

883 

.135 

1,273 

8.8 

.249 

507 

.229 

603 

.211 

708 

.195 

821 

.182 

942 

.152 

1,357 

S.i 

.278 

538 

.255 

641 

.235 

752 

.218 

872 

.204 

1,001 

.169 

1.442 

8.t 

.808 

570 

.283 

678 

.261 

796 

.242 

923 

.226 

1,060 

.188 

1,527 

8.8 

.840 

601 

.312 

716 

.288 

840 

.267 

974 

.249 

1,119 

.207 

1,612 

4.0 

.378 

633 

.342 

754 

.315 

885 

.293 

1,026 

.273 

1,178 

.228 

1,697 

4.2 

.408 

665 

.374 

791 

.345 

929 

.320 

1,077 

.299 

1,237 

.249 

1,782 

4.4 

.444 

697 

.407 

829 

.375 

973 

.348 

1,129 

.325 

1,296 

.271 

1,866 

4.8 

.482 

728 

.441 

867 

.407 

1,017 

.378 

1,180 

.353 

1,.355 

.294 

1,951 

4.8 

.521 

760 

.476 

905 

.440 

1,062 

.409 

1,231 

.381 

1,414 

.318 

2,036 

5.0 

.581 

792 

.513 

942 

.474 

1,106 

.440 

1,28^ 

.411 

1,472 

.342 

2,121 

5.2 

.602 

823 

.552 

980 

.510 

1.150 

.473 

1,334 

.441 

1,531 

.368 

2,206 

5.4 

.645 

855 

.591 

1,018 

.546 

1,194 

.507 

1,385 

.473 

1,590 

.394 

2,291 

5.8 

.690 

887 

.632 

1,055 

.583 

1,239 

.542 

1,437 

.506 

1,649 

.421 

2,376 

5.1 

.735 

918 

.674 

1,093 

.622 

1,283 

.578 

1,488 

.540 

1 ,708 

.4.50 

2,460 

6.0 

.782 

950 

.717 

1,131 

.662 

1,327 

.615 

1,539 

.574 

1,767 

.479 

2,545 

7.0 

1.040 

1,109 

.953 

1,319 

.879 

1,548 

.817 

1,796 

.762 

2,061 

.636 

2,968 

FRICTION  IN  PIPES. 


153 


The  following  formula,  deduced  by  William  Cox,  gives  practically 
the  same  results  as  the  foregoing  table  and  will  be  found  useful  in  many 

instances:  F = +5F— 2),  where  = friction  head;  L = length 

of  pipe  in  feet;  D = diameter  of  pipe  in  inches;  V = velocity  in  feet  per 
second. 

Friction  of  Knees  and  Bends.— This  subject  has  not  been  investigated  suffi- 
ciently to  enable  the  engineer  to  make  exact  allowance  for  this  factor,  but 


the  following  formulas  may  be  taken  as  giving  close  approximate  results. 
It  is  well  to  bear  in  mind  that  right  angles  should  be  avoided  whenever 
possible,  and  that  bends  should  be  made  with  as  large  a radius  as  circum- 
stances will  allow. 


Fig.  17. 


A = angle  of  bend  or  knee  with  forward  line 
of  direction; 

V = velocity  of  water  in  feet  per  second; 

R = radius  of  center  line  of  bend; 
r = radius  of  bore  of  pipe  (or  i diameter); 

K = coefficient  for  angles  of  knees; 

L = coefficient  for  curvature  of  bends; 

H = head  of  water  in  feet  necessary  to  over- 
come the  friction  of  the  bends,  or  knees. 
H = .0155  V^K. 


The  value  of  K is  as  follows  for  different  angles: 


= 

1 20° 

40° 

60° 

80° 

90° 

100° 

120° 

K = 

1 .046 

.139 

.364 

.74 

.98 

1.26 

1.86 

For  bends, 


154 


HYDRA  ULICS. 


Values  of  L with  various  ratios  of  the  radius  of  bend  to  radius  of  bore: 


When  ^ = 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

In  circular  section  L 

.131 

.138 

.158 

.206 

.294 

.44 

.66 

.98  ! 

1.4 

2.0 

In  rectangular  L 

.124 

.135 

j.l8 

.25 

.4 

.64 

1.01 

1.55 

2.3 

3.2 

RESERVOIRS. 

Reservoir  Site. — In  selecting  a site  for  a reservoir,  the  following  points 
should  be  observed: 

1.  A proper  elevation  above  the  point  at  which  the  water  is  required. 

2.  The  total  supply  available,  including  observations  as  to  the  rainfall 
and  snowfall. 

3.  The  formation  and  character  of  the  ground,  with  reference  to  the 
amount  of  absorption  and  evaporation. 

The  most  desirable  formation  of  ground  for  a reservoir  site  is  one  of  com- 
pact rock,  like  granite,  gneiss,  or  slate;  porous  rocks,  like  sandstones  and 
limestones,  are  not  so  desirable.  Steep  bare  slopes  are  best  for  the  country 
surrounding  a reservoir,  as  the  water  escapes  from  them  quickly.  The 
presence  of  vegetation  above  the  reservoir  causes  a considerable  amount  of 
absorption;  but,  at  the  same  time,  the  rainfall  is  usually  greater  in  a region 
covered  with  vegetation  than  in  a barren  region,  hence  the  streams  have  a 
more  uniform  flow.  A reservoir  must  be  made  large  enough  to  hold  a 
supply  capable  of  meeting  the  maximum  demand.  The  area  of  a reservoir 
should  be  determined,  and  a table  made  showing  its  contents  for  every  foot 
in  depth,  so  that  the  amount  of  water  available  can  always  be  known. 


DAMS. 

Dams  are  used  for  retaining  water  in  reservoirs,  for  diverting  streams  in 
placer  mining,  and  for  storing  debris  coming  from  placer  mines  in  canons 
or  ravines. 

Foundations  for  dams  must  be  solid  to  prevent  settling,  and  water-tight  to 
prevent  leakage  under  the  base  of  the  dam.  Whenever  possible,  the  founda- 
tion should  be  solid  rock.  Gravel  is  better  than  earth,  but  when  gravel  is 
employed  it  will  be  necessary  to  drive  sheet  piling  under  the  upper  toe  of 
the  dam,  to  prevent  water  from  seeping  through  the  formation  under  the 
dam.  Vegetable  soil  should  be  avoided,  and  all  porous  material,  such  as 
sand,  gravel,  etc.  should  be  stripped  off  until  hard  pan  or  solid  rock  is 
reached.  In  case  springs  occur  in  the  area  covered  by  the  foundation  of  the 
dam,  it  will  be  necessary  to  trace  them  up,  and  if  they  originate  on  the 
upper  side  to  conflne  their  flow  to  that  side  of  the  dam,  so  that  they  will 
have  no  tendency  to  ultimately  become  passageways  for  water  from  the 
upper  face  to  the  lower  face  of  the  dam,  thus  providing  holes  which  may 
ultimately  destroy  the  entire  foundation  of  the  structure. 

Wooden  Dams.— Wooden  dams  are  constructed  of  round,  sawed,  or  hewn 
lo^s.  The  timbers  are  usually  at  least  1 ft.  square,  or,  if  round,  from  18  to 
24  in.  in  diameter.  A series  of  cribs  from  8 to  10  ft.  square  are  constructed  bv 
building  up  the  lo^s  log-house  fashion  and  securing  them  together  with 
treenails.  The  individual  cribs  are  secured  to  one  another  with  treenails 
or  by  means  of  bolts.  The  cribs  are  usually  filled  with  loose  rock  to  keep 
them  in  place,  and  in  many  cases  are  secured  to  the  foundation  by  means 
of  bolts.  A layer  of  planking  on  the  upper  face  of  the  dam  makes  it  water- 
tight, and  if  the  spillway  is  over  the  crest  of  the  dam  it  will  be  necessary  to 
plank  the  top  of  the  cribs,  and,  in  most  cases,  to  provide  an  apron  for  the 
water  to  fall  on.  The  apron  may  be  set  on  small  cribs,  or  on  timbers  pro- 
jecting from  the  cribs  of  the  dam  itself. 

Abutments  and  Discharge  Gates.— Abutments  are  structures  at  the  ends  of  a 
dam.  They  may  be  constructed  from  timber,  masonry,  or  drv  stonework. 
If  possible,  abutments  should  have  a curved  outline,  and  should  be  so 
placed  that  there  is  no  possibility  of  the  water  overflowing  them,  or  getting 
behind  them  during  floods.  If  the  regular  discharge  from  a dam  takes  place 
from  the  main  face,  the  gates  may  be  arranged  in  connection  with  one  of 
the  abutments,  or  by  means  of  a tunnel  and  culvert  through  the  dam.  la 


DAMS. 


155 


either  case,  some  structure  should  be  constructed  above  the  outlet  so  as  to 
])revent  driftwood,  brush,  and  other  material  from  stopping  the  discharge 
gates.  When  the  discharge  gates  are  placed  at  one  side  of  the  dam,  they  are 
usually  arranged  outside  of  the  regular  abutment,  between  it  and  another 
special  abutment,  the  discharge  being  through  a series  of  gates  into  a flume, 
ditch,  or  pipe. 

Spillways  or  Waste  Ways.— These  are  openings  provided  in  a dam  for  the 
discharge  of  water  during  floods  or  freshets,  or  for  the  discharge  of  a portion 
not  being  used  at  any  time.  The  spillway  may  be  over  the  crest  of  the  dam, 
or,  where  the  topography  favors  such  a construction,  the  main  dam  may  be 
of  sufficient  height  to  prevent  water  from  ever  passing  its  crest,  the  spillway 
being  arranged  at  another  outlet  over  the  lower  dam.  Waste  ways,  proper, 
are  openings  through  the  dam,  and  are  intended  for  the  discharge  of  the 
large  quantities  of  water  that  come  down  during  freshets  or  floods.  In  the 
case  of  timber  dams,  the  waste  ways  are  usually  surrounded  by  heavy  cribs, 
and  have  an  area  of  from  40  to  *50  sq.  ft.  each.  There  are  two  general 
forms  of  construction  employed  for  waste'  ways.  One  consists  of  a compara- 
tively narrow  opening  in  the  dam,  extending  to  a considerable  depth  (8  or. 


10  ft.).  Water  is  allowed  to  discharge  through  this  during  flood  time,  blit 
when  it  is  desired  to  stop,  the  flow  planks  are  placed  across  the  up-stream 
face  of  the  opening  in  such  a manner  as  to  close  it.  The  opening,  which  is 
usually  not  over  3 or  4 ft.  wide,  is  provided  with  guides  on  the  upper  face  of 
the  dam,  and  between  which  the  planks  are  slid  down,  the  individual  pieces 
of  planking  being  at  least  1 ft.  longer  than  the  opening  that  they  are  to 
cover.  The  other  device  frequently  used  consists  in  providing  the  waste 
way,  at  one  side  of  the  regular  spillway,  with  a crest  2 or  3 ft.  lower  than  the 
regular  spillway.  The  crest  of  this  waste  way  is  composed  of  heavy  timber, 
and  4 or  5 ft.  above  there  is  arranged  a parallel  timber,  the  space  between 
the  two  being  closed  by  what  are  called  flash  boards.  These  are  made  from 
pieces  of  2"  or  3"  plank,  6 or  8 in.  wide.  The  planks  are  placed  against  both 
timbers  so  as  to  close  the  space.  The  individual  planks  are  made  long 
enough  so  that  they  extend  from  1 to  2 ft.  above  the  upper  timber,  and 
through  the  upper  end  of  each  plank  is  bored  a hole  through  which  a piece 
of  rope  is  passed  and  a knot  tied  in  the  end  of  the  rope.  ^ These  ropes  are 
secured  by  staples  to  the  upper  timber.  When  it  becomes  necessary  to  open 
the  waste  way,  men  go  upder  with  peevies,  cant  hooks,  or  pinch  bars,  and 
pry  up  the  planks  in  such  a way  as  to  draw  the  longer  end  out  of  contact 
with  the  lower  timber,  when  the  force  of  the  water  will  immediately  carry 
the  plank  down  the  stream  as  far  as  the  rope  will  allow  it  to  go^  After  the 
first  plank  has  been  loosened,  the  succeeding  ones  can  be  pulled  up  with 
comparative  ease,  and  two  men  can  open  a 25'  or  30'  section  of  waste  way  in 
a very  few  minutes.  The  ropes  keep  the  plank  from  being  lost,  and  the 
opening  can  be  closed  again  by  passing  the  plank  down  into  the  water  to 
one  side  of  the  opening  and  moving  them  into  the  current.  Some  skill  is 
required,  both  in  opening  and  closing  the  waste  ways. 

Stone  Dams. — Where  cement  or  lime  is  expensive,  and  suitable  rubble 
stone  can  be  obtained,  dams  are  frequently  constructed  without  the  use  of 
mortar.  The  upper  and  lower  faces  of  the  dam  should  be  of  hammer- 
dressed  stone,  carefully  bonded,  and  the  stones  in  the  lower  face  of  the  dam 
are  sometimes  anchored  by  means  of  bolts.  The  dam  can  be  made  water- 
tight by  means  of  a skin  of  planking  on  the  upper  face.  In  case  water 
should  ever  pass  over  the  crest  of  such  a dam,  much  of  it  would  settle 
through  the  openings  in  the  stone  into  the  interior  of  the  dam,  and  this 
would  subject  the  stones  in  the  lower  portion  of  the  face  to  a hydrostatic 


156 


HYDRAULICS. 


pressure,  provided  an  opening  was  not  made  for  the  escape  of  such  water. 
For  this  reason,  culverts  or  openings  should  be  made  through  the  lower 
portion  of  the  dam,  to  discharge  any  such  water.  When  such  dams  as  this 
are  constructed,  the  regular  spillway  is  not  placed  over  the  face  of  the  dam, 
but  at  some  other  point,  and  usually  over  a timber  dam. 

Earth  Dams. — Earth  dams  are  used  for  reservoirs  of  moderate  height. 
They  should  be  at  least  10  ft.  wide  on  top,  and  a height  of  more  than  60  ft.  is 
unusual.  When  the  material  of  which  the  dam  is  composed  is  not  water- 
tight, as,  for  instance,  gravel,  sand,  etc.,  it  is  sometimes  necessary  to  con- 
struct a puddle  wall  of  clay  in  the  center  of  the  regular  dam.  This  consists 
of  a narrow  dam  of  clay  mixed  with  a certain  proportion  of  sand.  The 
puddle  wall  should  not  be  less  than  from  6 to  8 ft.  thick  at  the  top  of  the 
dam,  and  should  be  ^ven  a slight  batter  on  each  side.  It  is  constructed 
during  the  building  of  the  dam,  and  should  be  protected  from  contact  with 
the  water  by  a considerable  thickness  of  earth  on  the  upper  face.  The 
upper  face  of  an  earthen  dam  is  frequently  protected  by  means  of  plank  or 
a pavement  of  stone.  The  lower  face  is  frequently  protected  by  means  of 
sod,  or  sod  and  willow  trees.  Sometimes  earth  dams  are  provided  with  a 
masonry  core  in  place  of  the  puddle  wall,  to  render  them  water-tight.  This 
consists  of  a masonry  wall  carried  to  an  impervious  stratum,  and  up  through 
the  center  of  the  dam.  The  masonry  core  should  never  be  less  than  2 or  3 ft. 
thick  at  the  top,  and  should  be  given  a batter  of  at  least  10^  on  each  side. 
At  the  regular  water  level,  earthen  dams  are  liable  to  have  a small  bench 
or  shelf  formed,  and  on  this  account,  during  the  construction,  such  a bench 
or  shelf  is  sometimes  built  into  the  earth  dam.  Fig.  18  shows  a dam  with  a 
masonry  core,  with  the  upper  face  covered  with  rubble  and  the  lower  face 
covered  with  grass. 

Debri«  Dims.— These  are  dams  or  obstructions  placed  across  the  bed  of 
streams  to  hold  back  tailings  from  mines,  and  to  prevent  damage  to  the 
valleys  below.  They  are  made  of  stone,  timber,  or  brush.  No  attempt  is 
made  to  render  the  debris  dam  water-tight,  the  only  object  being  that  it 
should  retard  the  flow  of  the  stream  and  give  it  a greater  breadth  of  dis- 
charge, so  that  the  water  naturally  drops  and  deposits  the  sediment  that 
it  is  carrying.  The  sediment  soon  silts  or  fills  up  against  the  face  of  the 
dam,  the  area  above  the  dam  becoming  a flat  expanse  or  plain  over  which 
the  water  finds  its  way  to  the  dam.  When  these  dams  are  constructed  of 
stone,  the  individual  stones  on  the  lower  face  and  crest  of  the  dam  should 
be  so  large  that  the  current  will  be  unable  to  displace  them,  while  the  upper 
face  and  core  of  the  dam  may  be  composed  of  finer  material.  In  case  a 
breach  should  occur  in  the  debris  dam,  it  will  not  necessarily  endanger  the 
region  farther  down  the  stream,  as  is  the  case  when  a break  occurs  in  a 
water  dam.  The  reason  for  this  is  that  the  debris  dam  is  not  made  water- 
tight, and  hence  there  is  never  much  pressure  against  it,  or  a large  volume 
of  water  held  back  that  can  rush  suddenly  down  the  stream  should  a break 
occur.  The  only  result  of  the  break  would  be  that  more  or  less  of  the  gravel 
behind  the  dam  would  be  washed  through  the  breach. 

Wing  Dams.— Wing  dams  are  used  for  turning  streams  from  their  courses, 
so  AS  to  expose  all  or  a portion  of  the  bed  for  placer  mining  or  other  pur- 
poses. They  are  usually  of  a temporary  natUT-e,  and  are  constructed  of 
brush  and  stones,  light  cribs  filled  with  stones,  and  of  large  stones,  or  timber. 
Sometimes  the  course  of  a stream  is  turned  by  an  obstruction  made  of  sand 
bags,  and  a win§-  dam  constructed  behind  this  of  frames  of  timber,  the  inter- 
vening space  being  filled  with  gravel  or  earth,  and,  in  some  cases,  the  timber 
being  covered  with  stone,  and  the  surface  riprapped  so  that  if  the  flow  ever 
comes  over  the  top  of  the  structure  it  will  not  destroy  it. 

Misonry  Dims. — When  high  masonry  dams  are  to  be  employed  they  should 
be  designed  by  a competent  hydraulic  engineer.  Masonry  dams  are  not,  as 
a rule,  used  for  hydraulic  mining,  owing  to  the  fact  that  the  length  of  time 
during  which  the  dam  is  required  rarely  warrants  the  expense  of  the  con- 
struction of  a masonry  dam. 


WATER-POWER. 

The  Theoretical  Efficiency  of  the  Water-Power.— The  gross  power  of  a fall  of 
water  is  the  product  of  the  weight  of  water  discharged  in  a unit  of  time,  and 
the  total  head  or  difference  in  elevation  of  the  surface  of  the  water,  above 
and  below  the  fall.  The  term  head,  used  in  connection  with  waterwheels, 


WATER-POWER. 


157 


is  the  difference  in  height  between  the  surface  of  water  in  the  penstock  and 
that  in  the  tailrace,  when  the  wheel  is  running. 

If  Q •=  cubic  feet  of  water  discharged  per  minute, 

W = weight  of  a cubic  foot  of  water  = 62.5  lb., 
and  H = total  head  in  feet, 

then  WQH  = gross  power  in  foot-pounds  per  minute, 

WQH  ^ 

— = the  horsepower. 


and 


33,000 

Substituting  the  value  for  Tf'  we  have 

- = .00189  Q H,  as  the  horsepower  of  a fall. 

ooj  000 

The  total  power  can  never  be  utilized  by  any  form  of  motor,  owing  to  the 
fact  that  there  is  a loss  of  head,  both  at  the  entrance  to,  and  exit  from,  the 
wheel,  and  there  are  also  losses  of  energy,  due  to  friction  of  the  water  in 
passing  through  the  wheel.  The  ratio  of  the  power  developed  by  the  wheel 
to  the  gross  power  of  the  fall,  is  the  efficiency  of  the  wheel.  A head  of  water 
can  be  made  use  of  in  any  one  of  the  following  ways: 

1.  By  its  weight,  as  in  the  water  balance,  or  overshot  wheel. 

2.  By  its  pressure,  as  in  the  hydraulic  engine,  hydraulic  presses,  cranes, 
etc.,  or  in  a turbine  water  wheel. 

3.  By  its  impulse,  as  in  the  undershot  and  impulse  wheels,  such  as 
Feltons,  etc. 

4.  By  a combination  of  the  above. 

The  Horsepower  of  a Running  Stream.— The  gross  horsepower,  as  seen  above,  is 

in  which  Q is  the  quantity  in  cubic  feet  per  minute  actually  impinging  on 
the  float  or  bucket,  and  H the  theoretical  head  added  to  the  velocity  of  the 
stream,  or 

in  which  v is  the  velocity  in  feet  per  second. 

For  example,  if  the  floats  of  an  undershot  waterwheel  were  2 ft.  X 10  ft.,  and 
the  stream  had  a velocity  of  3 ft.  per  second,  i.  e.,  v = 3,  we  would  have 

H ==  = .139,  and  Q = 2X  10  X3X  60  = 3,600  cu.  ft.  per  min. 


From  this,  H.  P.  = 3,600  X .139  X .00189  = .945  H.  P.,  or  a gross  horse- 
power for  practically  .05  sq.  ft.  of  wheel  surface;  but,  under  ordinary  circum- 
stances, it  would  be  impossible  to  attain  more  than  40^  of  this,  or  practically 
.02  horsepower  per  sq.  ft.  of  surface,  which  would  require  50  sq.  ft.  of  float 
surface  to  each  horsepower  furnished. 

Current  Motors.— A current  motor  fully  utilizes  the  energy  of  a stream 
only  when  it  is  so  arranged  that  it  can  take  all  of  the  velocity  out  of 
the  water;  that  is,  when  the  water  leaves  the  floats  or  vanes  with  no 
velocity.  It  is  evident  that  in  practice  we  can  never  even  obtain  a close 
approximation  to  these  results,  and  hence  only  a small  fraction  of  the 
energy  of  a running  stream  can  be  utilized  by  the  current  motor.  Current 
motors  are  frequently  used  to  obtain  small  amounts  of  power  from  a large 
stream,  as,  for  instance,  for  pumping  a limited  amount  of  water  for  irrigation. 
For  this  work,  an  ordinary  undershot  wheel  having  radial  paddles  is  usually 
employed.  At  one  end  of  the  wheel  a series  of  small  buckets  are  placed,  and 
so  arranged  that  each  bucket  will  dip  up  water  at  the  bottom  or  the  wheel 
and  discharge  it  into  the  launder,  near  the  top  of  the  wheel.  The  shape  of 
the  buckets  should  be  such  that  only  the  amount  of  water  which  the  bucket 
is  capable  of  carrying  to  the  launder  will  be  dipped  up,  for,  if  the  bucket 
is  constantly  slopping  or  pouring  water  as  it  ascends,  a large  amount 
of  useless  work  is  performed  in  raising  this  extra  water  and  then  pouring  it 
out  again,  as  only  the  portion  that  reaches  the  launder  can  be  of  any  service. 
Current  motors  are  not  practicable  for  furnishing  large  amounts  of  power. 


UTILIZING  THE  POWER  OF  A WATERFALL. 

The  power  of  a waterfall  may  be  utilized  by  a number  of  different  styles 
of  motors,  but  each  has  certain  advantages. 

Breast  and  Undershot  Wheels.— When  the  head  is  low  (not  over  5 or  6 ft.), 
breast  or  undershot  wheels  are  frequently  employed.  If  these  are  properly 


168 


HYDRAULICS. 


proportioned,  it  is  possible  to  realize  from  to  of  the  theoretical  power 
of  the  fall,  but  the  wheels  are  large  and  cumbersome  compared  with  the  duty 
they  perform,  and  not  often  installed  at  present,  especially  near  manufac- 
turing centers. 

Overshot  Wheels.— For  falls  up  to  40  or  50  ft.,  overshot  wheels  are  very 
commonly  employed,  and  they  have  been  used  for  even  greater  heads  than 
this.  The  overshot  wheel  derives  its  power  both  from  the  impulse  of  the 
water  entering  the  buckets,  and  from  the  weight  of  the  water  as  it  descends 
on  one  side  of  the  wheel  in  the  buckets.  The  latter  factor  is  by  far  the  more 
important  of  the  two.  When  properly  proportioned,  overshot  wheels  may 
realize  from  70^  to  90^  of  the  power  of  the  waterfall,  but  they  are  large  and 
cumbersome  compared  with  the  power  that  they  give,  and  are  not  often 
installed  except  in  isolated  regions,  where  they  are  made  from  timber  by 
local  mechanics. 

Impulse  Wheels.— For  heads  varying  from  50  ft.  up,  impulse  wheels  are 
very  largely  used.  These  are  also  sometimes  called  hurdy  gurdies,  and  are 
usually  of  the  Pelton  type,  consisting  of  a wheel  provided  with  buckets,  so 
arranged  about  its  periphery  that  they  receive  an  impinging  jet  of  water  and 
turn  it  back  upon  itself,  discharging  it  with  practically  no  velocity,  and  con- 
verting practically  all  the  energy  into  useful  work.  The  efficiency  of  these 
wheels  varies  from  85^^  to  90^^  under  favorable  circumstances.  This  style  of 
wheel  is  especially  adapted  for  very  high  heads  and  comparatively  small 
amounts  of  water.  There  are  a number  of  instances  where  wheels  are 
operating  under  a head  of  as  much  as  2,000  ft.  This  style  of  impulse  wheel 
is  an  American  development;  in  Europe,  a style  of  impulse  turbine  has  been 
used  to  some  extent,  but  has  not  found  very  much  favor  in  the  United  States. 

Turbines.— Turbines  or  reaction  wheels  are  very  largely  employed,  espe- 
cially for  moderate  heads.  When  properly  designed  to  fit  the  working 
conditions,  they  can  be  used  for  heads  varying  from  4 or  5 ft.  up  to  consider- 
ably over  100  ft.,  and  when  properly  placed  are  capable  of  utilizing  the 
entire  head,  a factor  that  gives  them  a decided  advantage  over  any  other 
style  of  waterwheel.  Turbines  are  capable  of  returning  85^  to  90^  of  the 
theoretical  energy  as  useful  power,  and  are  largely  used,  especially  where  a 
considerable  volume  of  water  at  a low  head,  or  a smaller  volume  at  a 
moderate  head,  can  be  obtained. 


PUMP  MACHINERY. 


Pumps  are  employed  for  unwatering  mines,  handling  water  at  placer 
mines,  irrigation,  water-supply  systems,  boiler  feeds,  etc. 

For  unwatering  mines,  two  general  systems  of  pumping  are  employed. 
(1)  The  pump  is  placed  in  the  mine  and  is  operated  by  a motor  on  the  sur- 
face, the  power  being  transmitted  through  a line  of  moving  rods.  (2)  Both 
the  motor  and  pump  are  placed  in  the  mine,  the  motor  being  an  engine 
driven  by  steam,  compressed  air,  hydraulic  motor,  or  an  electric  motor. 

Cornish  Pumps. — Any  method  of  operating  pumps  by  rods  is  commonly 
called  a Cornish  system.  Formerly,  the  motor  in  the  Cornish  system  con- 
sisted of  a steam  engine  placed  over  the  shaft  head,  which  operated  the 
pump  by  a direct  line  of  rods.  With  this  arrangement,  there  is  great  danger 
of  accident  to  the  engine  from  the  settling  of  the  ground  around  the  shaft, 
or  from  fire  in  the  shaft;  also,  the  position  of  the  motor  renders  access  to  the 
shaft  difficult.  To  overcome  these  objections,  the  engine  is  frequently 
placed  at  one  side  of  the  shaft,  and  the  rods  operated  by  a bob;  this  has 
become  the  common  practice,  and  is  generally  called  the  Cornish  rig.  The 
engine  employed  in  the  most  modern  plants  is  generally  of  the  Corliss 
type,  and  is  provided  with  a governor  to  guard  against  the  possibility  of  the 
engine  running  away,  in  case  the  rods  should  break. 

This  system  requires  no  steam  line  down  the  shaft,  and  is  independent  of 
the  depth  of  water  in  the  mine,  so  that  the  pump  is  not  stopped  by  the 
drowning  of  a mine,  but  the  moving  rods  are  a great  inconvenience  in  the 
shaft,  and  they  absorb  a great  amount  of  power  by  friction. 

Simple  and  Duplex  Pumps.— In  the  simple  pump,  a steam  cylinder  is  con- 
nected directly  to  a water  cylinder,  and  the  steam  valves  are  operated  by 
tappets.  Such  a pump  is  more  or  less  dependent  on  inertia  at  certain  points 
of  the  stroke  to  insure  the  motion  of  the  valves,  hence  will  not  start  from 


P TJMP  MA  C MINER  Y. 


159 


any  place,  but  is  liable  to  become  stalled  at  times.  In  the  duplex  pump, 
two  steam  cylinders  and  two  water  cylinders  are  arranged  side  by  side, 
and  the  valves  so  placed  that  when  one  piston  is  at  mid-stroke  it  throws 
the  steam  valve  for  the  other  cylinder,  etc.  With  this  arrangement,  the 
pump  will  start  from  any  point,  and  can  never  be  stalled  for  lack  of  steam, 
due  to  the  position  of  the  valves.  Ordinarily,  duplex  pumps  are  to  be  pre- 
ferred for  mine  work. 

The  packing  for  the  water  piston  of  a pump  maybe  either  inside  ov  outside. 
Any  form  of  packing  that  is  inside  the  cylinder,  either  upon  a moving  piston 
or  surrounding  the  ram, 
and  so  situated  that  any 
wear  will  allow  communi- 
cation between  the  oppo- 
site ends  of  the  cylinder, 
is  called  inside  packing. 

It  may  consist  simply  of 
piston  rings  about  the  pis- 
ton, as  in  the  case  of  an 
ordinary  steam-engine  pis- 
ton G,  Fig.  19,  or  stationary 
rings  may  be  employed 
about  the  outside  of  a mov- 


Fig.  19. 


ing  ram  or  long  piston  P. 

In  either  case,  the  cylinder  heads  have  to  be  removed  before  the  condition 
of  the  packing  can  be  inspected,  and  any  leak  does  not  make  itself  visible. 

When  outside  packing  is  employed,  separate  rams  are  used  in  opposite 
ends  of  the  cylinder,  there  being  no  internal  communication  between  the 
chambers  in  which  the  rams  work.  The  rams  are  packed  by  ordinary 
outside  stuffingboxes  and  glands.  The  arrangement  consists  practically  of 
two  single-acting  pumps  arranged  to  work  alternately,  so  that  one  is  forcing 
water  while  the  other  is  drawing  water.  Fig.  20  shows  a horizontal  section 
of  a cylinder  so  arranged,  together  with  the  yoke  rods  that  operate  the  ram 
at  the  farther  end  of  the  cylinder. 

As  a rule,  inside-packed  pumps  should  be  avoided  in  mines,  on  account  of 
the  fact  that  acid  or  gritty  waters  are  liable  to  cut  the  packing,  and  make  the 
pumps  leak  in  a very  short  time.  For  dipping  work  in  single  stopes  or 
entries,  small  single  or  duplex  outside-packed  pumps  may  be  employed. 
It  is  generally  best  to  operate  such  pumps  by  compressed  air,  for  the  exhaust 
will  then  be  beneficial  to  the  mine  air.  If  steam  is  employed,  it  is  frequently 
necessary  to  introduce  a trap  and  remove  entrailed  water  from  the  steam 
before  it  enters  the  pump,  and  to  dispose  of  the  exhaust  by  piping  it  out  or 
condensing  it.  Such  isolated  steam  pumps  are  about  the  most  wasteful  form 
of  steam-driven  motor  in  existence. 

For  sinking,  center-packed  single  or  duplex  pumps  are  usually  employed, 
the  duplex  style  being  the  better.  For  station  work,  where  much  water  is  to 
be  handled,  large  compound,  or  triple-expansion,  condensing,  duplex  pump- 
ing engines  are  employed.  They  may,  or  may  not,  be  provided  with  cranks 
and  a flywheel.  Engineers  differ  greatly  upon  this  point,  and,  as  a rule,  for 
very  high  lifts  and  ^reat  pressures,  the  flywheel  is  employed. 

The  main  points  in  consideration  are  the  first  cost  of  the  pump,  and  the 
amount  that  will  be  saved  by  using  the  more  expensive  engine.  The  large 
flywheel  pumping  engines  are  several  times  as  expensive  as  the  direct- 
acting  steam  pumps,  and  the  question  is  as  to  whether  their  greater  efficiency 

will  more  than  coun- 
terbalance  the  in- 
creased outlay.  Most 
engineers  favor  fly- 
wheel pumps  for 
handling  large  vol- 
umes of  water  where 
the  work  is  approxi- 
without  flywheels  or  cranks. 


Fig.  20. 


mately  constant,  and  direct-acting  pumps, 

for  handling  small  amounts  of  water,  or  for  very  irregular  service,  owing 
to  the  fact  that  if  the  flywheel  pump  is  driven  below  its  normal  speed  it  does 
not  govern  properly,  nor  work  economically.  Until  recently,  water  was 
removed  from  mines  in  lifts  of  about  300  to  350  ft.,  pumps  being  placed  at 
stations  along  the  shaft. 

While  a series  of  station  pumps  are  still  employed,  in  some  cases  they  are 


160 


PUMP  MACHINERY, 


generally  intended  to  take  care  of  water  coming  into  the  shaft,  or  workings 
at  or  near  their  level,  and  are  not  employed  for  handling  water  in  successive 
stages  or  lifts.  For  handling  the  hulk  of  the  water  from  the  bottom  of  the 
shaft,  large  pumping  engines  are  employed  that  frequently  force  the  water 
to  the  surface  from  depths  of  over  1,000  ft.  These  high-duty  pumping  plants, 
when  near  the  shaft  and  operated  by  steam  with  a condenser,  frequently 
show  a veij  high  efficiency.  When  air  is  employed  to  operate  such  a plant, 
a much  higher  efficiency  can  be  obtained  if  the  compressed  air  is  heated 
before  using  in  the  high-pressure  cylinder,  and  during  its  passage  from  the 
high-pressure  to  the  low-pressure  cylinder.  This  has  been  very  successfully 
accomplished  by  means  of  a steam  reheater,  the  small  amount  of  steam 
necessary  being  conveyed  to  the  station  in  the  small  pipe,  and  entirely  con- 
densed in  the  reheater,  from  which  it  is  trapped  as  water. 

The  duty  of  steam  pumps  is  approximately  as  follows: . For  small-sized 
steam  pumps,  the  steam  consumption  is  from  130  to  200  lb.  per  horsepower 
per  hour,  when  operating  in  the  workings  of  a mine  at  some  distance  from 
the  boiler.  For  larger  sizes  of  simple  steam  pumps,  the  consumption  runs 
from  80  to  130  lb.  of  steam  per  horsepower  per  hour.  Compound-condensing 
pumps,  such  as  are  commonly  used  as  station  pumps,  consume  from  40  to 
70  lb.  of  steam  per  horsepower  per  hour.  Triple-expansion,  condensing, 
high-class  pumping  engines  consume  from  24  to  26  lb.  per  horsepower  per 
hour.  The  Cornish  pump  consumes  varied  amounts  of  steam  in  proportion 
to  the  water  delivered,  depending  largely  on  the  friction  of  the  gearing, 
bobs,  rods,  etc.,  but  its  efficiency  is  usually  considerably  below  the  best  class 
of  pumping  engines. 

Speed  of  Water  Through  Valves,  Pipes,  and  Pump  Passages.— The  speed  of  water 
through  the  valves  and  passages  of  a pump  should  not  exceed  250  ft.  per 
minute,  and  care  should  be  taken  to  see  that  the  passages  are  not  too 
abruptly  deflected.  The  flow  of  water  through  the  discharge  pipe  should 
not  exceed  500  ft.  per  minute,  but  for  single-cylindered  pumps  it  is  usually 
figured  at  between  250  and  400  ft.  per  minute.  In  the  case  of  very  large 
pumps,  greater  velocities  may  be  allowed.  The  suction  pipe  for  -the  pump 
should  be  larger  than  the  discharge  pipe.  Ordinarily,  the  suction  pipe  for  a 
pump  should  not  exceed  250  ft.  in  length,  and  should  not  contain  more  than 
two  elbows.  The  following  formula  gives  the  diameter  of  the  suction  and 
discharge  pipes  of  a pump: 

(r  = U.  S.  gallons  per  minute; 

d'  = diameter  of  suction  pipe  in  inches; 

d"=  diameter  of  discharge  pipe  in  inches; 

‘*'=4.95^1; 

<*"=  4-95^1;. 

v'  = velocity  of  water  in  feet  per  minute  in  the  suction  pipe  = from 
.50?/'  to  .75?/'; 

r"  = velocity  of  water  in  feet  per  minute  in  the  discharge  pipe. 


A : 
D 
P : 

P ■■ 
E : 


RATIO  OF  STEAM  AND  WATER  CYLINDERS  IN  A 
DIRECT-ACTING  PUMP. 

area  of  steam  cylinder;  H = head  of  water  ^ 2.309  p; 


diameter  of  steam  cylinder; 
steam  pressure  in  pounds  per 
square  inch; 

pressure  per  square  inch,  corresponding  to  the  head  H 
„ work  done  in  pump  cylinder 

efficiency  of  pump  = — ^ ' 

work  done  in  steam  cylinder 


a — area  of  pump  cylinder; 
d = diameter  of  pump  cylinder; 

.433  H\ 


ap 

EP' 

EAI\ 

d --= 

t) 

P\l 

\ P 

ap  ^ 

II 

II 

P ’ 

E~A* 

P = 

E A P^ 
a ’ 

11=  2.309  FP  X — 
a 

CAPACITY  AND  HORSEPOWER  OF  PVMPS, 


161 


If  ^ = 75/.,  then  H = 1.732  P X 

E is  commonly  taken  at  from  .7  to  .8  for  ordinary  direct-acting  pumps. 
For  the  highest  class  of  pumping  engines  it  may  amount  to  .9.  The  steam 
pressure  P is  the  mean  effective  pressure,  according  to  the  indicator  dia- 
gram; the  pressure  p is  the  mean  total  pressure  acting  on  the  pump  plunger 
or  piston,  including  the  suction,  as  would  he  shown  by  the  indicator  dia- 
gram of  the  water  cylinder.  The  pressure  on  the" pump  cylinder  is  frequently 
much  greater  than  that  due  to  the  height  of  the  lift,  on  account  of  the 
friction  in  the  valves  and  passages,  which  increases  rapidly  with  the  velocity 
of  the  flow. 

Piston  Speed  of  Pumps.— For  small  pumps,  it  is  customary  to  assume  a 
speed  of  100  ft.  per  minute,  but,  in  the  case  of  very  small  short-stroke  pumps, 
this  is  too  high,  owing  to  the  fact  that  the  rapid  reverses  make  the  flow 
through  the  valves  and  change  in  the  direction  of  the  current  too  frequent. 
When  the  stroke  of  the  pump  is  somewhat  longer  (18  in.  or  more),  higher 
speeds  can  be  employed,  and  in  the  case  of  large  pumping  engines  having 
long  strokes,  speeds  of  as  much  as  200  to  250  ft.  per  minute  are  successfully 
used  without  jar  or  hammer. 

Boiler  Feed-Pumps.— In  practice,  it  has  been  shown  that  a piston  speed 
greater  than  100  ft.  per  minute  results  in  excessive  wear  and  tear  on  a 
boiler  feed-pump,  especially  when  the  water  is  warm.  This  is  due  to  the 
fact  that  vapor  forms  in  the  cylinders,  and  results  in  a water  hammer.  In 
determining  the  proper  size  of  a pump  for  feeding  a steam  boiler,  not  only 
the  steam  employed  in  running  the  engine,  but  that  necessary  for  the 
pumps,  heating  system,  etc.  must  be  taken  into  consideration. 


THEORETICAL  CAPACITY  OF  PUMPS  AND  THE  HORSEPOWER 


REQUIRED  TO  RAISE  WATER. 


Let 


Then, 


Q ~ cubic  feet  of  water  per  minute; 

G = U.  S.  gallons  per  minute; 

O'  = U.  S.  gallons  per  hour; 
d = diameter  of  cylinder  in  inches; 

I = stroke  of  piston  in  inches; 

N = number  single  strokes  per  minute; 

V = speed  of  piston  in  feet  per  minute; 

W — weight  moved  in  pounds  per  minute; 

P = pressure  in  pounds  per  square  feet  = 62.5  X H ; 
p = pressure  in  pounds  per  square  inch  = .433  X H* 
U = height  of  lift  in  feet; 

H.  P.  = horsepower. 

d2 


^ = 4* 


Q=4 

NdH 


= .0004545  Wd2/. 


231 


IN 

144  ’ 12 


.0034  iV^d2 1 Qf  = .204  Nd^  I 


The  diameter  of  piston  required  for  a given  capacity  per  minute  will  be 
d = = 17.15^'^,  ord  = 13.54^|  = 4.95^f. 

The  actual  capacity  of  a pump  will  vary  from  60/  to  95/  of  the  theoretical 
capacity,  depending  on  the  tightness  of  the  piston,  valves,  suction  pipe,  etc. 
„ p _ _QP  _ QRX  144:  X .433  ^ QH  ^ Gp_ 

* * 33,000  33,000  529.2  1,714.5* 

The  actual  horsepower  required  will  be  considerably  greater  than  the 
theoretical,  on  account  of  the  friction  in  the  pump;  hence,  at  least  20/  should 
be  added  to  the  power  for  friction  and  usually  about  50/  more  is  added  to 
cover  leaks,  etc.,  so  that  the  actual  horsepower  required  by  the  pump  is 
about  70/  more  than  the  theoretical. 

Example  1. — If  it  is  desired  to  find  the  size  of  a pump  that  will  throw 
30  gal.  of  water  per  minute  up  125  ft.,  from  the  bottom  of  a pit  or  prospect 
shaft  to  the  station  pump  at  the  main  shaft,  it  may  be  accomplished  as 
follows: 

An  allowance  of  probably  25/  should  be  made  with  a small  pump  of  this 
character,  to  overcome  slippage  or  leaking  through  the  valves,  past  the  piston, 


162 


p mrp  MA  CHINEE  1 : 


etc.,  and  hence  -we  'vvill  call  the  total  amount  of  water  to  be  handled  40  gal 
per  minute.  The  formula  for  the  diameter ^f  piston  is 


Assuming  that  v = 100  ft.  per^nute,  we  have 

d = 4.95]/ A = 4.95  X .63  = 3.13. 


In  practice,  a 3^"  pump  would  probably  be  employed. 

Example  2.— If  it  is  desired  to  find  the  approximate  horsepower  necessary 
to  lift  30  gal.  per  minute  in  the  above  example,  without  determining  the  size 
of  the  pump,  it  can  be  done  as  follows: 


G XP  _ 30  X .433  X 125 
1,714.5  1,714.5 


= .95,  or  practically  1 H.  P. 


In  order  to  cover  leakage  through  valves,  friction,  etc.,  an  addition  of  at 
least  should  be  made  to  a very  small  pump  like  this,  and  so  we  would 
count  on  U H.  P. 

Depth  of  Suction.— Theoretically,  a perfect  pump  will  raise  w^ater  to  a 
height  of  nearly  34  ft.  at  the  sea  level;  but,  owing  to  the  fact  that  a perfect 
vacuum  can  never  be  attained  with  the  pump,  that  the  water  always  con- 
tains more  or  less  air,  and  that  more  or  less  watery  vapor  will  form  below 
the  piston,  it  is  never  possible  to  reach  this  theoretical  limit,  and,  in  practice, 
it  is  not  possible  to  draw  water  much,  if  any,  over  30  ft.  at  the  sea  level,  even 
when  the  water  is  cold.  Warm  water  cannot  be  lifted  as  high  as  cold  water, 
owing  to  the  fact  that  a larger  amount  of  watery  vapor  forms.  With  boiler 
feed-pumps  handling  hot  water,  the  water  should  flow  to  the  pumps 
by  gravity. 

Amount  of  Water  Raised  by  a Single-Acting  Lift  Pump. — In  the  case  of  all 
pumps  having  a piston  or  ram,  the  amount  of  water  lifted  is  usually  con- 
siderably less  than  the  piston  displacement,  owing  to  the  leakage  through 
the  valves,  etc.,  but  with  single-acting  lift  pumps,  having  buoket  plungers 
with  a clack  valve  in  the  plunger,  the  amount  lifted  may  actually  exceed 
the  plunger  displacement,  that  is,  the  volume  of  water  may  actually  be 
greater  than  the  length  of  the  stroke  multiplied  by  the  number  of  strokes, 
for,  during  the  up  stroke,  the  water  both  above  and  below  the  piston  is  set  in 
motion,  and  during  the  down  stroke,  the  inertia  of  the  water  actually  carries 
more  water  through  the  valve  than  would  pass  through  it  on  account  of  the 
space  passed  through.  This  increases  as  the  speed  or  number  of  strokes 
increases. 

Pump  Valves. — As  a rule,  a large  number  of  small  valves  having  a compar- 
atively small  opening  are  preferable  to  a small  number  of  large  valves  with 
a greater  opening,  and  most  modern  pumps  are  built  upon  these  lines.  A 
small  valve  represents  a proportionately  larger  surface  of  discharge  with  the 
same  lift  than  the  large  valve,  hence  whatever  the  total  area  of  the  valve- 
seat  opening,  its  full  contents  can  be  discharged  with  less  lift  through 
numerous  small  valves  than  through  one  large  valve.  Cornish  pumps 
generally  have  one  large  metal  valve. 

Power  Pumps.— Where  comparatively  small  amounts  of  water  are  to  be 
handled,  and  power  is  available,  belt-driven  power  pumps  are  very  much 
more  efficient  than  small  steam  pumps. 

Electrically  Driven  Power  Pumps.— Where  water  is  to  be  delivered  from 
isolated  workings  to  the  sumps  for  the  large  station  pumps,  electrically 
driven  power  pumps  are  far  more  efficient  than  steam  pumps.  In  some 
cases  it  is  probably  best  to  equip  the  entire  mine  with  electric  pumps,  both 
in  the  isolated  workings  and  at  the  stations,  on  account  of  the  fact  that  they 
can  be  driven  by  a high-class  compound-condensing  engine  on  the  surface, 
directly  connected  to  a generator,  and  furnishing  electricity  through  con- 
ductors to  the  various  pumps. 

The  total  efficiency  of  a series  of  small  electric  pumps  that  aggregate  a 
sufficient  amount  of  power  to  enable  this  arrangement  to  be  used,  is  very 
much  higher  than  the  total  efficiency  of  a number  of  small  isolated  steam  or 
compressed-air  pumps  introduced  into  the  workings.  -With  compound- 
condensing  engines  upon  the  surface,  operating  electric  pumps  underground, 
the  steam  consumption  per  pump  horsepower  per  hour,  for  the  smaller 
sizes,  would  only  be  about  40  lb.  per  horsepower  per  hour;  for  medium-sized 
electric  pumps,  about  30  lb.  of  steam  per  hour,  and  larger  sizes  from  20  to 
80  lb.  per  horsepower  per  hour.  It  will  be  seen  from  these  figures  that  for 


PUMV  AND  WATER  MEMORANDA. 


163 


pumping  from  isolated  portions  of  the  mine  the  electric  pump  is  much  more 
efficient  than  the  steam  pump,  and  owing  to  the  fact  that  the  current  can 
frequently  be  obtained  from  the  lines  operating  the  underground  haulage 
system,  furnishing  light,  etc.,  it  is  evident  that  this  system  of  pumping  has 
a great  future  before  it  in  connection  with  mining. 

The  following  table  gives  the  gallons  per  minute  delivered  from  various 
sized  pumps  operating  at  different  piston  speeds: 

Pump  and  Water  Memoranda. 


164 


PUMP  MACHINERY. 


MISCELLANEOUS  FORMS  OF  WATER  ELEVATORS. 

Jet  Pump.— In  this  form,  the  energy  of  the  jet  of  water  is  utilized  for 
raising  a larger  volume  through  a small  distance,  or  a mixture  of  water  and 
solid  material  through  a short  distance. 

Vacuum  Pump.— The  pulsometer,  which  is  the  most  important  representa- 
tive of  this  class,  consists  of  two  chambers  in  a large  casting,  with  suitable 
automatic  valves  arranged  at  the  top  and  bottom  of  the  chambers.  Steam  is 
introduced  into  one  of  the  chambers,  then  the  valve  at  the  top  closed.  This 
steam  will  condense,  forming  a vacuum  that  draws  water  from  the  suction 
into  the  chamber.  When  the  chamber  is  filled  with  water,  steam  is  again 
introduced  and  forces  the  water  out  through  the  discharge  pipe.  The 
operation  is  then  repeated,  more  water  being  drawn  in  by  the  condensation 
of  the  steam.  The  two  chambers  work  alternately,  one  being  engaged  in 
drawing  water  in  while  the  other  forces  it  out.  The  total  steam  efficiency 
of  this  form  of  pump  is  small,  though  it  may  actually  be  above  that  of  small 
steam  pumps  employed  in  isolated  portions  of  a mine.  The  advantages  are 
that  the  pump  possesses  no  intricate  mechanism,  no  reciprocating  parts, 
requires  no  lubrication,  and  is  not  injured  by  gritty  or  acid  materials.  On 
this  account  it  may  be  employed  for  pumping  water  in  concentration  works, 
coal-washing  plants,  and  similar  places  where  the  water  is  liable  to  contain 
grit  or  dirt. 

Air-Lift  Pumps.— By  introducing  compressed  air  at  the  bottom  of  a pipe 
submerged  in  any  liquid,  the  air  in  the  pipe  rises  as  bubbles,  and  so  reduces 
the  specific  gravity  of  the  fluid  in  the  pipe.  This  causes  the  fluid  in  the  pipe 
to  rise  above  the  level  of  that  surrounding  the  pipe.  The  difference  in 
specific  gravity  can  never  be  great,  and  hence  the  fluid  can  never  be 
elevated  to  any  considerable  height  without  having  the  lower  end  immersed 
to  a correspondingly  great  depth.  On  this  account  it  is  frequently  necessary 
to  drill  a well  considerably  below  the  water-bearing  strata,  so  as  to  obtain 
the  proper  ratio  between  the  submerged  portion  of  the  pipe  and  the  height 
to  which  the  water  is  to  be  lifted.  Some  advantages  of  this  form  of  pump 
are  that  there  are  no  moving  parts,  no  lubrication  is  required,  and  gritty 
material  does  not  interfere  with  the  operation.  If  the  pump  is  constructed 
of  suitable  material,  it  may  be  employed  for  handling  acids  or  solutions  in 
electrolytic  or  chemical  works.  This  style  of  pump  is  also  quite  extensively 
employed  for  pumping  water  from  Artesian  wells.  It  has  not  been  successful 
as  a mine  pump,  owing  to  the  ratio  between  the  part  immersed  and  the  lift. 

Centrifugal  Pumps.— The  height  of  lift  depends  on  the  tangential  velocity 
of  the  revolving  disk  of  pump  and  the  quantity  of  water  discharged,  and  is 
proportional  to  the  area  of  the  discharge  orifices  at  the  circumference  of  the 
disk.  The  most  efficient  total  lift  for  the  centrifugal  pump  is,  approximately, 
17  ft.,  and  for  small  lifts  the  centrifugal  pump  is  much  more  efficient  than 
any  style  of  piston  pump.  For  a given  lift,  the  total  efficiency  of  a centrif- 
ugal pump  increases  with  the  size  of  the  pump.  Centrifugal  pumps  are 
always  designated  by  the  size  of  their  outlet,  as,  for  instance,  a 2"  or  4"  pump, 
meaning  with  a 2"  or  4"  discharge  pipe.  Centrifugal  pumps  are  not  at 
all  effective  for  dealing  with  great  heads,  and  hence  have  never  come 
into  competition  with  piston  pumps  for  this  class  of  work.  For  lifting 
large  volumes  of  water  against  a low  head,  as  in  irrigation  or  drainage 
problems,  they  are  remarkably  efficient.  Under  the  most  favorable  circum- 
stances, the  efficiency  of  the  centrifugal  pump  may  be  practically  70^;  that  is, 
the  pump  may  do  an  amount  of  work  upon  the  water  that  is  theoretically 
equal  to  70^  of  the  power  furnished  to  the  pump.  Pumping  engines  work- 
ing against  high  heads,  and  operated  by  the  most  improved  class  of  engines, 
may  attain  an  efficiency  of  practically  85^. 

Centrifugal  Pump  as  a Dredge.— When  dredging  is  done  by  means  of  centrif- 
ugal pumps,  a greater  amount  of  power  is  necessary,  and  the  pump  has  to 
be  run  at  a greater  speed  than  when  pumping  water,  owing  to  the  fact  that 
the  fluid  being  handled  has  a greater  density  than  water.  When  dealing 
with  fine  sand,  as  much  as  50^  of  the  bulk  of  the  material  handled  may  be 
sand,  though,  as  a rule,  the  amount  of  solid  material  in  the  water  dredged 
only  runs  from  30^  to  .35^  of  the  total. 

Water  Buckets.— Where  only  a limited  amount  of  water  collects  in  the 
mine  workings,  it  is  frequently  removed  by  means  of  a special  water  bucket 
or  water  car  during  the  hours  that  the  h(')isting  engine  would  otherwise  be 
idle.  Wlu  n*  very  large  amounts  of  water  are  to  be  removed,  it  has  also 


SINKING  PUMPS. 


165 


been  found  economical  to  remove  them  by  means  of  special  water  buckets. 
This  is  especially  true  in  the  case  of  deep  shafts. 

One  of  the  best  illustrations  of  this  class  of  work  is  the  Gilberton  water 
shaft,  which  has  been  equipped  at  the  Gilberton  Colliery  of  the  Phila- 
delphia and  Reading  Coal  & Iron  Co.  The  collieries  draining  to  this  shaft 
require  the  removal  of  6,000,000  gal.  of  water  per  24  hours  during  the  wet 
season,  and  this  has  to  be  lifted  from  a depth  of  1,100  ft.  In  order  to  accom- 
plish the  work  by  means  of  steam  pumps,  it  required  a number  of  pump 
stations  in  different  parts  of  the  mine,  each  of  which  had  to  be  attended  by 
a pumpman,  and  a large  number  of  steam  lines  were  required  in  the  mine. 
In  order  to  remove  the  danger  of  fire  caused  by  these  steam  lines,  and  to 
dispense  with  the  large  amount  of  labor  otherwise  necessary,  it  was  decided  to 
hoist  the  water,  and  a shaft  22  ft.  X 26  ft.  8 in.  outside  of  timbers,  was  sunk. 
This  shaft  contains  two  compartments  7 ft.  X 7 ft.,  in  which  the  water 
buckets  are  operated,  and  two  compartments  7 ft.  X 11  ft.  8 in.  that  are 
utilized  for  cages  to  lower  men,  timber,  and  other  supplies.  The  water 
tanks  employed  in  the  special  water  compartments  are  5 ft.  6 in.  in  diameter, 
and  14  ft.  long.  They  are  provided  with  a special  device  sliding  on  regular 
cage  guides,  and  empty  themselves  automatically  at  the  surface  by  means 
of  a trip  or  sliding  valve.  Two  pairs  of  direct-acting  hoisting  engines,  with 
45"  X 60"  cylinders,  operating  drums  14  ft.  8 in.  in  diameter  by  15  ft.  face, 
are  employed.  These  operate  the  water  buckets  in  cages  by  means  of  2" 
crucible  steel  ropes,  at  50  revolutions  per  minute,  which  is  equivalent  to  a 
piston  speed  of  500  ft.  per  minute.  The  drums  will  hoist  two  tanks  of  2,400 
gal.  per  minute.  This  gives  an  output  of  7,000,000  gal.  per  24  hours.  By 
slightly  increasing  the  speed  of  the  engine  this  amount  can  be  increased  lOfo, 
which  is  25^  in  excess  of  the  calculated  maximum  demand  on  the  shaft. 
The  cages  in  the  cage  compartments  are  so  arranged  that  they  can  be  discon- 
nected, and  water  buckets  substituted  for  them.  This  would  be  a total 
output  of  over  14,000,000  gal.  per  24  hours  at  the  normal  speed  of  the 
engine.  One  great  advantage  of  this  style  of  pumping  plant  is  that  there  is 
absolutely  no  fear  of  drowning  the  pumps. 

Some  years  ago  the  Hamilton  iron  mine,  in  Michigan,  was  drowned  by 
a sudden  inrush  of  water  that  drove  the  pumpmen  from  the  pumps.  In 
order  to  remove  this  large  volume  of  water,  special  bailing  buckets  were 
substituted  for  the  ordinary  mine  skips.  These  bailing  buckets  ran  on  the 
inclined  skip  road,  and  unwatered  the  mine  in  a remarkably  short  time. 

Sinking  Pumps.— Sinking  pumps  may  be  either  single  or  duplex  in  their 
action,  and  may  be  inside  or  outside  packed.  Outside-packed  single-acting 
pumps  are  in  many  ways  preferable,  owing  to  the  fact  that  they  are  less 
liable  to  get  out  of  order.  One  requisite  of  any  sinking  pump  is  that  it  should 
have  as  few  exposed  parts  as  possible,  and  that  these  parts  should  be  so  placed 
that  they  will  be  protected  from  injury  by  blasting  to  as  great  an  extent  as 
possible.  Sinking  pumps  are  usually  provided  with  a telescopic  section  in  the 
suction  pipe,  and  sometimes  also  in  the  discharge  pipe,  so  that  they  can  be 
moved  down  several  feet  without  having  to  break  the  joints  of  the  piping. 

Pumps  for  Acid  Waters.— Where  mine  waters  are  acid  in  their  nature,  brass 
or  brass-lined  pumps  are  usually  employed, 
and  in  some  cases  even  wooden  pumps 
have  been  used,  as,  for  instance,  in  the 
Swedish  copper  mines,  though  this  prac- 
tice is  disappearing  in  favor  of  the  use  of 
brass  or  copper  linings.  The  pipes  for  such 
pumps  should  be  of  brass  or  copper  tubing, 
or  should  be  lined  with  some  substance 
that  will  not  be  affected  by  the  acid  of  the 
water.  Sometimes  wooden  linings  are  em- 
ployed, placed  as  shown  in  Figs.  21  and  22, 

Fig.  21  being  a section  of  the  pipe  with  the 
lining  complete,  and  Fig.  22  a cross-section 
of  one  of  the  individual  boards  used  in  the 
lining.  These  are  usually  made  of  pine 
about  I in.  thick,  and  are  grooved  on  each 
end  as  shown.  They  are  sprung  in  so  as  to  complete  a circle  on  the  inside 
of  the  pipe,  and  then  long,  thin,  wooden  keys  driven  into  the  grooves. 
When  the  water  is  allowed  to  go  into  the  pipes,  the  linings  swell  and  make 
all  joints  perfectly  tight.  Elbows  and  other  crooked  sections  are  lined  with 
sheet  lead  beaten'in  with  a mallet. 


Fig.  21. 


Fig.  22. 


160 


FUELS. 


FUELS. 


The  value  of  any  fuel  is  measured  by  the  number  of  heat  units  that  its 
combustion  will  generate,  a unit  of  heat  being  the  amount  required  to  heat 
1 lb.  of  water  1°  F.  The  fuels  used  in  generating  steam  are  composed  mainly 
of  carbon  and  hydrogen,  ash,  and  moisture,  with  sometimes  small  quantities 
of  other  substances  not  materially  affecting  their  value. 

Combustible  is  that  portion  which  will  burn;  the  ash  or  residue  varies 
from  2^  to  36^  in  different  fuels. 

The  following  table  gives,  for  the  more  common  combustibles,  the  air 
required  for  complete  combustion,  the  temperature  with  different  proportions 
of  air,  the  theoretical  value,  and  the  highest  attainable  value  under  a steam 
boiler,  assuming  that  the  gases  pass  off  at  320°,  the  temperature  of  steam  at 
75  lb.  pressure,  and  the  incoming  draft  to  be  at  60°;  also,  that  with  chimney 
draft  twice  and  with  blast  only  the  theoretical  amount  of  air  is  required  for 
combustion. 

Table  of  Combustibles. 


Air  Re- 
quired. 

Temperature  of 
Combustion. 

Theoretical 

Value. 

Highest 
Attainable 
Value  Un- 
der Boiler. 

Kind  of 
Combustible. 

Pounds  per  Pound 
of  Combustible. 

With  Theoretical 
Supply  of  Air. 

With  1^  Times  Theoret- 
ical Supply  of  Air. 

With  Twice  Theoret- 
ical Supply  of  Air. 

With  Three  Times  The- 
oretical Supply  of  Air. 

Pounds  of  Water  Raised 
1°  per  Pound  of 
Combustible.  | 

Lb.  of  Water  Evapora- 
ted From  and  at  212°, 
with  1 Lb.  Combustible. 

With  Chimney  Draft. 

With  Blast,  Theoretical 
Supply  of  Air  at  60°, 

Gas  320°. 

Hvdrogen  

36.00 

5,750 

3,860 

2,860 

1,940 

62,032 

64.20 

Petroleum 

15.43 

5,050 

3,515 

2,710 

1,850 

21,000 

21.74 

18.55 

19.90 

( Charcoal "I 

( 'arbon  -j  Coke  > 

12.13 

4,580 

3,215 

2,440 

1,650 

14,500 

15.00 

13.30 

14.14 

(Anthracite....  j 

('oal,  Cumberland, 

12.06 

4,900 

3,360 

2,550 

1,730 

15,370 

15.90 

14.28 

15.06 

Coal,  Coking  bituminous 

11.73 

5,140 

3,520 

2,680 

1,810 

15,837 

16.00 

14.45 

15.19 

Coal,  Cannel 

11.80 

4,850 

14,600 

3,330 

2,540 

1,720 

15,080 

15.60 

14.01 

14.76 

Coal,  Lignite 

9.30 

3,210 

2,490 

1,670 

11,745 

12.15 

10.78 

11.46 

Peat,  Kiln  dried 

7.6814,470 

3,140 

2,420 

1,660 

9,660 

10.00 

8.92 

9.42 

Peat,  Air  dried,  25^  water 

5.76 

4,000 

2,820 

2,240 

1,550 

7,000 

7.25 

6.41 

6.78 

Wood,  Kiln  dried 

6.00 

4,080 

2,910 

2,260 

1,530 

7,245 

7.50 

6.64 

7.02 

Wood,Airdried,20^  water 

4.80 

3,700 

2,607 

2,100 

1,490 

5,600 

5.80 

4.08 

4.39 

The  effective  value  of  all  kinds  of  wood  per  pound,  w'hen  dry,  is  substan- 
tially the  same.  This  is  usually  estimated  at  .4,  the  value  of  the  same  weight 
of  coal.  The  following  are  the  weights  and  comparative  values  of  different 
woods  by  the  cord; 


Wood. 


Hickory  (shell  bark) 
Hickory  (red  heart) 

White  oak 

Red  oak 

Sjn-uce 

New  .Tersey  pine  


Weight. 

Wood. 

Weight. 

4,469 

Beech 

3,126 

3,705 

Hard  maple 

2,878 

3,821 

Southern  pine 

3,375 

3, -254 

Virginia  pine 

2,680 

2,325 

Yellow  pine 

1,904 

2,137 

White  pine 

1,868 

SLACK. 


167 


Much  is  said  nowadays  about  the  wonderful  saving  that  is  to  be  expected 
from  the  use  of  petroleum  for  fuel.  This  is  all  a myth,  and  a moment’s 
attention  to  facts  is  sufficient  to  convince  any  one  that  no  such  possibility 
exists.  Petroleum  has  a heating  capacity,  when  fully  burned,  equal  to  from 
21,000  to  22,000  B.  T.  U.  per  lb.,  or,  say,  50^  more  than  coal.  But,  owing  to 
the  ability  to  burn  it  with  less  losses,  it  has  been  found,  through  extended 
experiments  by  the  pipe  lines,  that  under  the  same  boilers,  and  doing  the 
same  work,  1 lb.  of  petroleum  is  equal  to  1.8  lb.  of  coal.  The  experiments  on 
locomotives  in  Russia  have  shown  practically  the  same  value,  or  1.77.  Now, 
a gallon  of  petroleum  weighs  6.7  lb.  (though  the  standard  buying  and  selling 
weight  is  6.5  lb.),  and  therefore  an  actual  gallon  of  petroleum  is  equivalent 
under  a boiler  to  12  lb.  of  coal,  and  190  standard  gallons  are  equal  to  a gross 
ton  of  coal.  It  is  very  easy  with  these  data  to  determine  the  relative  cost. 
At  the  wells,  if  the  oil  is  worth,  say,  2 cents  a gallon,  the  cost  is  equivalent 
to  ^3.80  per  ton  for  coal  at  the  same  place,  while  at,  say,  3 cents  per  gallon, 
the  lowest  price  at  which  it  can  be  delivered  in  the  vicinity  of  New  York,  it 
costs  the  same  as  coal  at  $5.70  per  ton.  The  Standard  Oil  Company  estimates 
that  173  gal.  are  equal  to  a gross  ton  of  coal,  allowing  for  incidental  savings, 
as  in  grate  bars,  carting  ashes,  attendance,  etc. 

Sawdust  can  be  utilized  for  fuel  to  good  advantage  by  a special  furnace 
and  automatic  feeding  devices.  Spent  tan  bark  is  also  used,  mixed  with 
some  coal,  or  it  may  be  burned  without  the  coal  in  a proper  furnace.  Its 
value  is  about  one-fourth  that  of  the  same  weight  of  wood  as  it  comes  from 
the  press,  but,  when  dried,  its  value  is  about  85^  of  the  same  weight  of  wood 
in  same  state  of  dryness. 

It  has  been  estimated  that,  on  an  average,  1 lb.  of  coal  is  equal,  for  steam- 
making purposes,  to  2 lb.  dry  peat,  2|  to  2i  lb.  dry  wood,  2|-  to  3 lb.  dried  tan 
bark,  2f  to  3 lb.  cotton  stalks,  3i  to  3f  lb.  wheat  or  barley  straw,  and  6 to  8 lb. 
wet  tan  bark. 

Natural  gas  varies  in  quality,  but  it  is  usually  worth  2 to  2i  times  the  same 
weight  of  coal,  or  about  30,000  cu.  ft.  are  equal  to  a ton  of  coal. 

Shck,  or  the  screenings  from  coal,  when  properly  mixed — anthracite  and 
bituminous— and  burned  by  means  of  a blower  on  a grate  adapted  to  it,  is 
nearly  equal  in  combustible  value  to  coal,  but  its  percentage  of  refuse  is 
greater. 

The  accompanying  table  of  proximate  analyses  and  heating  values  of 
American  coals  was  compiled  by  Mr.  William  Kent,  for  the  1898  edition  of 
the  Babcock  & Wilcox  Co.’s  book,  “ Steam.”  The  analyses  are  selected 
from  various  sources,  and,  in  general,  are  averages  of  many  samples.  The 
heating  values  per  pound  of  combustible  are  either  obtained  from  direct 
calorimetric  determinations  or  calculated  from  ultimate  analyses,  except 
those  marked  (?),  which  are  estimated  from  the  heating  values  of  coals 
of  similar  composition.  The  figures  in  the  last  column  are  obtained  by 
dividing  the  figures  in  the  preceding  column  by  965.7,  the  number  of  heat 
units  required  to  evaporate  1 lb.  of  water  at  212°  into  steam  of  the  same 
temperature. 

The  heating  values  per  pound  of  combustible  given  in  the  table,  except 
those  marked  (?),  are  probably  within  3^  of  the  average  actual  heating  values 
of  the  combustible  portion  of  the  coals  of  the  several  districts.  When  the 
percentage  of  moisture  and  ash  in  any  given  lot  of  coal  is  known,  the 
heating  value  per  pound  of  coal  may  be  found,  approximately,  by  multi- 
plying the  heating  value  per  pound  of  combustible  of  the  average  coal  of  the 
district  by  the  difference  between  100^  and  the  sum  of  the  percentages  of 
moisture  and  ash. 

The  heating  effect  is  calculated  on  the  basis  of  the  coal  burned  to  carbon 
dioxide  and  liquid  water  at  100°  C.,  and  is  stated  either  in  calories  per  kilo- 
gram or  English  heat  units  per  pound.  The  theoretical  evaporative  effect  is 
calculated  by  dividing  the  number  of  calories  per  kilogram  by  536,  or  the 
number  of  English  heat  units  per  pound  by  965.  In  either  case,  it  expresses 
the  theoretical  number  of  kilograms  or  pounds  of  water  converted  into  steam 
from  and  at  100°  C.,  by  1 kilogram  or  1 lb.  of  coal. 

A committee  of  the  Western  Society  of  Engineers,  of  Pittsburg,  report 
that  1 lb.  of  §ood  coal  = 7i  eu.  ft.  of  natural  gas.  When  burned  with  just 
enough  air,  its  temperature  of  combustion  is  4,200°  F.  The  Westinghouse 
Air  Brake  Co.  found  from  experiment  that  1 lb.  Youghiogheny  coal 
— 12i  cu.  ft.  natural  gas,  or  1,000  cu.  ft.  natural  gas  = 81.6  lb.  coal.  Indiana 
natural  gas  gives  1,000,000  B.  T.  U.  for  1,000  cu.  ft.  and  weighs  .045  lb.  per 
cu.  ft. 


168 


FUELS. 


Proximate  Analyses  and  Heating  Values  of  American  Coals. 


Coal. 

Moisture. 

Volatile  Matter. 

Fixed  Carbon. 

Ash. 

1 Sulphur. 

Heating  Value  per  Lb. 

Coal,  B.  T.  U. 

Volatile  Matter  Per  Cent. 

of  Combustible. 

Fixed  Carbon. 

Per  Cent,  of  Combustible. 

Heating  Value  per  Lb. 

Combustible. 

Theoretical  Evaporation 

From  and  at  212°  per  Lb. 

Combustible. 

Anthracite. 

Northern  Coal  Field  . 

3.42 

4.38 

83.27 

8.20 

.73 

13,160 

5.00 

95.00 

14,900 

15.42 

East  Middle  Coal  Field 

3.71 

3.08 

86.40 

6.22 

.58 

13,420 

3.44 

96.56 

14,900 

15.42 

West  Middle  Coal  Field 

3.16 

3.72 

81.59 

10.65 

.50 

12,840 

4.36 

95.64 

14,900 

15.42 

Southern  Coal  Field  . 

3.09 

4.28 

83.81 

8.18 

.64 

13,220 

4.85 

95.15 

14,900 

15.42 

Semianthracite. 

Loyalsock  Field  . . 

1.30 

8.10 

83.34 

6.23 

1.63 

13,920 

8.86 

91.14 

15,500 

16.05 

Bernice  Basin  . . . 

.65 

9.40 

83.69 

5.34 

.91 

13,700 

10.98 

89.02 

15,500 

16.05 

Semibituminous. 

Broad  Top,  Pa.  . . . 

.79 

15.61 

77.30 

5.40 

.90 

14,820 

17.60 

82.40 

15,800 

16.36 

Clearfield  Co.,  Pa.  . . 

.76 

22.52 

71.82 

3.99 

.91 

14,950 

24.60 

75.40 

15,700 

16.25 

Cambria  Co.,  Pa.  . . 

.94 

19.20 

71.12 

7.04 

1.70 

14,450 

22.71 

77.29 

15,700 

16.25 

Somerset  Co.,  Pa.  . . 

1.58 

16.42 

71.51 

8.62 

1.87 

14,200 

20.37 

79.63 

15,800 

16.36 

Cumberland,  Md.  . . 

1.09 

17. .30 

73.12 

7.75 

.74 

14,400 

19.79 

80.21 

15,800 

16.36 

Pocahontas,  Va.  . . . 

1.00 

21.00 

74.39 

3.03 

.58 

15,070 

22.50 

77.50 

15,700 

16.25 

New  River,  W.  Va. 

.85 

17.88 

77.64 

3.36 

.27 

15,220 

18.95 

81.05 

15,800 

16.36 

Bituminous. 

Connellsville,  Pa.  . . 
Youghiogheny,  Pa.  . 

1.26 

30.12 

59.61 

8.23 

.78 

14,050 

34.03 

65.97 

15,300 

15.84 

1.03 

36.50 

59.05 

2.61 

.81 

14,450 

38.73 

61.27 

15,000 

15.53 

Pittsburg,  Pa.  . . . 

1.37 

35.90 

52.21 

8.02 

1.80 

13,410 

41.61 

58.39 

14,800 

15.32 

Jefferson  Co.,  Pa.  . . 

1.21 

32.53 

60.99 

4.27 

1.00 

14,370 

35.47 

64.53 

15,200 

15.74 

Middle  Kittaning  Seam,  Pa. 
Upper  Freeport  Seam,  Pa. 

1.81 

35.33 

53.70 

7.18 

1.98 

13,200 

40.27 

59.73 

14,500 

15.01 

and  Ohio  . . . . 

1.93 

35.90 

50.19 

9.10 

2.89 

13,170 

43.59 

56.41 

14,800 

15.32 

Thacker,  W.  Va.  . . 

1.38 

35.04 

56.03 

6.27 

1.28 

14,040 

39.33 

60.67 

15,200 

15.74 

Jackson  Co.,  Ohio  . . 

3.83 

32.07 

57.60 

6.50 

13,090 

35.76 

64.24 

14,600 

15.11 

Brier  Hill,  Ohio  . . 
Hocking  Valley,  Ohio  . 

4.80 

34.60 

56.30 

4.30 

13,010 

38.20 

61.80 

14,300 

14.80 

6.59 

34.97 

48.85 

8.00 

1.59 

12,130 

42.81 

57.19 

14,200 

14.70 

Vanderpool,  Ky.  . . 

4.00 

34.10 

54.60 

7.30 

12,770 

38.50 

61.50 

14.400 

14.91 

Muhlenberg  Co.,  Ky.  . 

4.33 

33.65 

55.50 

4.95 

1.57 

13,060 

38.86 

61.14 

14,400(?) 

14.91 

Scott  Co.,  Tenn.  . . 

1.26 

35.76 

53.14 

8.02 

1.80 

13,700 

34.17 

65.83 

15,100(?) 

15.63 

Jefferson  Co.,  Ala.  . . 

1.55 

34.44 

59.77 

2.62 

1.42 

13,770 

37.63 

62.37 

14,400(?) 

14.91 

Big  Muddy,  111. . . . 

7.50 

30.70 

53.80 

8.00 

12,420 

36.30 

63.70 

14,700 

15.22 

Mt.  Olive,  111 

11.00 

35.65 

37.10 

13.00 

10,490 

47.00 

53.00 

13,800 

14.29 

Streator,  111 

12.00 

33.30 

40.70 

14.00 

10,580 

45.00 

55.00 

14,300 

14.80 

Missouri 

Lignite  and  Lignitic  Coals. 

6.44 

37.57 

47.94 

8.05 

12,230 

43.94 

56.06 

14,300(?) 

14.80 

Iowa 

8.45 

37.09 

35.60 

18.86 

8,720 

51.03 

48.97 

12,000(?) 

12.42 

Wyoming 

8.19 

38.72 

41.83 

11.26 

10,390 

48.07 

51.93 

12,900(?) 

13.35 

Utah 

9.29 

41.97 

44.37 

3.20 

1.18 

11,030 

48.60 

51.40 

12,600(?) 

13.04 

Oregon  lignite  . . . 

15.25 

42.98 

33.32 

7.11 

1.66 

8,540 

54.95 

45.05 

11,000(7) 

11.39 

A British  thermal  unit  (B.  T.  U.)  is  the  quantity  of  heat  required  to  raise  the 
temperature  of  1 lb.  of  water  1°  F.  at  or  near  the  temperature  of  maximum 
density,  39.1°  F. 

A calorie  is  the  quantity  of  heat  required  to  raise  the  temperature  of 
1 kilogram  of  water  1°  C.  at  or  about  4°  C. 

A pound  calorie  is  the  quantity  of  heat  necessary  to  raise  the  temperature 
of  1 lb.  of  water  1°  C. 

1 French  calorie  = 3.968  British  thermal  units. 

1 B.  T.  U.  = .252  calorie. 

1 lb.  calorie  = f B.  T.  U.  = .4536  calorie. 

The  heating  value  of  any  coal  may  be  calculated  from  its  ultimate 
analysis,  with  a probable  error  not  exceeding  2^,  by  Dulong’s  formula: 

)• 

in  which  C.  //,  and  0 are,  respectively,  the  percentages  of  carbon,  hydrogen, 
and  oxygen. 


Heating  value  per  lb.  = 146  (7  -f  ( 


CLASSIFICATION  OF  COALS. 


169 


Heat  in  pound  calorie  = 8,080  C -f  34,462  yH  ~ 

or  = 8,080  C + 34,462  f ) + 2,250  S. 

Heat  in  B.  T.  U.  = 14,650  C — 62,100  (^H  - 

in  which  C,  0,  H,  and  S represent  the  weights  of  carbon,  oxygen,  hydro- 
gen, and  sulphur  in  1 lb.  of  the  substance. 


i)- 


Composition  of  Fuels. 


{Mechanical  Draft,  B.  F.  Sturtevant  Co.) 


Description. 

Carbon. 

Hydro- 

gen. 

Oxy- 

gen. 

Nitro- 

gen. 

Sul- 

phur. 

Ash: 

Anthracite. 

France  

90.9 

1.47 

1.53 

1.00 

.80 

4.3 

Wales 

91.7 

3.78 

1.30 

1.00 

.72 

1.5 

Rhode  Island  

85.0 

3.71 

2.39 

1.00 

.90 

7.0 

Pennsylvania 

78.6 

2.50 

1.70 

.80 

.40 

14.8 

Semibituminous. 

Maryland 

80.0 

5.00 

2.70 

1.10 

1.20 

8.3 

Wales 

88.3 

4.70 

.60 

1.40 

1.80 

3.2 

Bituminous. 

Pennsylvania 

75.5 

4.93 

12.35 

1.12 

1.10 

5.0 

Indiana 

69.7 

5.10 

19.17 

1.23 

1.30 

3.5 

Illinois  

61.4 

4.87 

35.42 

1.41 

1.20 

5.7 

Virginia 

57.0 

4.96 

26.44 

1.70 

1.50 

8.4 

Alabama  

53.2 

4.81 

32.37 

1.62 

1.30 

6.7 

Kentucky 

49.1 

4.95 

41.13 

1.70 

1.40 

7.2 

Cape  Breton 

67.2 

4.26 

20.16 

1.07 

1.21 

6.1 

Vancouver  Island 

66.9 

5.32 

8.76 

1.02 

2.20 

15.8 

Lancashire  gas  coal 

80.1 

5.50 

8.10 

2.10 

1.50 

2.7 

Boghead  cannel 

63.1 

8.90 

7.00 

.20 

1.00 

19.8 

Lignite. 

California  brown  

49.7 

3.78 

30.19 

1.00 

1.53  ' 

13.8 

Australian  brown 

73.2 

4.71 

12.35 

1.11 

.63 

8.0 

Petroleum. 

Pennsvlvania  (crude) 

84.9 

13.70 

1.40 

Caucasian  (light)  

86.3 

13.60 

.10 

Caucasian  (heavy)  

86.6 

12.30 

1.10 

Refuse 

87.1 

11.70 

1.20 

CLASSIFICATION,  COM  POSITION,  AN  D PROPERTI  ES  OF  COALS. 

Coals  may  be  broadly  divided  into  two  classes:  Anthracite,  or  hard,  coal; 
and  bituminous,  or  soft,  coal. 

Anthracite,  or  Hard,  Coal.— Specific  gravity,  1.30  to  1.70.  This  is  the  densest, 
hardest,  and  most  lustrous  of  all  varieties.  It  burns  with  little  fiame  and 
no  smoke,  but  gives  a great  heat.  Contains  very  little  volatile  combustible 
matter.  Color,  deep  black,  shining;  sometimes  iridescent.  Fracture, 
conchoidal. 

Semianthracite  coal  is  not  so  dense  nor  so  hard  as  the  true  anthracite. 
Its  percentage  of  volatile  combustible  matter  is  somewhat  greater,  and  it 
ignites  more  readily. 

Bituminous,  or  Soft,  Coal.— Specific  gravity,  1.25  to  1.40.  It  is  generally 
brittle;  has  a bright  pitchy  or  greasy  luster,  and  is  rather  fragile  as  compared 
with  anthracite.  It  burns  with  a yellow  smoky  fiame,  and  gives,  on  distil- 
lation, hydrocarbon  oils  or  tar. 

Under  the  term  “ bituminous  ” are  included  a number  of  varieties  of  coal 
that  differ  materially  under  the  action  of  heat,  giving  rise  to  the  general 
classification:  Coking  or  caking  coals,  and  free-burning  coals. 

Semibituminous  coal  has  the  same  general  characteristics  as  the  bituminous, 
although  it  is  usually  not  so  hard,  and  its  fracture  is  more  cuboidal.  The 


170 


FUELS. 


percentage  of  volatile  combustible  matter  is  less.  It  kindles  readily,  and 
burns  quickly  with  a steady  fire,  and  is  much  valued  as  a steam  coal. 

Coking  coals  are  those  that  become  pasty  or  semi  viscid  in  the  fire;  and, 
when  heated  in  a close  vessel,  become  partially  fused  and  agglomerate  into  a 
mass  of  coherent  coke.  This  property  of  coking  may,  however,  become 
greatly  impaired,  if,  indeed,  not  entirely  destroyed,  by  weathering. 

Free-burning  coals  have  the  same  general  characteristics  as  the  coking 
coals,  but  they  burn  freely  without  softening,  and  do  not  fuse  or  cake 
together  in  any  sensible  degree. 

Splint  coal  has  a dull  black  color,  and  is  much  harder  and  less  frangible 
than  the  coking  coal.  It  is  readily  fissile,  like  slate,  but  breaks  with 
difficulty  on  cross-fracture.  It  ignites  less  readily,  but  makes  a hot  fire, 
constituting  a good  house  coal. 

Weights  and  Measurements  of  Coal. 

* {Coze  Bros.  <&  Co.,  Chicago,  III.) 


Coal. 

Weight  per 
Cubic  Foot. 
Pounds. 

Cubic  Feet 
per  Ton, 
2,000  Lb. 

Coal. 

Weight  per 

Cubic  Foot. 

Pounds. 

Cubic  Feet 

per  Ton, 

2,000  Lb. 

Lehigh  lump 

55.26 

36.19 

Free-burning  egg... 

56.07 

35.67 

Lehigh  cupola 

55.52 

36.02 

Free-burning  stove 

56.33 

35.50 

Lehigh  broken 

56.85 

35.18 

Free-burning  nut  — 

56.88 

35.16 

Lehigh  egg 

57.74 

34.63 

Pittsburg  

46.48 

43.03 

Lehigh  stove 

58.15 

34.39 

Illinois  

47.22 

42.35 

Lehigh  nut 

58.26 

34.32 

Connellsville  coke 

26.30 

76.04 

Lehigh  pea 

53.18 

37.60 

Hocking 

49.30 

40.56 

Lehigh  buckwheat... 

54.04 

37.01 

Indiana  block 

43.85 

45.61 

Lehigh  dust  

57.25 

34.93 

Erie 

48.07 

41.61 

Ohio  cannel 

49.18 

40.66 

Cannel  coal  differs  from  the  ordinary  bituminous  coal  in  its  texture.  It  is 
compact,  with  little  or  no  luster  and  without  any  appearance  of  a banded 
structure.  It  breaks  with  a smooth  conchoidal  fracture,  kindles  readily,  and 
burns  with  a dense  smoky  fiame.  It  is  rich  in  volatile  matter,  and  makes  an 
excellent  gas  coal.  Color,  dull  black  and  grayish  black. 

Lignite,  or  brown  coal,  often  has  a lamellar  or  woody  structure;  is  some- 
times pitch  black,  but  more  often  rather  dull  and  brownish  black.  It  kindles 
readily  and  burns  rather  freely  with  a yellow  fiame  and  comparatively  little 
smoke,  but  it  gives  only  a moderate  heat.  It  is  generally  non-coking.  The 
percentage  of  moisture  present  is  invariably  high— from  10^  to  30^. 

The  subdivisions  given  above  are  entirely  arbitrary,  as  the  different 
varieties  of  coal  are  found  to  shade  insensibly  into  one  another.  The  follow- 
ing are  two  classifications  according  to  percentages  of  volatile  combustible 
matter: 

Classification  of  Coal  According  to  Volatile  Combustible. 


Coal. 

Per  Cent. 

Kent. 

Per  Cent. 

Anthracite 

2.5  to  6 

0to7 

Semianthracite 

7 to  10 

7.5  to  12 

Semibituminous  

12  to  20 

12.5  to  25 

Bituminous 

over  20 

25  to  50 

Lignite 

over  50 

The  Composition  of  Coals.— A proximate  analysis  determines  the  proportion 
of  those  products  of  a coal  having  the  most  important  bearing  on  its  uses. 
These  substances  as  usually  presented  are:  Moisture,  or  water,  volatile  com- 


PROPERTIES  OF  COALS. 


171 


bustible  matter,  fixed  carbon,  sulphur,  and  ash.  In  addition  to  these,  the 
following  physical  properties  are  generally  given:  Color  of  ash,  specific 
gravity,  and  strength  or  hardness.  The  determination  of  these  eight  factors 
gives  a fair  general  idea  of  the  adaptabilities  of  a coal. 

Moisture,  or  water,  in  coal,  has  no  fuel  value,  is  an  inert  constituent,  dug, 
handled,  and  hauled,  and  finally  expelled  at  a cost  of  fuel.  Each  per  cent, 
of  moisture  means  20  lb.  less  fuel  for  each  ton  of  coal. 

Volatile  combustible  matter  is  an  important  constituent  of  coal,  the  amount 
and  quality  deciding  whether  a coal  is  suitable  for  the  manufacture  of 
illuminating  gas.  The  coking  of  coal  also  is  largely  dependent  on  this 
constituent.  When  a large  percentage  of  volatile  combustible  matter  is 
present,  coals  ignite  easily  and  burn  with  a long  yellow  flame,  and,  in 
ordinary  combustion,  give  out  dense  smoke,  and  form  soot.  This  quality 
makes  a fuel  objectionable  for  railway  and  sometimes  for  naval  use. 

The  fixed  carbon  is  the  principal  combustible  constituent  in  coal,  and,  in 
bituminous  and  semibituminous  coals,  the  steaming  value  is  in  proportion  to 
the  percentage  of  fixed  carbon.  Though  the  fixed  carbon  of  a coal  evapo- 
rates much  less  water  than  an  equivalent  weight  of  the  volatile  combustible 
matter  when  properly  burnt,  in  practice,  so  much  of  the  latter  is  lost  through 
careless  firing,  or  improper  furnace  construction,  that  the  relative  steaming 
value  of  a coal  may  be  fairly  approximated  by  assuming  the  carbon  to  be 
the  only  useful  constituent. 

Sulphur  will  burn  and  develop  heat,  and  is  not  inert  like  moisture  and 
ash.  But  it  corrodes  grates  and  boilers;  in  the  blast  furnace  it  injures  iron, 
and  produces  a hot  short  pig,  and  is  objectionable  in  coal  for  forge  use.  In 
gas  making,  the  sulphur  must  be  removed.  It  usually  occurs  in  coal  in  the 
form  of  iron  pyrites,  which,  oxidizing,  causes  disintegration,  and  sometimes 
spontaneous  combustion.  It  is  then  an  element  of  danger  and  loss. 

Ash  is  an  inert  constituent,  which  means  20  lb.  of  weight  to  be  handled 
and  20  lb.  loss  per  ton  of  coal  for  each  per  cent,  present.  Water  in  coal  is 
removed  at  the  cost  of  fuel,  while  ashes  are  removed  at  extra  cost  of  labor. 
It  is  estimated  that  if  the  cost  of  stoking  coal  is  6f^  of  the  cost  of  coal  (coal 
at  ^3.00  per  ton,  and  labor  at  SI. 00  per  day),  and  with  cost  of  handling  ashes 
double  that  of  stoking  coal,  5^  of  ash  will  lessen  the  fuel  value  of  coal  over 
6^;  10^  ash,  over  12^;  and  so  on. 

The  color  of  the  ash  furnishes  a rough  estimate  of  the  amount  of  iron  con- 
tained in  a fuel.  Iron  in  an  ash  makes  it  more  fusible,  and  increases  its 
tendency  to  clinker.  In  domestic  consumption,  where  the  temperature  is 
low,  the  quantity  of  ash  is  of  more  importance  than  its  fusibility,  but  for 
steam  purposes,  where  an  excessive  heat  is  required,  ashes  of  a clinkering 
coal  will  fuse  into  a vitreous  mass  and  accumulate  upon  the  grate  bars  and 
exclude  the  passage  of  necessary  air.  The  practicability  of  employing  a coal 
will  often  be  determined  by  the  quality  of  the  clinkering  of  the  ashes. 
Under  such  conditions,  such  coals  are  best  whose  ashes  are  nearly  pure 
white  and  which  contain  little  or  no  alkali  nor  any  lime,  and  do  not  contain 
silica  and  alumina. 

The  specific  gravity  is  an  important  factor  when  there  is  restriction  of 
space,  as  on  railway  cars  and  in  ship  bunkers.  A given  bulk  of  anthracite 
coal  will  weigh  from  10^  to  15^  more  than  the  same  bulk  of  bituminous  coal, 
so  that  from  10^  to  15^  more  pounds  of  fuel  can  be  carried  in  the  same  place. 
The  average  specific  gravity  of  anthracite  coal  is  1.5,  and  a cubic  yard  weighs 
about  2,531  lb. 

The  average  specific  gravity  of  American  bituminous  coals,  and  of  grades 
intermediate  between  them  and  anthracite,  is  about  1.325,  and  1 cu.  yd. 
weighs  about  2,236  lb. 

Strength  or  hardness  is  valuable  in  preventing  waste.  In  soft  coal,  much  is 
ground  to  dust  in  mining  and  at  the  tipple.  In  railway  transportation,  soft 
coal  is  crushed,  which  further  increases  the  loss,  and  the  coal  reaches  market 
in  bad  condition.  A very  soft  coal  is  shipped  in  lump,  and  is  not  in  so  wide 
demand.  For  marine  use,  a soft  coal  is  objectionable,  because  of  disintegra- 
tion by  the  motion  of  the  ship.  Strength  is  a requisite  for  the  use  of  raw 
coal  in  the  blast  furnace,  and  also  to  prevent  excessive  loss  of  coal  through 
the  grates  in  ordinary  furnaces. 

Steaming  Coals.— For  steam  making,  the  superiority  of  coals  high  in  com- 
bustible constituents  is  admitted,  and  those  with  the  higher  percentage  of 
fixed  carbon  are  the  most  desirable.  But  the  consideration  of  the  steaming 
qualities  of  a coal  involves,  also,  a consideration  of  the  form  of  furnace  and 
of  all  the  conditions  of  combustion.  The  evaporative  power  of  a coal  in 


172 


FUELS. 


practice  cannot  be  stated  without  reference  to  the  eonditions  of  combustion, 
and  every  practical  test  of  a coal,  to  be  thorough,  should  lead  to  a determi- 
nation of  the  best  form  of  furnace  for  that  coal,  and  should  furnish  knowl- 
edge as  to  what  class  of  furnaces  in  actual  use  such  coal  is  specially  adapted. 
It  IS  not  sufficient  that  in  comparative  tests  of  coals  the  same  conditions 
should  exist  with  each,  but  there  should  also  be  determined  the  best 
conditions  for  each  coal. 

Of  coals  high  in  fixed  carbon,  the  semianthracites  and  the  semibitumi- 
nous  rank  as  high  as  the  anthracites  in  meeting  the  various  requirements  of 
a quick  and  efficient  steaming  coal. 

For  railway  use,  these  coals  have  been  found  to  excel  anthracites  in 
evaporating  power.  The  comparative  absence,  in  semibituminous  coals,  of 
smoke,  which  means  loss  of  combustible  matter  as  well  as  discomfort  to  the 
traveler,  is  sufficient  to  suggest  the  superiority  of  these  coals  over  bituminous 
coals  for  such  use.  In  fact,  the  high  rate  of  combustion  and  the  strong  draft 
necessary  in  locomotives  is  particularly  unfavorable  to  the  economic  com- 
bustion of  bituminous  coal.  Such  semibituminous  coals  are  also  specially 
well  suited  for  small  tubular  boilers,  firebox  steam  boilers,  or  other  forms 
with  small  unlined  combustion  chambers,  in  which  the  gases  from  bitumi- 
nous coals  become  cooled,  are  not  burnt,  and  deposit  soot  in  the  tubes. 

Steaming  coal  should  kindle  readily  and  burn  quickly  but  steadily,  and 
should  contain  only  enough  volatile  matter  to  insure  rapid  combustion.  It 
should  be  low  in  ash  and  sulphur,  should  not  clinker,  and  when  it  is  to  be 
transported  should  not  easily  crumble  and  break. 

Coals  for  Iron  Making.— For  the  manufacture  of  iron  and  for  metallurgical 
purposes,  coal  is  chiefly  used  after  being  converted  into  coke,  though  it  is 
also  used  to  a limited  extent  in  the  raw  state.  Coal  directly  used  must  be 
strong  and  not  swell  nor  disintegrate  so  as  to  choke  the  furnace.  It  should 
be  capable  of  producing  a high  heat  and  should  not  contain  a large  amount 
of  sulphur  or  phosphorus. 

Coke.— Coke  is  the  fixed  carbon  of  a coal,  a fused  and  porous  product  pro- 
duced by  the  distillation  of  the  gaseous  constituent.  For  metallurgical  use, 
it  should  be  firm,  tough,  and  bright,  with  a sonorous  ring,  and  should 
contain  not  over  K of  sulphur.  For  blast-furnace  use,  a dense  coke  is 
objectionable,  and  the  best  is  the  one  with  the  largest  cell  structure  and  the 
hardest  cell  wall.  A high  percentage  of  volatile  hydrocarbon  is,  as  a rule, 
necessary  for  a good  coking  coal. 

The  fusibility  of  the  carbon,  the  amount  of  disposable  hydrogen,  the 
tenacity  with  which  the  gaseous  constituents  are  held,  all  affect  the  results* 
in  coking.  Further,  coal  that  is  mined  near  the  outcrop,  and  has  been  sub- 
jected to  the  influence  of  the  weather,  loses  its  capacity  for  coking.  The 
process  of  manufacture  should,  however,  be  adapted  to  the  character  of  the 
coal,  as  it  has  an  important,  though  secondary,  influence  on  the  physical 
character,  uniformity  of  quality,  and  dryness  of  a coke.  • Coals  of  inferior 
grade  are  made  to  produce  good  coke  by  using  coke  ovens  in  which  the  heat 
of  the  gases  is  applied  externally  to  the  coke  chamber,  but  the  coal  is 
generally  first  carefully  crushed  and  washed.  Further,  the  depth  of  the 
charge  and  length  of  heating  have  an  important  bearing. 

As  at  present  understood,  and  in  the  present  mode  of  manufacture,  the 
essential  qualities  of  a good  coking  coal  are:  that  it  shall  contain  not  less  than 
20fc  nor  more  than  30/c  of  volatile  hydrocarbons,  and- not  too  much  ash;  that 
on  being  heated  it  must  pass  through  a thoroughly  fused  or  pasty  condition; 
and  that  when  in  this  condition,  it  must  part  with  its  volatile  matter  in  such 
a manner  as  to  form  innumerable  small  pores. 

If  a coal  contains  less  than  20fc  of  volatile  matter,  it  will  not  fuse  properly, 
while  if  it  has  more  than  30^  the  porous  structure  will  be  unduly  developed 
at  the  expense  of  the  strength  of  the  pore  walls;  on  the  other  hand,  many 
coals  lying  between  these  limits  will  not  fuse  at  all,  and  therefore  do  not 
coke,  while  others  fuse  properly  but  give  off  their  gas  so  as  to  form  large 
and  thin-walled  pores. 

Ordinary  analyses  do  not  indicate  whether  or  not  a coal  is  a good  coking 
coal,  and  they  indicate  simply  by  giving  the  amount  of  carbon,  ash,  and 
sulphur,  what  will  be  the  probable  purity  of  the  coke  formed.  The  coal  of 
the  Pittsburg  bed  in  the  Connellsville  basin  of  Pennsylvania  is  considered 
by  many  as  the  standard  coking  coal,  but  coals  whose  analysis  differ  very 
materially  from  that  of  Connellsville  undoubtedly  give  most  excellent  cokes, 
which  are  equal  to  or  very  nearly  equal  to,  that  from  Connellsville,  as,  for 
instance,  the  Pocahontas  coke,  Virginia. 


ANALYSIS  OF  COAL. 


173 


Domestic  Coals. — In  domestic  use,  coal  is  burned  in  open  grates,  in  closed 
stoves  with  ordinary  fire  bowls  and  flat  grates,  or  with  basket  grates  in  small 
furnaces  for  hot-air  heating,  and  in  cooking  stoves.  In  all  these,  the  coal 
that  sustains  a mild,  steady  combustion,  and  remains  ignited  at  a low  tem- 
perature with  a comparatively  feeble  draft,  is  the  best.  A coal  burning  with 
a smoky  flame  is  objectionable  as  producing  much  soot  and  dirt,  especially 
for  open  grates  or  cooking  purposes.  For  self-feeding  stoves,  or  for  base 
burners,  a dry  non-coking  coal  is  necessary.  A very  free  and  fiercely  burn- 
ing coal  is  not  desirable,  particularly  in  stoves,  as  the  temperature  cannot  be 
easily  regulated.  A sulphurous  coal  is  also  bad,  as  it  produces  stifling  gases 
with  a defective  draft,  and  corrodes  the  grates  and  fire  bowls.  The  difficulty 
from  clinkering  is  not  so  great  in  domestic  uses,  as  the  temperature  is  not 
generally  high  enough  to  fuse  the  ash.  A stony,  hard  ash  that  will  not  pass 
between  the  grate  bars  is  bad,  and  light  pulverulent  ash  is  best. 

Gas  Coals. — Mr.  H.  C.  Adams,  of  The  American  Gas  Light  Association, 
says:  “ The  essentials  of  a good  gas  coal  are  a low  percentage  of  ash,  say  5^, 
and  of  sulphur,  say  i of  a generous  share,  say  37^c  to  40^  of  volatile  matter, 
charged  with  rich  illuminating  hydrocarbons.  And  it  should  yield,  under 
present  retort  practice,  85  candle-feet  to  the  pound  carbonized.  It  should  be 
sufficiently  dense  to  bear  transportation  well,  so  that,  when  carried  long 
distances,  it  may  not  arrive  at  its  destination  largely  reduced  to  slack  or  fine 
coal  of  the  consistency  of  sand.  And  it  should  possess  coking  qualities  that 
will  bring  from  the  retorts,  after  carbonization,  about  60^  of  clean,  strong, 
bright  coke.” 

Blacksmith  Coals. — A good  coal  for  blacksmith  purposes  should  have  a 
high  heating  power,  should  contain  a very  small  amount  of  sulphur,  if 
any,  should  coke  sufficiently  to  form  an  arch  on  the  forge,  and  should 
also  be  low  in  ash. 

From  the  above,  it  is  readily  seen  that  the  analysis  of  a coal  does  not 
necessarily  determine  its  value  or  the  uses  to  which  it  can  be  put.  How- 
ever, by  examining  the  analyses  given  in  the  table  on  page  168,  certain 
standards  may  be  adopted  as  showing  in  a general  way  about  what  the 
analysis  of  coal  should  be  for  certain  purposes.  For  steam  purposes,  the 
semibituminous  coals  have  established  reputations.  For  gas  coals,  that 
from  Youghiogheny,  Pa.,  is  well  known.  For  blacksmiths.  Broad  Top  and 
Tioga  County,  Pennsylvania,  coals  are  standards;  while  for  coking,  Connells- 
ville  is  recognized  as  a standard. 

The  sizes  of  anthracite  coal  vary.  The  sizes  of  screen  mesh  and  bar  open- 
ings used  for  separating,  range  as  follows: 

Lump,  over  bars  placed  7 to  9 in.  apart. 

Steamboat,  over  bars  placed  3i  to  5 in.  apart  and  through  bars  7 in.  apart. 

Grate,  over  in.  and  through  4i  in.  square  mesh. 

Egg,  over  2 in.  and  through  2^  in.  square  mesh. 

Stove,  over  If  in.  and  through  2 in.  square  mesh. 

Chestnut,  over  f in.  and  through  If  in.  square  mesh. 

Pea,  over  fin.  and  through  f in.  square  mesh. 

Buckwheat,  over  f in.  and  through  f in.  square  mesh. 

No.  2 Buckwheat,  or  Bird’s-eye,  over  f in.  and  through  in.  square  mesh. 

The  sizes  of  bituminous  coal  are  Lump,  Nut,  and  Slack. 

All  coal  that  passes  over  bars  If  in.  apart  is  called  Lump. 

All  coal  that  passes  through  bars  If  in.  apart  and  over  bars  f in.  apart  is 
called  Nut 

All  coal  that  passes  through  bars  f in.  apart  is  called  Slack. 


ANALYSIS  OF  COAL. 

The  following  is  the  outline  of  the  method  recommended  for  the 
analysis  of  coal  by  a committee  of  the  American  Chemical  Society,  Messrs. 
W.  F.  Hillebrand,  C.  B.  Dudley,  and  W.  A.  Noyes: 

Sampling. — At  least  5 lb.  of  coal  should  be  taken  for  the  original  sample, 
with  care  to  secure  pieces  that  represent  the  average.  These  should  be 
broken  up  and  quartered  down  to  obtain  the  smaller  sample,  which  is  to 
be  reduced  to  a fine  powder  for  analysis.  The  quartering  and  grinding 
should  be  carried  out  as  rapidly  as  possible,  and  immediately  after  the 
original  sample  is  taken,  to  prevent  gain  or  loss  of  moisture.  The  pow- 
dered coal  should  be  kept  in  a tightly  stoppered  tube,  or  bottle,  until 
analyzed.  Unless  the  coal  contains  less  than  2^  of  moisture,  the  shipment 
of  large  samples  in  wooden  boxes  should  be  avoided. 


174 


FUELS. 


In  boiler  tests,  shovelfuls  of  coal  should  be  taken  at  regular  intervals  and 
put  in  a tight  covered  barrel,  or  some  air-tight  covered  receptacle,  and  the 
latter  should  be  placed  where  it  is  protected  from  the  heat  of  the  furnace. 

In  sampling  from  a mine,  the  map  of  the  mine  should  be  carefully 
examined  and  points  for  sampling  located  in  such  a manner  as  to  fairly 
represent  the  body  of  the  coal.  These  points  should  be  placed  close  to  the 
working  face.  Before  sampling,  make  a fresh  cut  of  the  face  from  top  to 
bottom  to  a depth  that  will  insure  the  absence  of  possible  changes  or  of 
sulphur  and  smoke  from  the  blasting  powders.  Clean  the  floor  and  spread 
a piece  of  canvas  to  catch  the  cuttings.  Then,  with  a chisel,  make  a cutting 
from  floor  to  roof,  say  3 in.  wide  and  about  1 in.  deep.  Do  not  chisel  out 
the  shale  or  other  impurities  that  it  is  the  practice  at  that  mine  to  reject. 
Measure  the  length  of  the  cutting  made,  but  do  not  include  the  impurities 
in  this  measurement.  With  a piece  of  flat  iron  and  a hammer,  break  all 
pieces  to  quarter-inch  cubes  or  less,  without  removing  from  the  cloth. 
Quarter  down  and  transfer  to  a sealed  bottle  or  jar.  For  the  “ run-of-mine  ” 
sample,  samples  taken  at  several  points  in  this  manner  should  be  mixed 
and  quartered  down.  If  the  vein  varies  in  thickness  at  different  points,  the 
samples  taken  at  each  point  should  correspond  in  amount  to  the  thickness 
of  the  vein.  For  instance,  a small  measure  may  be  filled  as  many  times 
with  the  coal  of  the  sample  as  the  vein  is  feet  in  thickness.  Should  there 
appear  differences  in  the  nature  of  the  coal,  it  will  be  more  satisfactory  to 
take,  in  addition  to  the  general  sample,  samples  of  such  portions  of  the 
vein  as  may  display  these  differences. 

Moisture.— Dry  1 g.  of  the  coal  in  an  open  porcelain  or  platinum  crucible 
at  104°  to  107°  C.  for  1 hour,  best  in  a double-walled  bath  containing  pure 
toluene.  Cool  in  a desiccator  and  weigh  covered. 

Volatile  Combustible  Matter. — Place  1 g.  of  fresh,  undried  coal  in  a platinum 
crucible,  weighing  20  to  30  g.,  and  having  a tightly  fitting  cover.  Heat  over 
the  full  flame  of  a Bunsen  burner  for  7 minutes.  The  crucible  should  be 
supported  on  a platinum  triangle  with  the  bottom  6 to  8 cm.  above  the  top 
of  the  burner.  The  flame  used  should  be  fully  20  cm.  high  when  burning 
free,  and  the  determination  made  in  a place  free  from  drafts.  The  upper 
surface  of  the  cover  should  burn  clear,  but  the  under  surface  should 
remain  covered  with  carbon.  To  find  “volatile  combustible  matter,” 
subtract  the  percentage  of  moisture  from  the  loss  found  here. 

Ash.— Burn  the  portion  of  coal  used  for  the  determination  of  moisture  at 
first  over  a very  low  flame,  with  the  crucible  open  and  inclined,  until  free 
from  carbon.  If  properly  treated,  this  sample  can  be  burned  much  more 
quickly  than  the  dense  carbon  left  from  the  determination  of  volatile 
matter. 

Fixed  Carbon. — This  is  found  by  subtracting  the  percentage  of  ash  from 
the  percentage  of  coke. 

Sulphur  (Eschka’s  Method).— Mix  thoroughly  1 g.  of  the  finely  powdered 
coal  with  1 g.  of  magnesium  oxide  and  i g.  of  dry  sodium  carbonate,  in  a thin 
75  to  100  c.  c.  platinum  dish  or  crucible.  The  magnesium  oxide  should  be 
light  and  porous,  not  a compact,  heavy  variety.  The  dish  is  heated  on  a 
triangle  over  an  alcohol  lamp,  held  in  the  hand  at  first.  Gas  must  not  be 
used,  because  of  the  sulphur  it  contains.  The  mixture  is  frequently  stirred 
with  a platinum  wire  and  the  heat  raised  very  slowly,  especially  with  soft 
coals.  The  flame  is  kept  in  motion  and  barely  touching  the  dish,  at  first, 
until  strong  glowing  has  ceased,  and  is  then  increased  gradually  until,  in 
15  minutes,  the  bottom  of  the  dish  is  at  a low  red  heat.  When  the  carbon 
is  burned,  transfer  the  mass  to  a beaker  and  rinse  the  dish,  using  about 
50  c.  c.  of  water.  Add  15  c.  c.  of  saturated  bromine  water  and  boil  for 
5 minutes.  Allow  to  settle,  decant  through  a filter,  boil  a second  and  third 
time  with  30  c.  c.  of  water,  and  wash  until  the  filtrate  gives  only  a slight 
opalescence  with  silver  nitrate  and  nitric  acid.  The  volume  of  the  filtrate 
should  be  about  200  c.  c.  Add  li  c.  c.  of  concentrated  hydrochloric  acid, 
or  a corresponding  amount  of  dilute  acid  (8  c.  c.  of  an  acid  of  8^).  Boil 
until  the  bromine  is  expelled,  and  add  to  the  hot  solution,  drop  by  drop, 
especially  at  first,  and  with  constant  stirring,  10  c.  c.  of  a 10^6  solution  of 
barium  chloride.  Digest  on  the  water  bath,  or  over  a low  flame,  with 
occasional  stirring  until  the  precipitate  settles  clear  quickly.  Filter  and 
wash,  using  either  a Gooch  crucible  or  a paper  filter.  The  latter  may  be 
ignited  moist  in  a platinum  crucible,  using  a low  flame  until  the  carbon 
is  burned. 

In  the  case  of  coals  containing  much  pyrites  or  calcium  sulphate,  the 


STEAM. 


175 


residue  of  magnesium  oxide  should  be  dissolved  in  hydrochloric  acid  and 
the  solution  tested  for  sulphuric  acid. 

When  the  sulphur  in  the  coal  is  in  the  form  of  pyrites,  that  compound  is 
converted  almost  entirely  into  ferric  oxide  in  the  determination  of  ash,  and, 
since  3 atoms  of  oxygen  replace  4 atoms  of  sulphur,  the  weight  of  the  ash 
is  less  than  the  weight  of  the  mineral  matter  in  the  coal  by  i the  weight  of 
the  sulphur.  While  the  error  from  this  source  is  sometimes  considerable, 
a correction  for  “proximate”  analyses  is  not  recommended.  When 
analyses  are  to  be  used  as  a basis  for  calculating  the  heating  effect  of  the 
coal,  a correction  should  be  made. 

The  analysis  of  a coal  may  be  reported  in  three  different  forms,  as  per- 
centages of  the  moist  coal,  of  the  dry  coal,  or  of  the  combustible.  Thus, 
suppose  1 g.  of  coal  is  analyzed,  and  the  first  heating  shows  a loss  of 
weight  of  .1  g,,  the  second  of  .3  g.,  the  third  .5  g.,  the  remainder,  or  ash, 
weighing  .1  g.,  the  complete  report  would  be  as  follows: 


Per  Cent. 

of  the 
Moist  Coal. 

Per  Cent. 

of  the 

Dry  Coal. 

Per  Cent, 
of  the 

Combustible. 

Moisture 

10 

Volatile  matter 

30 

33.33 

37.50 

Fixed  carbon 

50 

55.56 

62.50 

Ash  

10 

11.11 

Total  

100 

100.00 

100.00 

STEAM. 


A calculation  of  the  power  that  coal  possesses,  compared  with  the  useful 
work  which  steam  engines  exert,  shows  that  probably  in  the  very  best 
engines  not  one-tenth  of  the  power  is  converted  into  useful  work,  and  in 
some  very  bad  engines,  probably  not  one  one-hundredth.  There  are  many 
causes  for  this;  some  we  can  never  remedy,  because  to  do  so  it  would  be 
necessary  to  exhaust  the  steam  at  a lower  temperature  than  is  practical. 
There  are  other  causes  that  can  and  ought  to  be  removed.  We  want  good 
engines,  good  boilers,  high-pressure  steam,  expansive  working,  and  con- 
densing appliances. 

High-Pressure  Steam. — Why  should  we  use  high-pressure  steam?  There 
are  several  good  reasons.  Whatever  pressure  we  have  available  at  the 
steam  boiler,  a certain  amount  is  absorbed  in  overcoming  the  resistances  of 
the  engine  and  without  doing  any  useful  work.  Suppose  our  available 
steam  pressure  is  20  lb.,  and  10  lb.  are  so  absorbed;  that  leaves  us  only 
one-half;  but,  if  we  have  100  lb.  available,  it  would  leave  us  nine-tenths. 
High-pressure  steam  means  fewer  boilers  and  smaller  engines,  with  founda- 
tions and  houses  of  less  dimensions.  Then,  again,  the  amount  of  work  that 
it  is  possible  to  get  out  of  a given  quantity  of  steam  depends  on  the  differ- 
ence between  the  temperature  at  the  commencement  of  the  stroke  and  the 
temperature  at  the  end  of  the  stroke. 

Now,  there  is  a limit  as  to  how  low  the  temperature  can  be  at  the  end, 
and  as  we  raise  the  commencing  temperature,  we  enlarge  the  available 
difference.  We  may  put  the  advantages  of  high-pressure  steam  in  this  way. 
By  taking  a fixed  temperature  in  the  condenser  of,  say,  100°  F.,  and  initial 
temperatures  when  the  steam  enters  the  cylinder,  of  varying  amounts,  the 
theoretic  efficiency  of  that  steam  can  be  determined.  Commencing  with 
atmospheric  pressure,  we  have  an  efficiency  of  16.6^. 


Lb.  Per  Cent. 

10  20.0 

20  22.1 

30  23.7 

40  25.0 

50  26.1 

60  2’;.0 

80  28.6 


Lb.  Per  Cent. 

100 29.8 

125 31.1 

150 32.2 

200 33.9 

250 35.3 

300 36.5 


170 


BOILERS, 


We  can  only  get  in  practice  with  steam  a certain  proportion  of  the 
theoretic  power,  and  that  proportion  varies  with  the  pressure  of  the  steam. 

In  early  days  we  used  steam  at  atmospheric  pressure,  the  efficiency 
being  16.^;  afterwards,  we  had,  in  compound  engines  of  two  cylinders, 
steam  of  60  lb.,  the  efficiency  being  27^.  Now  we  have  triple-expansion 
engines,  using  steam  at  150  lb.,  the  efficiency  being  2,2.2‘fo.  It  will  be 
observed  that,  although  the  efficiency  increases  as  the  steam  pressure 
increases,  the  amount  of  that  increase  is  a diminishing  quantity,  and  it 
becomes  so  small  at  and  beyond  150  lb.  pressure  that  probably  any  gain  in 
efficiency  is  not  a satisfactory  set-off  to  the  additional  expense  of  strength- 
ening the  parts  of  the  engine.  But  then,  how  very  few  of  our  engines  work 
nearly  so  high  as  150  lb.  pressure. 

The  advantages  of  high-pressure  steam  are  not  yet  sufficiently  appreciated. 
It  is  not  merely  the  difference  between  60  lb.  and  120  lb.  Suppose  we  use 
steam  at  60  lb.;  probably  we  shall  get  50  lb.  at  engine,  and  resistances  of 
engine  will  absorb  10  lb.,  leaving  40  lb.  Now,  suppose  we  use  120  lb.,  we  can 
get  at  engine  110  lb.,  and  if  resistances  of  engine  absorb  10  lb.,  we  shall  have 
100  lb.  as  against  40  lb. 

Expansion  of  Steam.— By  “ expansion  of  steam  ” we  mean  that  at  a certain 
point  of  the  stroke  we  shut  off  steam  supply  from  the  boiler  to  the  cylinder, 
and  the  steam  already  within  the  cylinder  performs  the  remainder  of  the 
stroke  unaided.  Now,  suppose  we  do  not  expand  at  all.  Suppose  we  allow 
free  admission  of  steam  into  the  cylinder  all  through  the  stroke;  we  shall 
have  at  the  end  of  the  stroke  pressure  exactly  similar  to  the  pressure  with 
which  we  commenced.  Now,  we  cannot  work  a seam  of  coal  and  still  have 
the  coal  left;  we  cannot  get  work  out  of  steam  and  still  have  the  work  left 
in  it,  and  so,  if  our  steam  pressure  is  the  same  at  the  end  of  the  stroke  as  at 
the  beginning,  we  simply  discharge  twice  in  each  revolution  a whole 
cylinder  full  of  steam  that  has  done  no  work  at  all,  and  waste  it  just  the 
same  as  if  we  had  discharged  it  from  the  boiler  without  passing  through  the 
engine  at  all.  But  some  one  will  say,  work  has  been  done  upon  the  engine 
while  that  steam  was  in  the  cylinder.  True— and  the  explanation  is,  that 
while  the  steam  is  performing  work  its  heat  and  pressure  must  diminish, 
and  so  long  as  the  communication  with  the  boiler  is  open,  fresh  heat  comes 
from  the  boiler  into  the  cylinder  to  take  its  place,  and  at  the  end  of  the 
stroke  we  have  expended  heat  represented  by  the  capacity  of  two  cylinders, 
and  have  performed  work  as  represented  by  the  capacity  of  one  cylinder. 
Now,  suppose  we  close  the  communication,  and  beyond  a certain  point  of 
the  stroke  allow  no  more  steam  to  enter,  we  get  an  amount  of  work  from 
the  steam  already  in  the  cylinder,  represented  by  the  diminishing  pressure 
of  the  steam  by  expansion. 

Condensers.— The  effective  power  of  an  engine  does  not  depend  on,  and 
is  not  measured  by,  the  pressure  pushing  the  piston.  There  is  always  what 
is  termed  a hack  pressure  holding  the  piston  back,  and  the  real  effective 
pressure  is  evidently  the  difference  between  the  two.  Suppose  we  have  a 
locomotive  engine,  or  a winding  engine,  throwing  exhaust  into  the  open 
air.  The  back  pressure  cannot  be  less  than  the  pressure  of  the  open  air, 
and,  indeed,  to  overcome  it,  it  must  be  something  more.  But  if  we  can 
discharge  our  exhaust  into  some  vessel  from  which  atmospheric  pressure 
and  all  other  pressure  has  been  removed,  we  know  that  atmospheric  pres- 
sure amounts  to  about  15  lb.,  and  the  removal  of  that  from  the  front  of  the 
piston  is  as  good  as  adding  15  lb.  behind. 


BOILERS. 

The  steam  boiler  that  will  be  the  most  suitable  for  a certain  mine  will 
depend  on  the  nature  of  the  feedwater,  the  cost  of  fuel,  and  the  amount  of 
steam  required.  When  the  acid  water  from  the  mine  is  used  for  feedwater, 
and  fuel  is  cheap,  the  type  of  boiler  generally  used  is  either  the  plain 
cylinjirical  or  flue  boiler,  because  it  is  simple  in  construction  and  can 
therefore  be  easily  cleaned  and  cheaply  replaced  when  eaten  by  the  mine 
water.  The  tubular  or  locomotive  type  is  used  where  good  water  can  be 
obtained,  except  in  the  best  equipped  plants,  where  the  water-tube  boiler  is 
used.  Feedwater  taken  from  the  mine,  or  containing  acid,  should  be 
neutralized  by  lime  or  soda  before  being  used.  In  case  it  contains  minerals 
in  solution,  a feedwater  separator  should  be  employed  to  precipitate  the 
mineral  substance  before  the  water  is  allowed  to  enter  the  boiler. 


HORSEPOWER  OF  BOILERS. 


177 


We  always  calculate  the  strength  of  a boiler  in  the  direction  of  its 
diameter,  because,  theoretically,  a boiler  is  twice  as  strong  in  the  direction 
of  length  as  direction  of  diameter.  Many  causes  may  bring  about  boiler 
explosions.  First,  bad  materials;  second,  bad  workmanship;  third,  bad 
water,  which  eats  away  the  plates  by  internal  corrosion;  fourth,  water  lying 
upon  plates,  bringing  about  external  corrosion;  fifth,  overpressure;  sixth, 
safety  valves  sticking;  seventh,  water  getting  too  low;  eighth,  excessive 
firing';  ninth,  hot  gases  acting  on  plates  above  water  level;  tenth,  choking  of 
feedpipes;  eleventh,  insufficient  provision  for  expansiod  and  contraction; 
twelfth,  insufficient  steam  room  and  too  sudden  a withdrawal  of  a large 
quantity  of  steam;  thirteenth,  getting  up  steam,  or  knocking  off  a boiler 
too  suddenly;  fourteenth,  allowing  wet  ashes  to  lie  in  contact  with  plates. 
The  probable  causes  suggest  their  several  remedies. 

Wherever  possible,  and  except  under  certain  circumstances,  steam 
engines  should  not  be  placed  in  the  mine,  and  certainly  steam  boilers 
should  be  in  all  cases  placed  upon  the  surface.  Steam  injures  the  ventila- 
tion, increasing  the  temperature  where  already  too  high,  doing  injury  and 
causing  inconvenience  by  condensation,  and  many  fires  in  mines  have  been 
caused  by  underground  boilers. 

The  Lancashire  Boiler.— The  colliery  boiler  that  finds  much  favor  in  Eng- 
land is  that  class  of  Lancashire  boiler  which  is  28  or  30  ft.  long  and  7 or  8 ft. 
in  diameter,  and  has  two  large  flues  running  through.  There  is  no  doubt 
that  the  marine  type  will  generate  more  steam  with  a given  amount  of 
coal,  and,  consequently,  is  gaining  ground,  and  will  gain  ground  where 
coal  is  dear.  But  the  Lancashire  boiler  is  a good  steam  generator,  and  will 
not  only  work  longer  without  repairs,  but  is  less  troublesome  and  expensive 
to  repair.  The  favorite  construction  some  few  years  ago  was  wrought  iron 
with  double-riveted  horizontal  joints  and  Galloway  tubes  (Galloway 
tubes  are  simply  taper  tubes  running  across  the  flues  in  the  boiler),  and 
expansion  weldless  hoops  strengthening  the  flues  and  allowing  for  expan- 
sion and  contraction.  The  dimensions  were  7 ft.  diameter,  and  from 
28  to  30  ft.  long,  with  internal  flues  each  2 ft.  9 in.  diameter,  the  circular 
plates  being  about  i in.  and  the  end  plates  about  | in.  The  safe  working 
pressure  was  about  60  lb.  per  sq.  in.  Now  the  conditions  are  somewhat 
altered.  Steel  has  taken  the  place  of  iron,  giving  increased  strength,  and 
allowing  increased  diameter  and  increased  pressure.  Ring  plates  have  also 
abolished  a great  source  of  weakness  in  a boiler,  namely,  horizontally 
riveted  joints.  A good  Lancashire  boiler  now  will  measure  8 ft.  in 
diameter  and  30  ft.  long,  with  ring  plates  f in.  thick,  end  plates  probably 
f in.,  and  will  work  very  well  at  120  lb.  pressure  per  sq.  in. 

Horsepower  of  Boilers. — The  horsepower  of  a boiler  is  a measure  of  its 
capacity  for  generating  steam.  Boilermakers  usually  rate  the  horsepower 
of  their  boilers  as  a certain  fraction  of  the  heating  surface;  but  this  is  a 
very  indefinite  method,  for  with  the  same  heating  surface,  different  boilers 
of  the  same  type  may,  under  different  circumstances,  generate  different 
quantities  of  steam. 

In  order  to  have  an  accurate  standard  of  boiler  power,  the  American 
Society  of  Mechanical  Engineers  has  adopted  as  a standard  horsepower 
an  evaporation  of  30  lb.  of  water  per  hour  from,  a feedwater  temperature  of  100°  F. 
into  steam  at  70  lb.  gauge  pressure,  which  is  considered  equivalent  to 
34.5  units  of  evaporation;  that  is,  to  34.5  lb.  of  water  evaporated  from  a 
feedwater  temperature  of  212°  F.  into  steam  at  the  same  temperature. 

Example.— A boiler  evaporates  per  hour  1,980  lb.  of  water  from  a feed 
temperature  of  100°  into  steam  at  70  lb.  gauge  pressure.  What  is  the 
horsepower  of  the  boiler? 

Since,  under  the  given  conditions,  an  evaporation  of  30  lb.  is  equivalent 
to  1 horsepower,  the  number  of  horsepower  is  1,980  -h  30  = 66. 

In  the  various  types  of  boilers  there  is  a nearly  constant  ratio  between 
the  water-heating  surface  and  the  horsepower,  and  also  between  the  heating 
surface  and  the  grate  area.  These  ratios  are  given  in  the  table  on  page  178. 

If  the  heating  surface  of  a boiler  is  known,  the  horsepower  can  be  found 
roughly;  thus,  if  a return-tubular  boiler  has  a heating  surface  of  900  sq.  ft., 
its  horsepower  lies  between  = 50  H.  P.  and  = 64.3  H.  P.,  say  about 
57  H.  P. 

The  heating  surface  of  a boiler  is  the  portion  of  the  surface  exposed  to  the 
action  of  flames  and  hot  gases.  This  includes,  in  the  case  of  the  multi- 
tubular boiler,  the  portions  of  the  shell  below  the  line  of  brickwork,  the 
exposed  heads  of  the  shell,  and  the  interior  surface  of  the  tubes.  In  the 


178 


BOILERS. 


case  of  a water-tube  boiler,  the  heating  surface  comprises  the  portion  of 
the  shell  below  the  brickwork,  the  outer  surface  of  the  headers,  and  outer 
surface  of  tubes.  In  any  given  case,  the  heating  surface  may  be  calculated 

Ratio  of  Heating  Surface  to  Horsepower  and  of  Heating  Surface 
TO  Grate  Area. 


Type  of  Boiler. 

^ Heating  Surface 

Ratio  = . 

» Horsepower 

.r.  ..  Heating  Surface 

Grate  Area 

Plain  cylindrical 

6 to  10 

12  to  15 

Flue  

8 to  12 

20  to  25 

Return  - tubular 

14  to  18 

25  to  35 

Vertical  

15  to  20 

25  to  30 

Water-tube 

10  to  12 

35  to  40 

Locomotive  

1 to  2 

50  to  100 

by  the  rules  of  mensuration.  The  following  example  will  show  the  method 
of  calculating  the  heating  surface  of  a return-tubular  boiler; 

Example. — A horizontal  return-tubular  boiler  has  the  following  dimen- 
sions: Diameter,  60  in.;  length  of  tubes,  12  ft.;  internal  diameter  of  tubes, 
3 in.;  number  of  tubes,  82.  Assume  that  f of  the  shell  is  in  contact  with 
hot  gases  or  flame,  and  | of  the  two  heads  are  heating  surface. 

Circumference  of  shell  = 60  X 3.1416  188.496  = 188.5  in.,  say. 

Length  of  shell  = 12  X 12  = 144  in. 

Heating  surface  of  shell  = 188.5  X 144  X f = 18,096  sq.  in. 

Circumference  of  tube  ==  3 X 3.1416  = 9.425  in.,  nearly. 

Heating  surface  of  tubes  = 82  X 144  X 9.425  = 111,290.4  sq.  in. 

Area  of  one  head  = 60^  X .7854  ==  2,827.44  sq.  in. 

Two-thirds  area  of  both  heads  = f X 2 X 2,827.44  = 3,769.92  sq.  in. 

From  the  heads  must  be  subtracted  twice  the  area  cut  out  by  the  tubes; 
this  is  82  X 32  X .7854  X 2 = 1,159.26. 

Total  heating  surface  in  square  feet  = 

18,096  + 111,290.4  + 3,769.92  — 1,159.26  , 

— ■ — = 916.64  sq.  ft.  Ans. 

144 


Probable  Maximum  Work  of  a Plain  Cylindrical  Boiler  of  120  Sq.  Ft. 
Heating  Surface  and  12  Sq.  Ft.  Grate  Surface,  at 
Different  Rates  of  Driving. 


Rate'  of  driving;  lb. 
water  evaporated 
per  sq.  ft.  of  heating 
surface  per  hour  .... 

2 

3 

3.5 

4 

4.5 

5 

6 

7 

8 

Total  water  evapora- 
ted by  120  sq.  ft. 
heating  surface  per 
hour,  lb 

240.00 

360.00 

420.00 

480.00 

540.00 

600.00 

720.00 

840.00 

960.00 

Horsepower;  34.5  lb. 
per  nour  = 1 H.  P. 

. 6.96 

10.43 

12.17 

13.91 

15.65 

17.39 

20.87 

24.35 

27.83 

Pounds  water  evapo- 
rated per  lb.  com- 
bustible   

10.88 

11.30 

11.36 

11.29 

11.20 

11.05 

10.48 

9.48 

8.22 

Pounds  combustible 
burned  per  hour  ... 

22.10 

31.90 

37.00 

42.50 

48.20 

54.30 

68.70 

1 

88.60  116.80 

Pounds  combustible 
per  hour  per  sq.ft, 
of  grate 

1.85 

2.65 

3.08 

3.55 

4.02 

4.52 

5.72 

7.38 

1 9.73 

Pounds  combustible 
per  hour  per  horse- 
power   

3.17 

3.05 

3.04 

3.06 

3.08 

3.12 

3.30 

3.64 

j 

4.16 

1 

From  the  figures  in  the  last  line,  we  see  that  the  amount  of  fuel  required 
for  a given  horsepower  is  nearly  37^  greater  when  the  rate  of  evaporation  is 
8 lb.  than  when  it  is  3-5  lb. 


DANGER  OF  EXPLOSION. 


179 


The  figures  in  the  preceding  table  that  represent  the  economy  of  fuel,  viz., 
‘ Pounds  water  evaporated  per  lb.  combustible”  and  ” Pounds  combustible 
per  hour  per  horsepower,”  are  what  may  be  called  “maximum”  results, 
and  they  are  the  highest  that  are  likely  to  be  obtained  with  anthracite  coal, 
with  the  most  skilful  tiring  and  with  every  other  condition  most  favorable. 
Unfavorable  conditions,  such  as  poor  tiring,  scale  on  the  inside  of  the 
heating  surface,  dust  or  soot  on  the  outside,  imperfect  protection  of  the  top 
of  the  boiler  from  radiation,  leaks  of  air  through  the  brickwork,  or  leaks  of 
water  through  the  blow-off  pipe,  may  greatly  reduce  these  figures. 

Choice  of  a Boiler.— Questions  that  arise  under  this  head  in  regard  to  any 
boiler  are: 

1.  Is  the  grate  surface  sufficient  for  burning  the  maximum  quantity  of 
coal  expected  to  be  used  at  any  time,  taking  into  consideration  the  availa- 
ble draft,  the  quality  of  the  coal,  its  percentage  of  ash,  whether  or  not  the 
ash  tends  to  run  into  clinker,  and  the  facilities,  such  as  shaking  grates,  for 
getting  rid  of  the  ash  or  clinker? 

2.  Is  the  furnace  of  a kind  adapted  to  burn  the  particular  kind  of  coal 
used? 

3.  Is  the  heating  surface  of  extent  sufficient  to  absorb  so  much  of  the 
heat  generated  that  the  gases  escaping  into  the  chimney  shall  be  reasonably 
low  in  temperature,  say  not  over  450°  F.  with  anthracite,  and  550°  F.  with 
bituminous  coal? 

4.  Are  the  gas  passages  so  designed  and  arranged  as  to  compel  the  gas 
to  traverse  at  a uniform  rate  the  whole  of  the  heating  surface,  being  not  so 
large  at  any  point  as  to  allow  of  the  gas  finding  a path  of  least  resistance,  or 
short-circuiting,  or,  on  the  other  hand,  so  contracted  at  any  point  as  to 
cause  an  obstruction  to  the  draft? 

These  questions  being  settled  in  favor  of  any  given  boiler— and  they  may 
be  answered  favorably  for  boilers  of  many  of  the  common  types — the 
relative  merits  of  the  different  types  may  now  be  considered  with  reference 
to  their  danger  of  explosion;  their  probable  durability;  the  character  and 
extent  of  repairs  that  may  be  needed  from  time  to  time,  and  the  difficulty, 
delay,  and  expense  that  these  may  entail;  the  accessibility  of  every  part  of 
the  boiler  to  inspection,  internal  and  external;  the  facility  for  removal 
of  mud  and  scale  from  every  portion  of  the  inner  surface,  and  of  dust  and 
soot  from  the  exterior;  the  water  and  steam  capacity;  the  steadiness  of 
water  level,  and  the  arrangements  for  securing  dry  steam. 

Each  one  of  the  points  referred  to  above  should  be  considered  carefully 
by  the  intending  purchaser  of  any  type  of  boiler  with  which  he  is  not 
familiar  by  experience.  The  several  points  may  be  considered  more  in 
detail. 

Danger  of  Explosion.— All  boilers  may  be  exploded  by  overpressure,  such  as 
might  be  caused  by  the  combination  of  an  inattentive  fireman  and  an 
inoperative  safety  valve,  or  by  corrosion  weakening  the  boiler  to  such 
an  extent  as  to  make  it  unable  to  resist  the  regular  working  pressure;  but 
some  boilers  are  much  more  liable  to  explosion  than  others.  In  consider- 
ing the  probability  of  explosion  of  any  boiler  of  recent  design,  it  is  well  to 
study  it  to  discover  whether  or  not  it  has  any  of  the  features  that  are  known 
to  be  dangerous  in  the  plain  cylinder,  the  horizontal  tubular,  the  vertical 
tubular,  and  the  locomotive  boilers.  The  plain  cylinder  boiler  is  liable  to 
explosion  from  strains  induced  by  its  method  of  suspension,  and  by  changes 
of  temperature.  Alternate  expansion  and  contraction  may  produce  a line 
of  weakness  in  one  of  the  rings,  which  may  tinallv  cause  an  explosion.  A 
boiler  should  be  so  suspended  that  all  its  parts  are' free  to  change  their  posi- 
tion under  changes  of  temperature  without  straining  any  part.  The 
circulation  of  water  in  the  boiler  should  be  sufficient  to  keep  all  parts 
at  nearly  the  same  temperature.  Cold  feedwater  should  not  be  allowed  to 
come  in  contact  with  the  shell,  as  this  will  cause  contraction  and  strain 
The  horizontal  tubular  boiler,  and  all  externally-fired  shell  boilers,  are 
liable  to  explosion  from  overheating  of  the  shell,  due  to  accumulation  of 
mud,  scale,  or  grease,  on  the  portion  of  the  shell  lying  directly  over  the  fire, 
to  a double  thickness  of  iron  with  rivets,  together  with  some  scale,  over  the 
fire,  or  to  low  water  uncovering  and  exposing  an  unriveted  part  of  the  shell 
directly  to  the  hot  gases.  Vertical  tubular  boilers  are  liable  to  explosion 
from  deposit  of  mud,  scale,  or  grease,  upon  the  lower  tube-sheet,  and  from 
low  water  allowing  the  upper  part  of  the  tubes  to  get  hot  and  cease  to  act 
as  stays  to  the  upper  tube-sheet.  Locomotive  boilers  may  explode  from 
deposits  on  the  crown  sheet,  from  low  water  exposing  the  dry  crown  sheet 


180 


BOILERS, 


to  the  hot  gases,  and  from  corrosion  of  the  staybolts.  Double-cylinder 
boilers,  such  as  the  French  elephant  boiler,  and  the  boilers  used  at  some 
American  blast  furnaces,  have  exploded  on  account  of  the  formation  of  a 
“ steam  pocket  ” on  the  upper  portion  of  the  lower  drum,  the  steam  being 
prevented  from  escaping  from  out  of  the  rings  of  the  drum  by  the  lap  joint 
of  the  adjoining  ring,  thus  making  a layer  of  steam  about  i inch  thick 
against  the  shell,  which  was  directly  exposed  to  the  hot  gases. 

Questions  to  Be  Asked  Concerning  New  Boilers. — The  causes  mentioned 
above  are  only  a few  of  the  causes  of  explosions,  but  they  are  the  principal 
ones  that  are  due  to  features  of  design.  These  features  should  be  looked  for 
in  any  new  style  of  boiler,  and  if  they  are  found  they  should  be  considered 
elements  of  danger.  Such  questions  as  the  following  may  be  asked:  Is  the 
method  of  suspension  of  the  boiler  such  as  to  allow  its  parts  to  be  free  to 
move  under  changes  of  temperature?  Is  the  circulation  such  as  to  keep  all 
parts  at  practically  the  same  temperature?  Is  there  a shell  with  riveted 
seams  exposed  to  the  fire?  Is  there  a shell  exposed  to  the  fire  that  may  at 
any  time  be  uncovered  by  water?  Is  there  a crown  sheet  on  which  scale 
may  lodge?  Are  there  vertical  or  inclined  tubes  acting  as  stays  to  an  upper 
sheet,  the  upper  part  of  which  tubes  may  become  overheated  in  case  of 
low  water?  Are  there  any  stayed  sheets,  the  stays  of  which  are  liable  to 
become  corroded?  Is  there  any  chance  for  a steam  pocket  to  be  formed  on  a 
sheet  that  is  exposed  to  the  fire? 

In  addition  to  the  above-mentioned  features  of  design,  which  are 
elements  of  danger,  all  boilers,  as  already  stated,  are  liable  to  explosion  due 
to  corrosion.  Internal  corrosion  is  usually  due  to  acid  feedwater,  and  all 
boilers  are  equally  liable  to  it.  External  corrosion,  however,  is  more  liable 
to  take  place  in  some  designs  of  boilers  than  others,  and  in  some  locations 
rather  than  others.  If  any  portion  of  a boiler  is  in  a cold  and  damp  place,  it 
is  liable  to  rust  out.  For  this  reason  the  mud-drums  of  many  modern  forms 
of  boilers  are  made  of  cast  iron,  and  resist  rusting  better  than  either  wrought 
iron  or  steel.  If  any  part  of  a boiler,  other  than  a part  made  of  cast  iron,  is 
liable  to  be  exposed  to  a cold  and  damp  atmosphere,  or  covered  with  damp 
soot  or  ashes,  or  exposed  to  drip  from  rain  or  from  leaky  pipes,  and 
especially  if  such  part  is  hidden  by  brickwork  or  otherwise  so  that  it  can- 
not be  seen,  that  part  is  an  element  of  danger. 

Durability.— The  question  of  durability  is  partly  covered  by  that  of  danger 
of  explosion,  which  has  already  been  discussed,  but  it  also  is  related  to  the 
question  of  incrustation  and  scale.  The  plates  and  tubes  of  a boiler  may  be 
destroyed  by  internal  or  external  corrosion,  but  they  may  also  be  burned 
out.  it  may  be  regarded  as  impossible  to  burn  a plate  or  tube  of  iron  or 
steel,  no  matter  how  high  the  temperature  of  the  flame,  provided  one  side  of 
the  metal  is  covered  with  water.  If  a steam  pocket  is  formed,  so  that  the 
water  does  not  touch  the  metal,  or  if  there  is  a layer  of  grease  or  hard  scale, 
then  the  plate  or  tube  may  be  burned.  In  a water  tube  that  is  horizontal,  or 
nearly  so,  and  in  which  the  circulation  of  water  is  defective,  it  is  possible  to 
form  a mass  of  steam  that  will  drive  the  water  away  from  the  metal,  and 
thus  allow  the  tube  to  burn  out.  In  considering  the  probable  durability  of 
a boiler,  we  may  ask  the  same  questions  as  those  that  have  been  asked 
concerning  danger  of  explosion.  There  are,  however,  many  chances  of 
burning  out  a minor  part  of  a boiler  without  serious  danger,  to  one  chance 
of  a disastrous  explosion.  Thus  the  tubes  of  a water-tube  boiler,  if  allowed 
to  become  thickly  covered  with  scale,  might  be  burned  out  again  and  again 
without  causing  any  further  destruction  at  any  one  time  than  the  rupture 
of  a single  tube.  A new  type  of  boiler  should  be  questioned  in  regard  to  the 
likelihood  of  frequent  small  repairs  being  necessary,  as  well  as  in  regard  to 
its  liability  to  complete  destruction.  We  may  ask:  Is  the  circulation  through 
all  parts  of  the  boiler  such  that  the  water  cannot  be  driven  out  of  any  tube 
or  from  any  portion  of  a plate,  so  as  to  form  a steam  pocket  exposed  to  high 
temperature?  Are  there  proper  facilities  for  removing  the  scale  from  every 
portion  of  the  plates  and  tubes  ? 

Repairs.— The  questions  of  durability  and  of  repairs  are,  in  some  respects, 
related  to  each  other.  The  more  infrequent  and  the  less  extensive  the 
repairs,  the  greater  the  durability.  The  tubes  of  a boiler,  where  corroded  or 
burnt  out.  may  be  replaced  and  made  as  good  as  new.  The  shell,  when  it 
springs  a leak,  may  be  patched,  and  is  then  likely  to  be  far  from  as  good  as 
new.  When  the  shell  corrodes  badly  it  must  be  replaced,  and  to  replace  the 
shell  is  the  same  as  getting  a new  boiler.  Herein  is  the  advantage  of  the 
sectional  water-tube  boilers.  The  sections,  or  parts  of  a section,  may  be 


WATER  AND  STEAM  CAPACITY, 


181 


renewed  easily,  and  made  as  good  as  new,  while  the  shell,  being  far  removed 
from  the  fire  and  easily  kept  dry  externally,  is  not  liable  either  to  burning 
out  or  external  corrosion.  In  considering  the  merits  of  a new  style  of 
boiler,  with  reference  to  repairs,  we  may  ask  whp  t parts  of  the  boiler  are 
most  likely  to  give  out  and  need  to  be  repaired  or  replaced?  Are  these 
repairs  easily  effected,  how  long  will  they  require,  and,  after  they  are  made, 
is  the  boiler  as  good  as  new  ? 

Facility  for  Removal  of  Scale  and  for  Inspection.— These  questions  have 
already  been  discussed  to  some  extent  under  the  head  of  durability.  Some 
water-tube  boilers,  now  dead  and  gone,  were  some  years  ago  put  on  the 
market,  which  had  no  facilities  for  the  removal  of  scale.  It  was  claimed  by 
their  promoters  that  they  did  not  need  any,  because  their  circulation  was  so 
rapid.  Every  few  years  boilers  of  these  types  are  reinvented,  and  the  same 
claim  is  made  for  them,  that  their  rapid  circulation  prevents  the  formation 
of  scale.  The  fact  is  that  if  there  is  scale-forming  material  in  the  water  it 
will  be  deposited  when  the  water  is  evaporated,  and  no  amount  or  kind  of 
circulation  will  keep  it  from  accumulating  on  every  part  of  the  boiler,  and 
in  every  kind  of  tubes,  vertical,  horizontal,  and  inclined.  I have  seen 
the  nearly  vertical  circulating  tubes  of  a water-tube  boiler,  in  which  the 
circulation  is  nine  times  as  fast  as  the  average  circulation  in  the  inclined 
tubes,  nearly  full  of  scale;  that  is,  a 4"  tube  had  an  opening  in  it  of  less  than 
1 in.  in  diameter.  This  was  due  to  carelessness  in  blowing  off  the  boiler,  or 
exceptionally  bad  feedwater,  or  both.  If  circulation  would  prevent  scaling 
at  all,  it  would  prevent  it  here. 

Water  and  Steam  Capacity.— It  is  claimed  for*  some  forms  of  boilers  that 
they  are  better  than  others  because  they  have  a larger  water  or  steam 
capacity.  Great  water  capacity  is  useful  where  the  demands  for  steam  are 
extremely  fluctuating,  as  in  a rolling  mill  or  a sugar  refinery,  where  it  is 
desirable  to  store  up  heat  in  the  water  in  the  boilers  during  the  periods  of 
the  least  demand,  to  be  given  out  during  periods  of  greatest  demand.  Large 
water  capacity  is  objectionable  in  boilers  for  factories,  usually,  especially  if 
they  do  not  run  at  night,  and  the  boilers  are  cooled  down,  because  there  is  a 
large  quantity  of  water  to  be  heated  before  starting  each  morning.  If 
“ rapid  steaming  ” or  the  ability  to  get  up  steam  quickly  from  cold  water,  or 
to  raise  the  pressure  quickly,  is  desired,  large  water  capacity  is  a detriment. 
The  advantage  of  large  steam  capacity  is  usually  overrated.  It  is  useful  to 
enable  the  steam  to  be  drained  from  water  before  it  escapes  into  the  steam 
pipe,  but  the  same  result  can  be  effected  by  means  of  a dry  pipe,  as  in 
locomotive  and  marine  practice,  in  which  the  steam  space  in  the  boiler  is 
very  small  in  proportion  to  the  horsepower.  Large  steam  space  in  the 
boiler  is  of  no  importance  for  storing  energy  or  equalizing  the  pressure 
during  the  stroke  of  an  engine.  The  water  in  the  boiler  is  the  place  to  store 
heat,  and  if  the  steam  pipe  leading  to  an  engine  is  of  such  small  capacity 
that  it  reduces  the  pressure,  the  remedy  is  a steam  reservoir  close  to  the 
engine  or  a large  steam  pipe. 

Steadiness  of  Water  Level.— This  requires  either  a large  area  of  water  sur- 
face, so  that  the  level  may  be  changed  slowly'by  fluctuations  in  the  demand 
for  steam  or  in  the  delivery  of  the  feed-pump,  or  else  constant,  and  preferably 
automatic,  regulation  of  the  feedwater  supply  to  suit  the  steam  demand. 
A rapidly  lowering  water  level  is  apt  to  expose  dry  sheets  or  tubes  to  the 
action  of  the  hot  gases,  and  thus  be  a source  of  danger.  A rapidly  rising 
level  may,  before  it  is  seen  by  the  fireman,  cause  water  to  be  carried  over 
into  the  steam  pipe,  and  endanger  the  engine. 

Water  Circulation.— Positive  and  complete  circulation  of  the  water  in  a 
boiler  is  important  for  two  reasons:  (1)  To  keep  all  parts  of  the  boiler  of  a 
uniform  temperature,  and  (2)  to  prevent  the  adhesion  of  steam  bubbles  to 
the  surface,  which  may  cause  overheating  of  the  metal.  It  is  claimed  by 
some  manufacturers  that  the  rapid  circulation  of  water  in  their  boilers 
tends  to  make  them  more  economical  than  others.  I have  as  yet,  however, 
to  find  any  proof  that  increased  rapidity  of  circulation  of  water  beyond 
that  nsually  found  in  any  boiler  will  give  increased  economy.  We  know 
that  increased  rate  of  flow  of  air  over  radiating  surfaces  increases  the 
amount  of  heat  transmitted  through  the  surface,  but  this  is  because  by  the 
increased  circulation,  cold  air  is  continually  brought  into  contact  with 
the  surface,  making  an  increased  difference  of  temperature  on  the  two  sides, 
which  causes  increased  transmission.  But  by  increasing  the  rapidity  of 
circulation  in  a steam  boiler  we  cannot  vary  the  difference  of  temperature  to 
any  appreciable  extent,  for  the  water  and  the  steam  in  the  boiler  are  at 


182 


BOILERS. 


about  the  same  temperature  throughout.  The  ordinary  or  “ Scotch  ’’  form 
of  marine  boiler  shows  an  exception  to  the  general  rule  of  uniformity  of 
temperature  of  water  throughout  the  boiler,  but  the  temperature  above  the 
level  of  the  lower  lire  tubes  is  practically  uniform. 


INCRUSTATION  AND  SCALE. 

Nearly  all  waters  contain  foreign  substances  in  a greater  or  less  degree, 
and  though  this  may  be  a small  amount  in  each  gallon,  it  becomes  of 
importance  where  large  quantities  are  evaporated.  For  instance,  a 100  H.  P. 
boiler  evaporates  30,000  lb.  of  water  in  10  hours,  or  390  tons  per  month;  in 
comparatively  pure  water  there  would  be  88  lb.  of  solid  matter  in  that 
quantity,  and  in  many  kinds  of  spring  water  as  much  as  2,000  lb. 

The  nature  and  hardness  of  the  scale  formed  of  this  matter  will  depend 
on  the  kind  of  substances  held  in  solution  and  suspension.  Analyses  of  a 
great  variety  of  incrustations  show  that  carbonate  and  sulphate  of  lime 
form  the  larger  part  of  all  ordinary  scale,  that  from  carbonate  being  soft 
and  granular,  and  that  from  sulphate,  hard  and  crystalline.  Organic 
substances  in  connection  with  carbonate  of  lime  will  also  make  a hard  and 
troublesome  scale. 

The  presence  of  scale  or  sv'diment  in  a boiler  results  in  loss  of  fuel, 
burning  and  cracking  of  the  boiler,  predisposes  to  explosion,  and  leads  to 
extensive  repairs.  It  is  estimated  that  the  presence  of  in.  of  scale  causes 
a loss  of  13^  of  fuel;  I in.,  38^;  and  \ in.,  60fc.  The  Railway  Master 
Mechanics’  Association  of  the  United  States  estimates  that  the  loss  of  fuel, 
extra  repairs,  etc.,  due  to  incrustation,  amount  to  an  average  of  S750  per 
annum  for  every  locomotive  in  the  Middle  and  Western  States,  and  it  must 
be  nearly  the  same  for  the  same  power  in  stationary  boilers. 

Causes  of  Incrustation. — 

1.  Deposition  of  suspended  matter. 

2.  Deposition  of  salts  from  concentration. 

3.  Deposition  of  carbonates  of  lime  and  magnesia,  by  boiling  off  carbonic 
acid,  which  holds  them  in  solution. 

4.  Deposition  of  sulphates  of  lime,  because  sulphate  of  lime  is  soluble  in 
cold  water,  less  soluble  in  hot  water,  insoluble  above  270°  F. 

5.  Deposit  of  magnesia,  because  magnesium  salts  decompose  at  high 
temperatures. 

6.  Deposition  of  lime  soap,  iron  soap,  etc.,  formed  by  saponification  of 
grease. 

Method  of  Preventing  Incrustation.— 

1.  Filtration. 

2.  Blowing  off. 

3.  Use  of  internal  collecting  apparatus,  or  devices,  for  directing  the 
circulation. 

4.  Heating  feedwater. 

5.  Chemical  or  other  treatment  of  water  in  boiler. 

6.  Introduction  of  zinc  in  boiler. 

7.  Chemical  treatment  of  water  outside  of  boiler. 


Troublesome  Substance. 

Trouble. 

Remedy  or  Palliation. 

Sediment,  mud,  clay,  etc. 

Incrustation. 

Filtration;  blowing  off. 

Readily  soluble  salts. 

Incrustation. 

Blowing  off. 

Bicarbonates  of  lime,  magnesia,  and  iron. 

Incrustation. 

Heating  feed;  addition  of  caustic  soda, 
lime,  or  magnesia,  etc. 

Sulphate  of  lime. 

Incrustation. 

Addition  of  carbonate  of  soda,  barium 
chloride,  etc. 

Chloride  and  sulphate  of  magnesium. 

Corrosion. 

Addition  of  carbonate  soda,  etc. 
Addition  of  barium  chloride,  etc. 

Carbonate  of  soda  in  large  amounts. 

Priming. 

Acid  (in  mine  water). 

Corrosion. 

Alkali. 

Dissolved  carbonic  acid  and  oxygen. 

Corrosion. 

Heating  feed;  addition  of  caustic  soda, 
slaked  lime,  etc. 

Grease  (from  condensed  water). 

Corrosion. 

Slaked  lime  and  filtering.  Substitute 
mineral  oil. 

Organic  matter  (sewage). 

Priming. 

Precipitate  with  alum  or  ferric  chloride, 
and  filter. 

Organic  matter. 

Corrosion. 

Precipitate  with  alum  or  ferric  chloride, 
and  filter. 

PREVENTION  OF  SCALE. 


183 


Means  of  Prevention.— It  is  absolutely  essential  to  the  successful  use  of  any 
boiler,  except  in  pure  water,  that  it  be  accessible  for  the  removal  of  scale, 
for  though  a rapid  circulation  of  water  will  delay  the  deposit,  and  certain 
chemicals  will  change  its  character,  yet  the  most  certain  cure  is  periodical 
inspection  and  mechanical  cleaning.  This  may,  however,  be  rendered  less 
frequently  necessary,  and  the  use  of  very  bad  water  more  practical  by  the 
employment  of  some  preventives.  The  following  are  fair  samples  of  those 
in  use,  with  their  results: 

M.  Bidard’s  observations  show  that  “ anti-incrustators  ” containing 
organic  matter  help  rather  than  hinder  incrustations,  and  are  therefore 
to  be  avoided. 

Oak,  hemlock,  and  other  barks  and  woods,  sumac,  catechu,  logwood,  etc. 
are  effective  in  waters  containing  carbonates  of  lime  or  magnesia,  by  reason 
of  their  tannic  acid,  but  are  injurious  to  the  iron  and  not  to  be  recom- 
mended. 

Molasses,  cane  juice,  vinegar,  fruits,  distillery  slops,  etc.  have  been  used 
with  success  so  far  as  scale  is  concerned,  by  reason  of  the  acetic  acid  that 
they  contain,  but  this  is  even  more  injurious  to  the  iron  than  tannic  acid, 
while  the  organic  matter  forms  a scale  with  sulphate  of  lime  when  it  is 
present. 

Milk  of  lime  and  metallic  zinc  have  been  used  with  success  in  waters 
charged  with  bicarbonate  of  lime,  reducing  the  bicarbonate  to  the  insoluble 
carbonate. 

Barium  chloride  and  milk  of  lime  are  said  to  be  used  with  good  effect  at 
Krupp’s  works,  in  Prussia,  for  waters  impregnated  with  gypsum. 

Soda  ash  and  other  alkalies  are  very  useful  in  waters  containing  sulphate 
of  lime,  by  converting  it  into  a carbonate,  and  so  forming  a soft  scale 
easily  cleaned.  But  when  used  in  excess  they  cause  foaming,  particularly 
where  there  is  oil  coming  from  the  engine,  with  which  they  form  soap.  All 
soapy  substances  are  objectionable  for  the  same  reason. 

Petroleum  has  been  much  used  of  late  years.  It  acts  best  in  waters  in 
which  sulphate  of  lime  predominates.  Sulphate  of  lime  is  the  injurious 
substance  in  nearly  all  mine  waters,  and  petroleum,  when  properly 
prepared,  is  a good  preventive  of  scale  and  pitting.  Crude  petroleum 
should  not  be  used,  as  it  sometimes  helps  in  forming  a very  injurious  scale. 
Refined  petroleum,  on  the  other  hand,  is  useless,  as  it  vaporizes  at  a 
temperature  below  that  of  boiling  water.  Therefore,  only  such  prepara- 
tions should  be  used  as  will  not  vaporize  below  500°  F. 

Tannate  of  soda  is  a good  preparation  for  general  use,  but  in  waters  con- 
taining much  sulphate,  it  should  be  supplemented  by  a portion  of  carbonate 
of  soda  or  soda  ash. 

A decoction  from  the  leaves  of  the  eucalyptus  is  found  to  work  well  in 
some  waters  in  California. 

For  muddy  water,  particularly  if  it  contain  salts  of  lime,  no  preventive  of 
incrustation  will  prevail  except  filtration,  and  in  almost  every  instance  the 
use  of  a filter,  either  alone  or  in  connection  with  some  means  of  precipita- 
ting the  solid  matter  from  solution,  will  be  found  very  desirable. 

In  all  cases  where  impure  or  hard  waters  are  used,  frequent  “blowing” 
from  the  mud-drum  is  necessary  to  carry  off  the  accumulated  matter, 
which  if  allowed  to  remain  would  form  scale. 

When  boilers  are  coated  with  a hard  scale,  difficult  to  remove,  it  will  be 
found  that  the  addition  of  i lb.  caustic  soda  per  horsepower,  and  steaming 
for  some  hours,  according  to  the  thickness  of  the  scale,  just  before  cleaning, 
will  greatly  facilitate  that  operation,  rendering  the  scale  soft  and  loose. 
This  should  be  done,  if  possible,  when  the  boilers  are  not  otherwise  in  use. 


COVERING  FOR  BOILERS,  STEAM  PIPES,  ETC. 

The  losses  by  radiation  from  unclothed  pipes  and  vessels  containing 
steam  are  considerable,  and  in  the  case  of  pipes  leading  to  steam  engines,  are 
magnified  by  the  action  of  the  condensed  water  in  the  cylinder.  It  there- 
fore is  important  that  such  pipes  should  be  well  protected.  The  following 
table  gives  the  loss  of  heat  from  steam  pipes  naked,  and  clothed  with  wool  or 
hair  felt,  of  different  thickness,  the  steam  pressure  being  assumed  at  75  lb., 
and  the  exterior  air  at  60°. 

There  is  a wide  difference  in  the  value  of  different  substances  for  protec* 
tion  from  radiation,  their  values  varying  nearly  in  the  reverse  ratio  to  their 
conducting  power  for  heat,  up  to  their  ability  to  transmit  as  much  heat  as 


184 


BOILERS. 


the  surface  of  the  pipe  will  radiate,  after  which  they  become  detrimental, 
rather  than  useful,  as  covering.  This  point  is  reached  nearly  at  baked  clay 
or  brick. 

Table  of  Loss  of  Heat  From  Steam  Pipes. 


Outside  Diameter  of  Pipe,  Without  Felt. 


1 Thickness  of  Covering.  In 

2 In.  Diameter. 

4 In. 

Diameter. 

6 In.  Diameter. 

' 8 In. 

Diameter. 

12  In.  Diameter. 

Loss  in  Units 
per  Foot  Run  per 
Hour. 

Ratio  of  Loss. 

Feet  in  Length  per 

H.  P.  Lost. 

Loss  in  Units 
per  Foot  Run  per 
Hour. 

1 Ratio  of  Loss. 

Feet  in  Length  per 
H.  P.  Lost. 

J 1SS  in  Units 
per  Foot  Run  per 
Hour. 

o 

o 

.2 

Feet  in  Length  per 

H.  P.  Lost. 

Loss  in  Units 

per  Foot  Run  per 

Hour. 

Ratio  of  Loss. 

1 Feet  in  Length  per  I 

1 H.  P.  Lost. 

Loss  in  Units 

per  Foot  Run  per 

Hour. 

Ratio  of  Loss. 

Feet  in  Length  per 

1 H.  P.  Lost.  1 

0 

219.0 

1.00 

132 

390.8 

1.00 

75 

624.1 

1.000 

46 

729.8 

1.000 

40 

1,077.4 

1.000 

26 

1 

4 

100.7 

.46 

288 

180.9 

.46 

160 

65.7 

.30 

441 

117.2 

.30 

247 

187.2 

.300 

154 

219.6 

.301 

132 

301.7 

.280 

92 

1 

43.8' 

.20 

662 

73.9 

.18 

392 

111.0 

.178 

261 

128.3 

.176 

225 

185.3 

.172 

157 

2 

28.4 

.13 

1,020 

44.7 

.11 

648 

66.2 

.106 

438 

75.2 

.103 

385 

98.0 

.091 

294 

4 

19.8 

.09 

1,464 

28.1 

.07 

1,031 

41.2 

.066 

703 

46.0 

.063 

630 

60.3 

.056 

486 

6 

23.4 

.06 

1,238 

33.7 

.054 

860 

34.3 

.047 

845 

45.2 

.042 

642 

A smooth  or  polished  surface  is  of  itself  a good  protection,  polished  tin 
or  Russia  iron  having  a ratio,  for  radiation,  of  53  to  100  for  cast  iron.  Mere 
color  makes  but  little  difference. 


Table  of  Conducting  Power  of  Various  Substances. 


{From  Peclet.) 


Substance. 

Conducting 

Power. 

Substance. 

Conducting 

Power. 

Blotting  paper 

.274 

Wood,  across  fiber. 

.83 

Eiderdown  

.314 

Cork  

1.15 

Cotton  or  Wool,  \ 
any  density  j 

.323 

Coke,  pulverized  

India  rubber  

1.29 

1.37 

Hemp,  canvas 

.418 

Wood,  with  fiber  

1.40 

Mahogany  dust  ...: 

.523 

Plaster  of  Paris 

3.86 

Wood  ashes  

.531 

Baked  clay 

4.83 

Straw  

.563 

Glass  

6.60 

Charcoal  powder  

.636 

Stone 

13.68 

Hair  or  wool  felt  has  the  disadvantage  of  becoming  soon  charred  from 
the  heat  of  steam  at  high  pressure,  and  sometimes  of  taking  fire  therefrom. 
This  has  led  to  a variety  of  “cements”  for  covering  pipes— composed  gen- 
erally of  clay  mixed  with  different  substances,  as  asbestos,  paper  fiber, 
charcoal,  etc.  A series  of  careful  experiments,  made  at  the  Massachusetts 
Institute  of  Technology  in  1871,  showed  the  condensation  of  steam  in  a pipe 
covered  by  one  of  them,  as  compared  with  a naked  pipe,  and  one  clothed 
with  hair  felt,  was  100  for  the  naked  pipe,  67  for  the  “cement”  covering, 
and  27  for  the  hair  felt. 

The  presence  of  sulphur  in  the  best  coverings  and  its  recognized  injurious 
effects  make  it  imperative  that  moisture  be  kept  from  the  coverings,  for, 
if  present,  it  will  surely  combine  with  the  sulphur,  thus  making  it  active. 
Stated  in  other  words,  keep  the  pipes  and  coverings  in  good  repair.  Much 
of  the  inefficiency  of  coverings  is  due  to  the  lack  of  attention  given  them; 
they  are  often  seen  hanging  loosely  from  the  pipe  which  they  are  supposed 
to  protect. 


CARE  OF  BOILERS. 


185 


Table  op  Relative  Value  of  Non-Conductors. 


{From  Chas.  E.  Emery,  Ph.  D. ) 


Non-Conductor. 

Value. 

Non-Conductor. 

Value. 

Wool  felt  

1.000 

Loam,  dry  and  open  

.550 

Mineral  wool  No.  2 

.832 

Slaked  lime  

.480 

Mineral  with  tar 

.715 

Gas-house  carbon 

.470 

Sawdust 

.680 

Asbestos  

.363 

Mineral  wool  No.  1 

.676 

Coal  ashes 

.345 

Charcoal 

.632 

Coke  in  lumps  

.277 

Pine  wood  across  fiber 

.553 

Air  space  undivided  

.136 

Carbonate  of  magnesia,  as  compared  with  wool  felt  at  1.000,  has  a rela- 
tive value  of  .472.  This  is  determined  from  tests  by  Prof.  Ordway,  of  Boston, 
and  adjusted  to  results  shown  in  Prof.  Emery’s  tests. 

“ Mineral  wool,”  a fibrous  material  made  from  blast-furnace  slag,  is  a 
good  protection,  and  is  incombustible. 

Cork  chips,  cemented  together  with  water  glass,  make  one  of  the  best 
coverings  known. 

A cheap  jacketing  for  steam  pipes,  but  a very  efficient  one,  may  be 
applied  as  follows:  First,  wrap  the  pipe  in  asbestos  paper,  though  this  may 
be  dispensed  with;  then  lay  slips  of  wood  lengthways,  from  6 to  12,  accord- 
ing to  size  of  pipe,  binding  them  in  position  with  wire  or  cord,  and 
around  the  framework  thus  constructed  wrap  roofing  paper,  fastening  it 
by  paste  or  twine.  For  fianged  pipe,  space  may  be  left  for  access  to  the 
bolts,  which  space  should  be  filled  with  felt.  If  exposed  to  weather,  use 
tarred  paper,  or  paint  the  exterior.  A French  plan  is  to  cover  the  surface 
with  a rough  flour  paste,  mixed  with  sawdust  until  it  forms  a moderately 
stiff  dough.  Apply  with  a trowel  in  layers  of  about  i in.  thick;  give  4 or  5 
layers  in  all.  If  iron  surfaces  are  well  cleaned  from  grease,  the  adhesion  is 
perfect.  For  copper,  first  apply  a hot  solution  of  clay  in  water.  A coating 
of  tar  renders  the  composition  impervious  to  the  weather. 


DATA  FOR  PROPORTIONING  AN  ECONOMIZER. 

( The  Green  Fuel  Economizer  Co.,  Matteawan,  N.  Y.) 

The  following  estimate  is  given  for  the  amount  of  heating  surface  to  be 
provided  in  an  economizer  to  be  used  in  connection  with  a given  amount  of 
boilers: 

By  allowing  4 sq.  ft.  of  heating  surface  per  boiler  horsepower  (Centennial 
rating,  34i  lb.  of  water  evaporated  from  and  at  212°  = 1 H.  P.),  we  are  able 
to  raise  the  feedwater  60°  for  every  100°  reduction  in  the  temperature  enter- 
ing the  economizer  with  gases  from  450°  to  600°.  These  results  are  cor- 
roborated by  Mr.  Barrus’s  tests. 

With  the  temperature  of  the  gases  entering  the  economizer  at  600°  to  700°, 
we  have  allowed  4i  to  5 sq.  ft.  of  heating  surface  per  boiler  horsepower, 
and  for  every  100°  reduction  of  gases  we  have  obtained  about  65°  rise  in 
temperature  of  the  water;  the  temperature  of  the  feedwater  entering  aver- 
aging from  60°  to  120°. 

With  5,000  sq.  ft.  of  boiler  heating  surface  (plain  cylinder  boilers)  develop- 
ing 1,000  H.  P.,  we  should  recommend  using  5 sq.  ft.  of  economizer  heating 
surface  per  B.  H.  P.,  or  an  economizer  of  about  500  tubes,  and  it  should  heat 
the  feedwater  about  300°. 


CARE  OF  BOILERS. 

1.  Safety  Valves.— Great  care  should  be  exercised  to  see  that  these  valves 
are  ample  in  size  and  in  working  order.  Overloading  or  neglect  frequently 
leads  to  the  most  disastrous  results.  Safety  valves  should  be  tried  at  least 
once  every  day,  to  see  that  they  act  freely. 

2.  Pressure  Gauge.— The  steam  gauge  should  stand  at  zero  when  the 
pressure  is  off,  and  it  should  show  same  pressure  as  the  safety  valve  when 
that  is  blowing  off.  If  not,  then  one  is  wrong,  and  the  gauge  should  be 
tested  by  one  known  to  be  correct. 


186 


BOILERS. 


3.  Water  Level,— The  first  duty  of  an  engineer  before  starting,  or  at  the 
beginning  of  his  watch,  is  to  see  that  the  water  is  at  the  proper  height.  Do 
not  rely  on  glass  gauges,  fioats,  or  water  alarms,  but  try  the  gauge-cocks. 
If  they  do  not  agree  with  water  gauge,  learn  the  cause  and  correct  it. 

4.  Gauge-cocks  and  water  gauges  must  be  kept  clean.  Water  gauges  should 
be  blown  out  frequently,  and  the  glasses  and  passages  to  them  kept  clean. 
The  Manchester,  England,  Boiler  Association  attributes  more  accidents  to 
inattention  to  water  gauges  than  to  all  other  causes  put  together. 

5.  Feed-Pump  or  Injector.— These  should  be  kept  in  perfect  order,  and  be 
of  ample  size.  No  make  of  pump  can  be  expected  to  be  continuously 
reliable  without  regular  and  careful  attention.  It  is  always  safe  to  have  two 
means  of  feeding  a boiler.  Check-valves  and  self-acting  feed-valves  should 
be  frequently  examined  and  cleaned.  Satisfy  yourself  frequently  that  the 
valve  is  acting  when  the  feed-pump  is  at  work. 

6.  Low  Water.— In  case  of  low  water,  immediately  cover  the  fire  with 

ashes  (wet  if  possible)  or  any  earth  that  may  be  at  hand.  If  nothing  else  is 
handy,  use  fresh  coal.  Draw  fire  as  soon  as  it  can  be  done  without  increas- 
ing the  heat.  Neither  turn  on  the  feed,  start  nor  stop  engine,  nor  lift  safety 
valve  until  fires  are  out  and  the  boiler  cooled  down.  ' 

7.  Blisters  and  Cracks.— These  are  liable  to  occur  in  the  best  plate  iron. 
When  the  first  indication  appears,  there  must  be  no  delay  in  having  it 
carefully  examined  and  properly  cared  for. 

8.  Fusible  plugs,  when  used,  must  be  examined  when  the  boiler  is  cleaned, 
and  carefully  scraped  clean  on  both  the  water  and  fire  sides,  or  they  are 
liable  not  to  act. 

9.  Firing.— Fire  evenly  and  regularly,  a little  at  a time.  Moderately 
thick  fires  are  most  economical,  but  thin  firing  must  be  used  where  the 
draft  is  poor.  Take  care  to  keep  grates  evenly  covered,  and  allow  no  air 
holes  in  the  fire.  Do  not  “clean”  fires  oftener  than  necessary.  With 
bituminous  coal,  a “coking  fire,”  i.  e.,  firing  in  front  and  shoving  back 
when  coked,  gives  best  results  if  properly  managed. 

10.  Cleaning.— All  heating  surfaces  must  be  kept  clean  outside  and  in,  or 
there  will  be  a serious  waste  of  fuel.  The  frequency  of  cleaning  will  depend 
on  the  nature  of  fuel  and  water.  When  a new  feedwater  supply  is 
introduced,  its  effect  upon  the  boiler  should  be  closely  observed,  as  this  new 
supply  may  be  either  an  advantage  or  a detriment  as  compared  with  the 
working  of  the  boiler  previous  to  its  introduction.  As  a rule,  never  allow 
over  yV'  scale  or  soot  to  collect  on  surfaces  between  cleanings.  Handholes 
should  be  frequently  removed  and  surfaces  examined,  particularly  in 
case  of  a new  boiler,  until  proper  intervals  have  been  established  by 
experience. 

The  exterior  of  tubes  can  be  kept  clean  by  the  use  of  blowing  pipe  and 
hose  through  openings  provided  for  that  purpose.  In  using  smoky  fuel,  it  is 
best  to  occasionally  brush  the  surfaces  when  steam  is  off. 

11.  Hot  Feedwater.— Cold  water  should  never  be  fed  into  any  boiler  when 
it  can  be  avoided,  but  when  necessary  it  should  be  caused  to  mix  with  the 
heated  water  before  coming  in  contact  with  any  portion  of  the  boiler. 

12.  Foaming.— When  foaming  occurs  in  a boiler,  checking  the  outfiow  of 
steam  will  usually  stop  it.  If  caused  by  dirty  water,  blowing  down  and 
pumping  up  will  generally  cure  it.  In  cases  of  violent  foaming,  check  the 
draft  and  fires. 

13.  Air  Leaks.— Be  sure  that  all  openings  for  admission  of  air  to  boiler  or 
flues,  except  through  the  fire,  are  carefully  stopped.  This  is  frequently  an 
unsuspected  cause  of  serious  waste. 

14.  Blowing  Off.— If  feedwater  is  muddy  or  salt,  blow  off  a portion  fre- 
quently, according  to  condition  of  water.  Empty  the  boiler  every  week  or 
two,  and  fill  up  afresh.  When  surface  blow-  cocks  are  used,  they  should  be 
often  opened  for  a few  minutes  at  a time.  Make  sure  no  water  is  escaping 
from  the  blow-off  cock  when  it  is  supposed  to  be  closed.  Blow-off  cocks  and 
check-valves  should  be  examined  every  time  the  boiler  is  cleaned.  Never 
empty  the  boiler  while  the  brickwork  is  hot. 

15.  Leaks.— When  leaks  are  discovered,  they  should  be  repaired  as  soon 
as  possible. 

16.  Filling  Up.— Never  pump  cold  water  into  a hot  boiler.  Many  times 
leaks,  and,  in  shell  boilers,  serious  weaknesses,  and  sometimes  explosions 
are  the  result  of  such  an  action. 


THICKNESS  OF  BOILER  IRON. 


187 


17.  Dampness.— Take  care  that  no  water  comes  in  contact  with  the 
exterior  of  the  boiler  from  any  cause,  as  it  tends  to  corrode  and  weakeh 
the  boiler.  Beware  of  all  dampness  in  seatings  and  coverings. 

18.  Galvanic  Action.— Examine  frequently  parts  in  contact  with  copper  or 
brass,  where  water  is  present,  for  signs  of  corrosion.  If  water  is  salt  or  acid, 
some  metallic  zinc  placed  in  the  boiler  will  usually  prevent  corrosion,  but  it 
will  need  attention  and  renewal  from  time  to  time. 

19.  Rapid  Firing.— In  boilers  with  thick  plates  or  seams  exposed  to  the 
fire,  steam  should  be  raised  slowly,  and  rapid  or  intense  firing  avoided. 
With  thin  water  tubes,  however,  and  adequate  water  circulation,  no  dam- 
age can  come  from  that  cause. 

20.  Standing  Unused.— If  a boiler  is  not  required  for  some  time,  empty  and 
dry  it  thoroughly.  If  this  is  impracticable,  fill  it  quite  full  of  water,  and  put 
in  a quantity  of  common  washing  soda.  External  parts  exposed  to  damp- 
ness should  receive  a coating  of  linseed  oil. 

21.  Repair  of  Coverings.— All  coverings  should  be  looked  after  at  least  once 
a year,  given  necessary  repairs,  refitted  to  the  pipe,  and  the  spaces  due  to 
shrinkage  taken  up.  Little  can  be  expected  from  the  best  non-conductors  if 
they  are  allowed  to  become  saturated  with  water,  or  if  air-currents  are 
permitted  to  circulate  between  them  and  the  pipe. 

22.  General  Cleanliness.— All  things  about  the  boiler  room  should  be  kept 
clean  and  in  good  order.  Negligence  tends  to  waste  and  decay. 


THICKNESS  OF  BOILER  IRON  REQUIRED  AND  PRESSURE 
ALLOWED  BY  THE  LAWS  OF  THE  UNITED  STATES. 

Pressure  Equivalent  to  the  Standard  for  a Boiler  42  In.  in  Diam- 
eter AND  i In.  Thick. 


Diameter. 


16ths. 

34  In. 
Lb. 

36  In. 
Lb. 

38  In. 
Lb. 

40  In. 
Lb. 

42  In. 
Lb. 

44  In. 
Lb. 

46  In. 
Lb. 

5 

169.9 

160.4 

152.0 

144.4 

137.5 

131.2 

125.5 

4i 

158.5 

149.7 

141.8 

134.7 

128.3 

122.5 

117.2 

4 

135.9 

128.3 

121.6 

115.5 

110.0 

105.0 

100.0 

3| 

124.5 

117.6 

111.4 

105.9 

100.8 

96.2 

92.0 

31 

113.2 

106.9 

101.3 

96.2 

91.7 

87.5 

83.0 

3 

101.9 

96.2 

91.2 

82.6 

82.5 

78.7 

75.1 

The  rule  for  finding  the  proper  sectional  area  for  the  narrowest  part  of 
the  nozzle  is  given  by  Rankine,  S.  E.,  page  477,  as  follows: 

. . . , cubic  feet  per  hour  gross  feedwater 

Area  in  square  inches  = . ■ 

8001/  pressure  in  atmospheres 


Delivery  in  Gallons  per  Hour  with  a Pressure 
Diameter  of  per  Square  Inch  of 

Throat.  Decimals 


of  an  Inch. 

30  Lb. 

45  Lb. 

60  Lb. 

75  Lb. 

90  Lb. 

.10 

56 

69 

80 

89 

98 

.15 

127 

.156 

180 

201 

221 

.20 

226 

278 

321 

360 

393 

.25 

354 

434 

502 

561 

615 

.30 

505 

624 

722 

807 

884 

188 


BOILERS. 


Pressure  of  Steam  at  Different  Temperatures. 


{Results  of  Experiments  Made  by  the  Franklin  Institute.) 


Pressure. 
Inches  of 
Mercury. 

Tempera- 

ture. 

Degrees  F. 

Pressure. 
Inches  of 
Mercury. 

Tempera- 

ture. 

Degrees  F. 

Pressure. 
Inches  of 
Mercury. 

Tempera- 

ture. 

Degrees  F. 

30 

212.0 

135 

298.5 

225 

331.0 

45 

235.0 

150 

304.5 

240 

336.0 

60 

250.0 

165 

310.0 

255 

340.5 

75 

264.0 

180 

315.5 

270 

345.0 

90 

275.0 

195 

321.0 

285 

349.0 

105 

284.0 

210 

326.0 

300 

352.5 

120 

291.5 

Maximum  Economy  of  Plain  Cylinder  Boilers. 


Pounds  of  Water  Evaporated  From  and  at  212°. 


Per  sq.  ft.  heating 
surface  per  hour 

1.70 

2.00 

2.60 

3.50 

4.00 

4.50 

5.00 

6.00 

7.00 

8.00 

Per  lb.  combustible, 
maximum  of  other 
boilers,  Centennial 
tests  

11.90 

12.00 

12.10 

12.05 

12.00 

11.85 

11.70 

11.50 

10.85 

9.80 

8.50 

Subtract  extra  radia- 

tion loss  for  cylin- 
der boilers 

1.32 

1.12 

.87 

.75 

.64 

.56 

.50 

.45 

.37 

.32 

.28 

Probable  maximum 
per  lb.  combus- 
tible, cylinder 
boilers 

10.58 

10.88 

11.23 

11.30 

11.36 

11.29 

11.20 

11.05 

10.48 

9.48 

8.22 

Scheme  for  Boiler  Test. 


1 

Number  of  test  

2 

Made  by 

3 

Type  of  boiler 

4 

Date  of  test 

-5 

Duration  of  test 

Hr. 

Dimensions  and  Proportions. 

6 

Number  of  boilers  tested  

7 

Diameter,  boiler  

In. 

8 

Length,  boiler 

Ft.  In. 

9 

Width,  grate  

Ft.  In. 

10 

Length,  grate 

Ft.  In. 

11 

Number  of  tubes  

No. 

12 

Diameter  of  tubes 

In. 

13 

Length  of  tubes 

Ft.  In. 

14 

Total  water  heating  surface 

Sq.  Ft. 

15 

Total  steam  heating  surface  

Sq.  Ft. 

16 

Grate  surface  per  boiler 

Sq.  Ft. 

17 

Per  cent,  air  space  in  grate 

18 

Ratio  water  heating  to  grate  surface 

19 

Area  of  stack  

Sq.  Ft. 

20 

Height  stack  above  dead  plates 

Ft. 

21 

Ratio  stack  area  to  grate  surface  

Average  Pressures. 

22 

Atmosphere  by  barometer  

In. 

23 

Steam  pressure  by  gauge  - 

Lb. 

CHIMNEYS. 


189 


Scheme  for  Boiler  {Continued), 


24 

25 

26 
27 
'28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 


39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 


Force  chimney  draft,  inches  water 

Force  blast  in  ash  pit,  inches  water 

Average  Temperatures. 

Of  external  air 

Of  hreroom  

Of  steam  

Of  feedwater  before  heater 

Of  feedwater  after  heater 

Of  stack  gases 

Fuel. 

Kind  of  coal  

Total  coal  consumed 

Moisture  in  coal 

Total  dry  coal  consumed  

Total  ash  and  refuse  

Per  cent,  ash  and  refuse  in  dry  coal  

Total  combustible  consumed 

Calorimetric  Tests. 

Per  cent,  moisture  in  steam 

Degrees  superheat  in  steam 

Water. 

Total  water  pumped  into  boiler 

Water  evaporated  corrected  for  quality  of  steam 

Equiv.  water  evap.  to  dry  steam  from  and  at  212°  

Equiv.  water  evap.  to  dry  steam  from  and  at  212°  per  hour 
Economic  Evaporation. 

Water  evap.  per  lb.  dry  coal  actual  pressures  and  temp 

Equiv.  water  evap.  lb.  dry  coal  from  and  at  212° 

Equiv.  water  evap.  lb.  combustible  from  and  at  212° 

Rate  of  Combustion. 

Dry  coal  burned  per  hr.  per  sq.  ft.  grate  surface  

Combustible  burned  per  hr.  per  sq.  ft.  grate  surface  

Dry  coal  per  hour  per  H.  P.  developed  

Rate  of  Evaporation. 

Water  evap.  from  and ) Per  sq.  ft.  grate  surface  

at  212°  per  hour /Per  sq.  ft.  heating  surface 

Commercial  Horsepower. 

Basis  20  lb.  water  from  100°  feed  to  70  lb.  steam  per  hour.... 

Horsepower  builders  rating 

Heating  surface  to  one  horsepower  developed 

Per  cent,  total  horsepower  due  to  feed  heater. 


In. 

In. 

OF 

OF 

OF 

OF 

OF 

OF 


Lb. 


Lb. 

Lb. 


Lb. 


Lb. 

Lb. 

Lb. 

Lb. 

Lb. 

Lb. 

Lb. 

Lb. 

Lb. 

Lb. 

Lb. 

Lb. 

H.  P. 
H.  P. 

Sq.  Ft. 

fo 


CHIMNEYS. 

Chimneys  have  two  important  duties  to  perform,  the  first  being  to  carry 
otF  the  waste  furnace  ^ases,  which  requires  size,  and  the  second,  to  produce 
a draft  sufficient  to  insure  the  complete  combustion  of  the  fuel,  which 
requires  height.  The  area  of  a chimney  is  usually  made  from  f to  as  large 
as  the  area  of  the  furnace  grates,  or  of  about  the  same  cross-section  as  the 
cross-sectional  area  of  the  flues  or  tubes;  we  have,  therefore,  a comparatively 
simple  method  of  determining  one  of  the  required  dimensions  of  a chimney, 
and,  when  this  is  known,  it  becomes  an  easy  matter  to  determine  the  height 
of  the  chimney  when  the  horsepower  of  the  boiler  has  been  ascertained. 

The  horsepower  of  a boiler  being  given,  and  the  necessary  chimney  area 
having  been  determined,  the  following  rule  gives  the  required  height  that 
the  chimney  must  be  to  produce  the  necessary  draft: 

Rule.— From  3.33  times  the  area  of  the  chimney  in  square  feet,  subtract  twice  the 
square  root  of  the  area  of  the  chimney  in  square  feet,  and  divide  the  given  horsepower 
by  the  remainder.  The  square  of  tlie  quotient  will  be  the  height  of  the  chimney  in  feet. 

Let  A = area  of  chimney; 

H ==  horsepower  of  boiler; 
h = height  of  chimney. 

( — 

\ 3.33  4 -2/^/ 


Then, 


190 


STEAM  ENGINES. 


Example.— What  must  be  the  height  of  a chimney  that  is  to  have  a cross- 
sectional  area  of  7 sq.  ft.,  and  to  supply  the  draft  for  a 141-horsepower  boiler  ? 

h = ( ^ — t=Y= 

\3.33  X 7 — 2l/  7 / \3.33  X 7 — (2  X 2.65)  J 

Forced  Draft.— The  use  of  forced  draft  as  a substitute  for,  or  as  an  aid  to, 
natural  chimney  draft  is  becoming  quite  common  in  large  boiler  plants. 
Its  advantages  are  that  it  enables  a boiler  to  be  driven  to  its  maximum 
capacity  to  meet  emergencies  without  reference  to  the  state  of  the  weather 
or  to  the  character  of  the  coal;  that  the  draft  is  independent  of  the  tempera- 
ture of  the  chimney  gases,  and  that  therefore  lower  flue  temperatures  may 
be  used  than  with  natural  draft;  and  in  many  cases  that  it  enables  a poorer 
quality  of  coal  to  be  used  than  is  required  with  natural  draft.  Forced  draft 
may  be  obtained:  First,  by  a steam  jet  in  the  chimney,  as  in  locomotives  and 
steam  fire-engines;  second,  by  a steam-jet  blower  under  the  grate  bars; 
third,  by  a fan  blower  delivering  air  under  the  grate  bars,  the  ash-pit  doors 
being  closed;  fourth,  by  a fan  blower  delivering  air  into  a closed  flreroom, 
as  in  the  “ closed  stoke-hold  ” system  used  in  some  ocean-going  vessels;  and 
fifth,  by  a fan  placed  in  the  flue  or  chimney  drawing  the  gases  of  combustion 
from  the  boilers,  commonly  called  the  induced-drajt  system.  Which  one  of 
these  several  systems  should  be  adopted  in  any  special  case  will  usually 
depend  on  local  conditions.  The  steam  jet  has  the  advantage  of  lightness 
and  compactness  of  apparatus,  and  is  therefore  most  suitable  for  locomotives 
and  steam  fire-engines,  but  it  also  is  the  most  wasteful  of  steam,  and  there- 
fore should  not  be  used  when  one  of  the  fan-blower  systems  is  available, 
except  for  occasional  or  temporary  use,  of  when  very  cheap  fuel,  such  as 
anthracite  culm  at  the  coal  mines,  is  used. 


STEAM  ENGINES. 

What  Is  a Good  Steam  Engine?— It  should  be  as  direct  acting  as  possible; 
that  is,  the  connecting  parts  between  the  piston  and  the  crank-shaft  should 
be  few  in  number,  as  each  part  wastes  some  power.  Formerly,  beam 
engines  were  all  the  rage.  They  were  well  enough  in  their  time  for  pump- 
ing, when  the  pump  Avas  at  one  end  of  the  beam  and  the  piston  at  the  other. 
Few  of  our  modern  colliery  engines  have  such  an  appendage,  except  in 
some  instances  for  pumping,  and  even  for  that  kind  of  work  the  better 
engines  have  no  beams.  The  moving  parts  of  an  engine  should  be  strong,  to 
resist  strains,  and  light,  so  as  to  offer  no  undue  resistance  to  motion;  parts 
moving  upon  each  other  should  be  well  and  truly  and  smoothly  finished,  to 
reduce  resistances  to  a minimum;  the  steam  should  get  into  the  cylinder 
easily  at  the  proper  time,  and  the  exhaust  should  leave  the  cylinder  as 
exactly  and  as  easily.  The  steam  pipes  supplying  steam  should  have 
an  area  one-tenth  the  combined  areas  of  the  cylinders  they  supply,  and 
exhaust  pipes  should  be  somewhat  larger.  The  cylinder  and  the  steam  pipes 
and  the  boiler  should  be  well  protected.  The  engine  should  be  capable  of 
being  started  and  stopped  and  reversed  easily  and  quickly. 

Rule. — To  find  the  indicated  horsepower  developed  by  an  engine,  multiply 
together  the  M.  E.  P.  per  square  inch,  the  area  of  the  piston,  the  length  of  stroke, 
and  the  number  of  strokes  per  minute.  This  gives  the  work  per  minute  in  foot- 
pounds. Divide  the  product  by  33,000;  the  result  will  be  the  indicated  horse- 
power of  the  engine. 

Let  I.  H.  P.  = indicated  horsepower  of  engine; 

P = M.  E.  P.  in  pounds  per  square  inch; 

A = area  of  piston  in  square  inches; 

L = length  of  stroke  in  feet; 

N = number  of  strokes  per  minute. 

Then,  the  above  rule  may  be  expressed  thus: 


I.  H.  P.  = 


PLAN 
33,000  ‘ 


The  number  of  strokes  per  minute  is  twice  the  number  of  revolutions  per 
minute.  For  example,  if  an  engine  runs  at  a speed  of  210  revolutions  per 
minute,  it  makes  420  strokes  per  minute.  A few  types  of  engines,  however, 
are  single  acting;  that  is,  the  steam  acts  on  only  one  side  of  the  piston. 
In  this  case,  only  1 stroke  per  revolution  does  work,  and,  consequently,  the 


RULES  FOR  ENGINE  DRIVERS. 


191 


number  of  strokes  per  minute  to  be  used  in  the  above  rule  is  the  same  as  the 
number  of  revolutions  per  minute. 

Example.— The  diameter  of  the  piston  of  an  engine  is  10  in.  and  the 
length  of  stroke  15  in.  It  makes  250  revolutions  per  minute,  with  a M.  E.  P. 
of  40  lb.  per  sq.  in.  What  is  the  horsepower  ? 

As  it  is  not  stated  whether  the  engine  is  single  or  double  acting,  assume 
that  it  is  double  acting.  Then,  the  number  of  strokes  is  250  X 2 = 500  per 
minute.  Hence, 

PXJiV^_40XlfX  (10-  X .7854)  X 500  _ 59  5 g p 
1.  H.  P.  33^000  33,000 

Approximate  Determination  of  M.  E.  P.— To  approximately  determine  the 
M.  E.  P.  of  an  engine,  when  the  point  of  apparent  cut-otf  is  known  and  the 
boiler  pressure,  or  the  pressure  per  square  inch  in  the  boiler  from  which 
the  supply  of  steam  is  obtained,  is  given: 

Rule.— Add  14.7  to  the  gauge  pressure,  and  multiply  the  result  by  the  number 
opposite  the  fraction  indicating  the  point  of  cut-off  in  the  following  table.  Subtract 
17  from  the  product,  and  multiply  by  .9.  The  result  is  the  M.  E.  P.  for  good, 
simple  non-condensing  engines. 

Or,  letting 

p = gauge  pressure; 
k — & constant  (see  following  table); 

M.  E.  P.  = mean  effective  pressure. 

Then,  M.  E.  P.  = .9[A:(p  + 14.7)  - 17]. 


Table. 


Cut-Off. 

Constant. 

Cut-Off. 

Constant. 

Cut-Off. 

Constant. 

.566 

f 

.771 

2 

.917 

.603 

.4 

.789 

.7 

.926 

.659 

h 

.847 

.937 

.3 

.708 

.6 

.895 

.8 

.944 

.743 

6 

s 

.904 

7 

s 

.951 

If  the  engine  is  a simple  condensing  one,  subtract  the  pressure  in  the 
condenser  instead  of  17.  The  fraction  indicating  the  point  of  cut-off  is 
obtained  by  dividing  the  distance  that  the  piston  has  traveled  when  the 
steam  is  cut  off  by  the  whole  length  of  the  stroke.  For  a f cut-off,  and  92  lb. 
gauge  pressure  in  the  boiler,  the  M.  E.  P.  is,  by  the  formula  just  given, 
.9 [.917(92  -P  14.7)  — 17]  = 72.6  lb.  per  sq.  in. 

Example. — Find  the  approximate  1.  H.  P.  of  a 9"  X 12"  non-condensing 
engine,  cutting  off  at  i stroke,  and  making  240  revolutions  per  minute.  The 
boiler  pressure  is  80  lb.  gauge. 

80  + 14.7  = 94.7.  The  constant  for  i cut-off  is  .847,  and  .847  X boiler 
pressure  = .847  X 94.7  = 80.21.  M.  E.  P.  = (80.21  — 17)  X .9  = 56.89  lb.  per 
sq.  in.  Then, 

PLAN_  56.89  X if  X (.7854  X 92)  X 240  X 2 

“ "Wor  “ “ "^poo  “ 


RULES  FOR  ENGINE  DRIVERS. 

If  a gauge  glass  breaks,  turn  off  the  water  first  and  then  the  steam,  to 
avoid  scalding  yourself. 

Don’t  buy  oil  or  waste  simply  because  it  is  very  cheap;  it  will  cost  more 
than  a good  article  in  the  end. 


192 


STEAM  ENGINES. 


In  cutting  rubber  for  gaskets,  etc.,  have  a dish  of  water  handy,  and  keep 
wetting  the  knife  blade;  it  makes  the  work  much  easier. 

Don’t  forget  that  there  is  no  economy  in  employing  a poor  fireman.  He 
can,  and  probably  will,  waste  more  coal  than  would  pay  the  wages  of  a first- 
class  man. 

An  ordinary  steam  engine  having  two  cylinders  connected  at  right  angles 
on  the  same  shaft  consumes  one-third  more  steam  than  a single-cylinder 
engine,  while  developing  only  the  same  amount  of  power. 

A fusible  plug  ought  to  be  renewed  every  three  months,  by  removing  the 
old  metal  and  refilling  the  case;  and  it  should  be  scraped  clean  and  bright 
on  both  ends  every  time  that  the  boiler  is  washed  out,  to  keep  it  in  good 
working  order. 

When  you  try  a gauge-cock,  don’t  jerk  it  open  suddenly,  for  if  the  water 
happens  to  be  a trifle  below  the  cock,  the  sudden  relief  from  pressure  at  that 
point  may  cause  it  to  lift  and  flow  out,  deceiving  you  in  regard  to  its  height. 
Whereas,  if  you  open  it  quietly,  no  lift  will  occur,  and  you  ascertain  surely 
whether  there  is  water  or  steam  at  that  level. 

Always  open  steam  stop-valves  between  boilers  very  gently,  that  they 
may  heat  and  expand  gradually.  By  suddenly  turning  on  steam  a stop- 
valve  chest  was  burst,  due  to  the  expansive  power  of  heat  unequally 
applied.  The  same  care  is  also  recommended  when  shutting  off  stop- valves. 
A fearful  explosion  once  occurred  by  shutting  a communicating  stop-valve 
too  suddenly— due  to  the  recoil. 

In  order  to  obtain  the  driest  possible  steam  from  a boiler,  there  should  be 
an  internal  perforated  pipe  (dry  pipe,  so  called)  fixed  near  the  top  of  the 
boiler,  and  suitably  connected  to  the  steam  pipe.  The  perforations  in  this 
pipe  should  be  from  one-quarter  to  one-half  greater  in  area  than  that  of  the 
steam  pipe.  Domes  are  of  no  use  as  steam  driers;  they  only  add  a very  little 
to  the  steam  space  of  a boiler,  and  are  often  a source  of  loss  by  radiation. 

If  a glass  gauge  tube  is  too  long,  take  a triangular  file  and  wet  it  with 
turpentine;  hold  the  tube  in  the  left  hand,  with  the  thumb  and  forefinger  at 
the  place  where  you  wish  to  cut  it,  saw  it  quickly  and  lightly  two  or  three 
times  with  the  edge  of  the  file,  and  it  will  mark  the  glass.  Now  take  the 
tube  in  both  hands,  both  thumbs  being  on  the  side  opposite  the  mark,  and 
an  ineh  or  so  apart,  and  then  try  to  bend  the  glass,  using  your  thumbs  as 
fulcrums,  and  it  will  break  at  the  mark,  Avhich  has  weakened  the  tube. 

A stiff  charge  of  coal  all  over  a furnace  will  lower  the  temperature  200° 
or  300°  in  a very  short  time.  After  the  coal  is  well  ignited  the  temperature 
will  rise  about  500°,  and  as  it  continues  burning  will  gradually  drop  about 
200°,  until  the  fireman  puts  in  another  charge,  when  the  sudden  fall  before 
mentioned  takes  place  again.  This  sudden  contraction  and  expansion 
frequently  causes  the  bursting  of  a boiler,  and  it  is  for  this  reason  that  light 
and  frequent  charges  of  coal,  or  else  firing  only  one-half  of  the  furnace  at  a 
time,  should  be  always  insisted  on. 

Be  careful  when  using  a wrench  on  hexagonal  nuts  that  it  fits  snugly,  or 
the  edges  of  the  nut  will  soon  become  rounded. 

Be  careful  how  you  use  a monkey  wrench,  for  if  it  is  not  placed  on  the  nut 
properly  the  strain  will  o'ften  bend  or  fracture  the  wrench. 

The  area  of  grate  for  a boiler  should  never  be  less  than  ^ sq.  ft.  per  I.  H.  P. 
of  the  engine,  and  it  is  seldom  advisable  to  increase  this  allowance  beyond 
i sq.  ft.  per  I.  H.  P. 

The  area  of  tube  surface  for  a boiler  should  not  be  less  than  2^  sq.  ft.  per 
I.  H.  P.  of  the  engine. 

The  ratio  of  heating  surface  to  grate  area  in  a boiler  should  be  30  to  1 as  a 
minimum,  and  may  often  be  increased  to  40  to  1,  or  even  more,  with 
advantage. 

Lap-welded  pipe  of  the  same  rated  size  has  always  the  same  outside 
diameter,  whether  common,  extra,  or  double  extra,  but  the  internal  diame- 
ter is  of  course  decreased  with  the  increased  thickness. 

A good  cement  for  steam  and  water  joints  is  made  by  taking  10  parts,  by 
weight,  of  white  lead,  3 parts  of  black  oxide  of  manganese,  1 part  of  litharge, 
and  mixing  them  to  the  proper  consistency  with  boiled  linseed  oil. 

To  harden  a cutting  tool,  heat  it  in  a coke  fire  to  a blood-red  heat  and 
plunge  it  into  a solution  of  salt  and  water  (1  lb.  of  salt  to  1 gal.  of  water), 
then  polish  the  tool,  heat  it  over  gas,  or  otherwise,  until  a dark  straw  and 
purple  mixed  color  shows  on  the  polish,  and  cool  it  in  the  salt  water. 

Small  articles  can  be  plated  with  brass  by  dipping  them  in  a solution  of 
9i  gr.  each  of  sulphate  of  copper  and  chloride  of  tin,  in  1?  pt.  of  water. 


BELTING  AND  VELOCITY  OF  PULLEYS. 


193 


Don;t  be  eternally  tinkering  about  your  engine,  but  let  well  enough 
alone. 

Don’t  forget  that  with  a copper  hammer  you  can  drive  a key  just  as  well 
as  with  a steel  one,  and  that  it  doesn’t  leave  any  marks. 

Keep  on  hand  slips  of  thin  sheet  copper,  brass,  and  tin,  to  use  as  liners, 
and  if  you  shape  some  of  them  properly,  much  time  will  be  saved  when  you 
need  them. 

A few  wooden  skewer  pins,  such  as  butchers  use,  are  very  useful  for 
many  purposes  in  an  engine  room.  Try  them. 

In  running  a line  of  steam  pipe  where  there  are  certain  rigid  points, 
make  arrangements  for  expansion  on  the  line  between  those  points,  or  you 
will  come  to  grief. 

Arrange  the  usual  work  of  the  engine  and  firerooms  systematically,  and 
adhere  to  it.  It  pays  well. 

Don’t  forget  that  cleanliness  is  next  to  godliness. 

Rubber  cloth  kept  on  hand  for  joints  should  be  rolled  up  and  laid  away 
by  itself,  as  any  oil  or  grease  coming  in  contact  with  it  will  cause  it  to  soften 
and  give  out  when  put  to  use. 

When  using  a jet  condenser,  let  the  engine  make  three  or  four  revolutions 
before  opening  the  injection  valve,  and  then  open  it  gradually,  letting  the 
engine  make  several  more  revolutions  before  it  is  opened  to  the  full  amount 
required. 

Open  the  main  stop-valve  before  you  start  the  fires  under  the  boilers. 

When  starting  fires,  don’t  forget  to  close  the  gauge-cocks  and  safety  valve 
as  soon  as  steam  begins  to  form. 

An  old  Turkish  towel,  cut  in  two  lengthwise,  is  better  than  cotton  waste 
for  cleaning  brass  work. 

Always  connect  your  steam  valves  in  such  a manner  that  the  valve 
closes  against  the  constant  steam  pressure. 

Turpentine  well  mixed  with  black  varnish  makes  a good  coating  for  iron 
smoke  pipes. 

Ordinary  lubricating  oils  are  not  suitable  for  use  in  preventing  rust. 

You  can  make  a hole  through  glass  by  covering  it  with  a thin  coating  of 
wax,  warming  the  glass  and  spreading  the  wax  on  it.  Scrape  oif  the  wax 
where  you  want  the  hole,  and  drop  a little  fluoric  acid  on  the  spot  with  a 
wire.  The  acid  will  cut  a hole  through  the  glass,  and  you  can  shape  the 
hole  with  a copper  wire  covered  with  oil  and  rottenstone. 

A mixture  of  1 oz.  of  sulphate  of  copper,  i oz.  of  alum,  | teaspoonful  of 
powdered  salt,  1 gill  of  vinegar  and  20  drops  of  nitric  acid  will  make  a hole 
in  steel  that  is  too  hard  to  cut  or  file  easily.  Also,  if  applied  to  steel  and 
washed  off  quickly,  it  will  give  the  metal  a beautiful  frosted  appearance. 


BELTING  AND  VELOCITY  OF  PULLEYS. 

Belts  should  not  be  made  tighter  than  necessary.  Over  half  the  trouble 
from  broken  pulleys,  hot  boxes,  etc.  can  be  traced  to  the  fault  of  tight  belts, 
while  the  machinery  wears  much  more  rapidly  than  when  loose  belts  are 
employed. 

The  speed  of  belts  should  not  be  more  than  3,000  or  3,750  ft.  per  minute. 

The  motion  of  driving  should  run  with  and  not  against  the  laps  of  the 
belts. 

Leather  belts  should  be  run  with  the  stronger  or  flesh  side  on  the  outside 
and  the  grain  (hair)  side  on  the  inside,  nearest  the  pulley,  so  that  the 
stronger  part  of  the  belt  may  be  subject  to  the  least  wear.  It  will  also  drive 
30^  more  than  if  run  with  the  flesh  side  nearest  the  pulley.  The  grain  side 
adheres  better  because  it  is  smooth.  Do  not  expose  leather  belts  to  the 
weather. 

When  the  length  of  a belt  cannot  be  conveniently  ascertained  by 
measuring  around  the  pulleys  with  a tape  line,  the  following  rule  will  be 
serviceable! 

Add  the  diameters  of  the  2 pulleys  together  and  divide  by  2;  multiply 
this  quotient  by  31,  and  to  the  product  add  twice  the  distance  between  the 
centers  of  the  shafts;  the  sum  will  be  the  length  required. 


194 


COMPRESSED  AIR. 


COMPRESSED  AIR* 

By  Prof.  Robert  Peele. 


An  air  compressor  consists  essentially  of  a cylinder  in  which  atmospheric 
air  is  compressed  by  a piston,  the  driving  power  being  steam  or  water. 

Classification  of  Compressors.— Steam-driven  compressors  in  ordinary  use 
may  be  classed  as  follows: 

(а)  Straight-line  type,  in  which  a single  horizontal  air  cylinder  is  set 
tandem  with  its  steam  cylinder,  and  provided  with  two  flywheels.  This 
pattern  is  generally  adapted  for  compressors  of  small  size. 

(б)  Duplex  type,  in  which  there  are  two  steam  cylinders,  each  driving  an 
air  cylinder,  and  coupled  at  90°  to  a crank-shaft  carrying  a flywheel. 

(c)  Horizontal,  cross-compound  engines,  each  steam  cylinder  set  tandem 
with  an  air  cylinder,  as  in  (6). 

{d)  Vertical,  simple,  or  compound  engines,  with  the  air  cylinders  set 
above  the  steam  cylinders. 

(e)  Compound  or  stage  compressors,  in  which  the  air  cylinders  themselves 
are  compounded.  The  compression  is  carried  to  a certain  point  in  one 
cylinder  and  successively  raised  and  Anally  completed  to  the  desired  pres- 
sure in  the  others.  They  may  be  either  of  the  straight-line  or  duplex  form, 
with  simple  or  compound  steam  cylinders. 

Classes  (a),  (&),  (c),  and  {e)  are  those  commonly  employed  for  mine 
service.  The  principle  of  compound,  or  two-stage,  air  compression  is 
recognized  as  applicable  for  even  the  moderate  pressures  required  in 
mining,  and  the  compressors  of  class  (e)  are  frequently  employed. 

Construction  of  Compressors.— Compressors  are  usually  built  with  a short 
stroke,  as  this  is  conducive  to  economy  in  compression  as  well  as  the  attain- 
ment of  a proper  rotative  speed.  In  ordinary  single-stage  compressors,  the 
usual  ratio  of  length  of  stroke  to  diameter  of  steam  cylinders  is  1^  to  1 or  1^ 
to  1.  In  some  makes,  such  as  the  Rand,  the  ratio  is  considerably  greater, 
varying  from  to  If  to  1,  as  in  several  large  plants  built  for  the  Calumet 
& Hecla  Mining  Co.  Many  compressors  have  length  and  diameter  of  steam 
cylinders  equal.  The  relative  diameters  of  the  air  and  steam  cylinders 
depend  on  the  steam  pressure  carried,  and  the  air  pressure  to  be  produced. 
In  mining  operations,  there  is  usually  but  little  variation  in  these  con- 
ditions. For  rock-drill  work,  the  air  pressure  is  generally  from  60  to  80  lb. 

In  using  water-power,  a compressor  is  driven  most  conveniently  by  a 
bucket  impact  wheel,  such  as  the  Pelton  or  Knight.  The  waterwheel  is 
generally  mounted  directly  on  the  crank-shaft,  without  the  use  of  gearing. 
Since  the  power  developed  is  uniform  throughout  the  revolution  of  the 
wheel,  the  compressor  should  be  of  duplex  form,  in  order  to  equalize  the 
resistance  so  far  as  possible.  The  rim  of  the  wheel  is  made  extra  heavy,  to 
supply  the  place  of  a flywheel.  When  direct-connected,  the  wheel  is  of 
relatively  large  diameter,  as  its  speed  of  rotation  must  of  necessity  be  slow. 
With  small  high-speed  wheels,  the  compressor  cylinders  may  be  operated 
through  belting  or  gearing.  In  most  cases,  however,  the  waterwheel  may 
be  large  enough  to  render  gearing  unnecessary.  Impact  wheels  may  be 
employed  with  quite  small  heads  of  water,  by  introducing  multiple  nozzles. 
To  prevent  the  water  from  splashing  over  the  compressor,  the  wheel  is 
enclosed  in  a tight  iron  or  wooden  casing.  The  force  of  the  water  is  regu- 
lated usually  by  an  ordinary  gate  valve.  If  the  head  be  great,  it  may  be 
necessary  to  introduce  means  for  deflecting  the  nozzle,  so  that,  when  the 
compressor  is  to  be  stopped  suddenly,  danger  of  rupturing  the  water 
main  will  be  avoided. 

Theory  of  Air  Compression.— The  useful  effect  or  efficiency  of  a compressor  is 
the  ratio  of  the  force  stored  in  the  compressed  air  to  the  work  that  has  been 
expended  in  compressing  it.  This  probably  never  reaches  80;^,  and  often 
falls  below  60/c. 


*See  ‘.‘Mines  and  Minerals,”  Vols.  XIX  and  XX,  for  complete  discussion  of  this  subject  by  the 
same  author. 


RATING  OF  COMPRESSORS. 


195 


Free  air  is  air  at  ordinary  atmospheric  pressure  as  taken  into  the  com- 
pressor cylinder.  As  commonly  used,  this  means  air  at  sea-level  pressure 
(14.7  lb.  per  sq.  in.)  at  60°  F. 

The  absolute  pressure  of  air  is  measured  from  zero,  and  is  equal  to  the 
assumed  atmospheric  pressure  plus  gauge  pressure.  Air-compression  calcu- 
lations depend  on  the  two  well-known  laws: 

1.  Boyle's  Law. — The  temperature  being  constant,  the  volume  varies 
inversely  as  the  pressure;  or  P F = P'  F'  = a constant;  in  which  F equals 
volume  of  given  weight  of  air  at  the  freezing  point,  and  the  pressure  P;  V' 
equals  the  volume  of  the  same  weight  of  air  at  the  same  temperature  and 
under  the  pressure  P'. 

2.  Gay-Lussac's  Law.  —The  volume  of  a gas  under  constant  pressure,  when 
heated,  expands,  for  each  degree  of  rise  in  temperature,  hy  a constant  pro- 
portional part  of  the  volume  that  it  occupied  at  the  freezing  point;  or, 
F'  = V {1  P a t°),  in  which  a equals  5^3  for  centigrade  degrees,  or  for 
Fahrenheit  degrees. 

Theoretically,  air  may  be  compressed  in  two  ways,  as  follows: 

1.  Isothermally,  when  the  temperature  is  kept  constant  during  compres- 
sion, and  in  this  case,  the  formula  P F = P'  F'  is  true. 

2,  Adidbatically,  when  the  temperature  is  allowed  to  rise  without  check 
during  the  compression. 

Since  the  pressure  rises  faster  than  the  volume  diminishes,  the  equation 

P'  / F 

P F = P'  F'  no  longer  holds,  and  we  have  = ( pv  ) » which  n equals 

1.406.  The  specific  heat  of  air  at  constant  pressure  is  .2375,  and  at  constant 
2375 

volume  .1689,  and  n = = 1.406. 

* iuoy 

In  practice,  compression  is  neither  isothermal  nor  adiabatic,  but  inter- 
mediate between  the  two.  The  values  of  n for  different  conditions  in 
practice  are  as  follows,  as  determined  from  a 2,000-horsepower  stage  com- 
pressor at  Quai  de  la  Gare,  Paris. 

For  purely  adiabatic  compression,  with  no  cooling  arrangements, 
n = 1.406;  in  ordinary  single-cylinder  dry  compressors,  provided  with  a 
water-jacket,  n is  roughly  1.3;  while  in  the  best  wet  compressors  (with  spray 
injection),  n becomes  1.2  to  1.25.  In  the  poorest  forms  of  compressor,  the 
value  n = 1.4  is  closely  approached.  For  large,  well-designed  compressors 
with  compound  air  cylinders,  the  exponent  n may  be  as  small  as  1.15. 

Rating  of  Compressors. — Compressors  are  rated  as  follows:  (1)  In  terms  of 
the  horsenower  developed  by  the  steam  end  of  the  compressor,  as  shown  bv 
indicator  cards  taken  when  running  at  full  speed,  and  when  the  usual 
volume  of  air  is  being  consumed.  (2)  Compressors  for  mines  are  often 
rated  roughly  as  furnishing  sufficient  air  to  operate  a certain  number  of  rock 
drills;  a 3"  drill  requires  a volume  of  air  at  60  lb.  pressure,  equal  to  100  or 
110  cu.  ft.  of  free  atmospheric  air  per  minute.  (3)  In  terms  of  cubic  feet  of 
free  air  compressed  per  minute  to  a given  pressure. 

As  the  actual  capacity  of  a compressor  depends  on  the  density  of  the 
intake  air,  it  will  obviously  be  reduced  in  working  at  an  altitude  above  sea 
level,  because  of  the  diminished  density  of  the  atmosphere.  The  following 
table  gives  the  percentages  of  output  at  different  elevations: 

Example.— Calculate  the  volume  of  air 
furnished  by  an  18"  X 24"  compressor  work- 
ing at  an  elevation  of  5,000  ft.  above  sea 
level,  revolving  95  times  per  minute,  and 
having  a piston  speed  of  380  ft.  per  minute. 
92  X 3.14  = 254.3  sq.  in.  = piston  area. 

X 380  = 668.8  cu.  ft.  = volume  dis- 
placed per  minute  by  the  piston;  deducting 
lO/o  for  loss  gives  602  cu.  ft.  At  sea  level  at 

15 

80  lb.  gauge  pressure,  this  equals  — — X 

602  = 95  cu.  ft.  At  an  elevation  of  5,000 
ft.,  the  output  of  a compressor  would  be 
95  X 85^  = 80.7  cu.  ft.  per  minute. 

Cooling.— Compressor  cylinders  may  be 
cooled  by  either  of  the  following  methods: 


Altitude. 

Feet. 

Atmospheric 

Pressure. 

Pounds. 

Percentages 
of  Output 
at  Sea  Level. 

0 

14.7 

100.0 

1,000 

14.2 

97.2 

2,000 

13.6 

93.5 

3,000 

13.1 

90.8 

4,000 

12.7 

88.4 

5,000 

12.2 

85.0 

6,000 

11.7 

82.0 

7,000 

11.3 

79.3 

8,000 

10.9 

77.0 

9,000 

10.5 

75.0 

10,000 

10.1 

72.0 

196 


COMPRESSED  AIR. 


(1)  by  injecting  water  into  the  cylinder,  known  as  wet  compressors;  or  (2)  by 
jacketing  the  cylinder  in  water,  known  as  dry  compressors. 

Dry  Versus  Wet  Compressors.— Up  to  about  the  year  1885  there  seemed  to 
be  little  doubt  among  mechanical  engineers  that  wet  compressors  were,  on 
the  whole,  superior  to  dry,  because,  by  bringing  the  air  into  direct  contact 
with  water,  the  heat  is  most  effectually  absorbed.  This  view  is  correct,  so 
far  as  heat  loss  alone  is  concerned,  provided  the  water  in  the  cylinder  is 
properly  applied.  But  the  question  of  heat  loss  is  not  the  only  consideration. 
Low  first  cost  and  simplicity  of  construction  are  often  more  advantageous 
than  a close  approximation  to  isothermal  compression.  Latterly,  the  wet 
system  has  lost  ground,  owing  to  the  fact  that  moisture  is  objectionable  in 
the  air,  as  it  forms  frost  in  the  exhaust  ports  of  the  drills,  and  stops  them  up, 
and  probably  no  wet  compressors  are  now  being  built  in  the  United  States. 
In  Europe,  also,  dry  compressors  have  grown  in  favor,  at  least  for  mining 
plants  and  others  of  moderate  size. 


TRANSMISSION  OF  AIR  IN  PIPES. 


The  actual  discharge  capacity  of  piping  is  not  proportional  to  the  cross- 
sectional  area  alone,  that  is,  to  the  square  of  the  diameter.  Although  the 
periphery  is  directly  proportional  to  the  diameter,  the  interior  surface 
resistance  is  much  greater  in  a small  pipe  than  in  a large  one,  because,  as 
the  pipe  becomes  smaller,  the  ratio  of  perimeter  to  area  increases. 

To  pass  a given  volume  of  compressed  air,  a 1"  pipe  of  given  length  re- 
quires over  three  times  as  much  head  as  a 2"  pipe  of  the  same  length. 
The  character  of  the  pipe,  also,  and  the  condition  of  its  inner  surface,  have 
much  to  do  with  the  friction  developed  by  the  flow  of  air.  Besides  imper- 
fections in  the  surface  of  the  metal,  the  irregularities  incident  on  coupling 
together  the  lengths  of  pipe  must  increase  friction.  There  are  so  few  relia- 
ble data  that  the  influences  by  which  the  values  of  some  of  the  factors  may 
be  modified  are  not  fully  understood;  and,  owing  to  these  uncertain  condi- 
tions, the  results  obtained  from  formulas  are  only  approximately  correct. 

Among  the  formulas  in  common  use,  perhaps  the  most  satisfactory  is  that 
of  I)’ Arcy.  As  adopted  for  compressed-air  transmission,  it  takes  the  form: 


= c^^ 


— P2) 


Wil 


in  which  D = volume  of  compressed  air  in  cubic  feet  per  minute  discharged 
at  final  pressure; 

c = coetficient  varying  with  diameter  of  pipe,  as  determined  by 
experiment; 

d = diameter  of  pipe  in  inches  (the  actual  diameters  of  If" 
and  ly'  pipe  are  1.38"  and  1.61",  respectively;  the  nomi- 
nal diameters  of  all  other  sizes  may  be  taken  for  calcu- 
lations); 

I = length  of  pipe  in  feet; 

Pi  = initial  gauge  pressure  in  pounds  per  square  inch; 

P2  = final  gauge  pressure  in  pounds  per  square  inch; 

wi  = density  of  air,  or  its  weight  in  pounds  per  cubic  foot,  at 
initial  pressure  pi. 

The  values  of  the  coefficients  c for  sizes  of  piping  up  to  12"  are: 


1" 

45.3 

5" 

59.0 

9" 

61.0 

2" 

52.6 

6" 

59.8 

10" 

61.2 

3" 

56.5 

7" 

60.3 

11" 

61.8 

4". 

58.0 

8" 

60.7 

12" 

62.0 

Some  apparent  discrepancies  exist  for  sizes  larger  than  9",  but  they  cause 
no  very  material  differences  in  the  results. 

Another  formula,  published  by  Mr.  Frank  Richards,  is  as  follows: 

10,000  D^a 

in  which  H = head  or  difference  of  pressure  required  to  overcome  friction 
and  maintain  the  flow  of  air; 

V = volume  of  compressed  air  delivered  in  cubic  feet  per 
minute; 

L = length  of  pipe  in  feet; 

D = diameter  of  pipe  in  inches; 
o = coefficient,  depending  on  the  size  of  pipe. 


TRANSMISSION  OF  AIR  IN  RIPFS. 


197 


Values  of  a for  nominal  diameters  of  wrought-iron  pipe: 


1" 

350 

3"  

730 

8"  

1.125 

U" 

500 

3F' 

787 

10" 

1.200 

U" - 

662 

4"  

.840 

12" 

1.260 

2"  

565 

5"  

934 

2i" 

650 

6"  

1.000 

The  values  of  a fur  and  li"  pipe  are  not  consistent  with  those  for 
other  sizes,  for  the  reason  stated  above.  In  using  this  formula  with  its 
constants,  the  calculated  losses  of  pressure  are  found  to  be  smaller,  and, 
conversely,  the  volumes  of  air  discharged  are  larger,  under  the  same  condi- 
tions, than  those  obtained  from  D’Arcy’s  formula. 

It  must  be  remembered  that,  within  certain  limits,  the  loss  of  head  or 
pressure  increases  with  the  square  of  the  velocity.  To  obtain  the  best  results, 
it  is  found  in  practice  that  the  velocity  of  flow  in  the  main  air  pipes  should 
not  exceed  20  or  25  ft.  per  second.  When  the  initial  velocity  much  exceeds 
50  ft.  per  second,  the  percentage  loss  becomes  very  large;  and,  conversely, 
by  using  piping  large  enough  to  keep  down  the  velocity,  the  friction  loss 
may  be  almost  eliminated.  For  example,  at  the  Hoosac  tunnel,  in  transmit- 
ting 875  cu.  ft.  of  free  air  per  minute,  at^an  initial  pressure  of  60  lb.,  through 
an  8"  pipe,  7,150  ft.  long,  the  average  loss  including  leakage  was  only  2 ib. 
A volume  of  500  cu.  ft.  of  free  air  per  minute,  at  75  lb.,  can  be  transmitted 
through  1,000  ft.  of  3"  pipe  with  a loss  of  4.1  lb.,  while  if  a 5"  pipe  were  used 
the  loss  would  be  reduced  to  .24  lb.  The  velocity  of  flow  in  the  latter  case 
is  only  10  ft.  per  second. 

In  driving  the  Jeddo  mining  tunnel,  at  Ebervale,  Pa.,  two  31"  drills  were 
used  in  each  heading,  with  a 6"  main,  the  maximum  transmission  distance 
being  10,800  ft.  This  pipe  was  so  large  in  proportion  to  the  volume  of  air 
required  for  the  drills  (230  cu.  ft.  free  air  per  minute)  that  the  loss  was 
reduced  to  an  extremely  small  quantity.  A calculation  shows  a loss  of 
.002  lb.,  and  the  gauges  at  each  end  of  the  main  were  found  to  record 
practically  the  same  pressure. 

A due  regard  for  economy  in  installation,  however,  must  limit  the  use  of 
very  large  piping,  the  cost  of  which  should  be  considered  in  relation  to  the 
cost  of  air  compression  in  any  given  case.  Diameters  of  from  4 to  6 in.  for 
the  mains  are  large  enough  for  any  ordinary  mining  practice.  Up  to  a 
length  of  3,000  ft.,  a 4"  pipe  will  carry,  per  minute,  480  cu.  ft.  of  free  air 
compressed  to  82  lb.,  with  a loss  of  2 lb.  pressure.  This  volume  of  air  will 
run  four  3"  drills.  Under  the  same  conditions,  a 6"  pipe,  5,000  ft.  long,  will 
carry  1,100  cu.  ft.  of  free  air  per  minute,  or  enough  for  10  drills. 

A mistake  is  often  made  in  putting  in  branch  pipes  of  too  small  a diam- 
eter. For  a distance  of,  say,  100  ft.,  a li"  pipe  is  small  enough  for  a single 
drill,  though  a 1"  pipe  is  frequently  used.  While  it  is,  of  course,  admissible 
to  increase  the  velocity  of  flow  in  short  branches  considerably  beyond  20  ft. 
per  second,  extremes  should  be  avoided.  To  run  a 3"  drill  from  a 1"  pipe 
100  ft.  long,  would  require  a velocity  of  flow  of  about  55  ft.  per  second, 
causing  a loss  of  10  lb.  pressure. 

The  piping  for  conveying  compressed  air  may  be  of  cast  or  wrought  iron. 
If  of  wrought  iron,  as  is  customary,  the  lengths  are  connected  either  by 
sleeve  couplings  or  by  cast-iron  flanges  into  which  the  ends  of  the  pipe 
are  screwed  or  expanded.  Sleeve  couplings  are  used  for  all  except  the 
large  sizes.  The  smaller  sizes,  up  to  li  in.,  are  butt-welded,  while  all  from 
li  in.  up  are  lap-welded,  to  insure  the  necessary  strength.  Wrought-iron 
spiral-seam  riveted  or  spiral-weld  steel  tubing*  is  sometimes  used.  It  is 
made  in  lengths  of  20  ft.,  or  less.  For  convenience  of  transport  in  remote 
regions,  rolled  sheets  in  short  lengths  may  be  had.  They  are  punched 
around  the  edges,  ready  for  riveting,  and  are  packed  closely— 4,  6,  or  more 
sheets  in  a bundle. 

All  joints  in  air  mains  and  branches  should  be  carefully  made.  Air  leaks 
are  more  expensive  than  steam  leaks  because  of  the  losses  already  suffered 
in  compressing  the  air.  The  pipe  may  be  tested  from  time  to  time  by  allow- 
ing the  air  at  full  pressure  to  remain  in  the  pipe  long  enough  to  observe  the 
gauge.  In  case  a leak  is  indicated,  it  should  be  traced  and  stopped  imme- 
diately. In  putting  together  screw  joints,  care  should  be  taken  that  none  of 
the  white  lead  or  other  cementing  material  is  forced  into  the  pipe.  This 
would  cause  obstruction  and  increase  the  friction  loss.  Also,  each  length  as 
put  in  place  should  be  cleaned  thoroughly  of  all  foreign  substances  that  may 
have  lodged  inside.  To  render  the  piping  readily  accessible  for  inspection 


198 


COMPRESSED  AIR. 


and  stoppage  of  leaks,  it  should,  if  buried,  be  carried  in  boxes  sunk  just 
below  the  surface  of  the  ground;  or,  if  underground,  it  should  be  supported 
upon  brackets  along  the  sides  of  the  mine  workings.  Low  points  in  pipe 
lines,  which  would  form  “pockets”  for  the  accumulation  of  entrained 
water,  should  be  avoided,  as  they  obstruct  the  passage  of  the  air.  In  long 
pipe  lines,  where  a uniform  grade  is  impracticable,  provision  may  be  made 
near  the  end  for  blowing  out  the  water  at  intervals,  when  the  air  is  to  be 
used  for  pumps,  hoists,  or  other  stationary  engines. 

For  long  lengths  of  piping,  expansion  joints  are  required,  particularly 
when  on  the  surface.  They  are  hot  often  necessary  underground,  as  the 
temperature  is  usually  nearly  constant,  except  in  shafts,  or  where  there  may 
be  considerable  variations  of  temperature  between  summer  and  winter. 

LOSSES  IN  THE  TRANSMISSION  OF  COMPRESSED  AIR. 

By  E.  Hill,  Norwalk  Iron  Works  Co. 

The  increasing  use  that  is  being  made  of  compressed-air  engines  for  mine 
and  underground  work  stimulates  the  inquiry  regarding  their  efficiency. 

The  situation  is  apparently  very  simple.  An  engine  drives  an  air  com- 
pressor, which  forces  air  into  a reservoir.  The  air  under  pressure  is  led 
through  pipes  to  the  air  engine,  and  is  there  used  after  the  manner  of  steam. 

The  resulting  power  is  frequently  a small  percentage  of  the  power 
expended.  In  a large  number  of  cases  the  losses  are  due  to  poor  designing, 
and  are  not  chargeable  as  faults  of  the  system  or  even  to  poor  workmanship. 

The  losses  are  chargeable,  first,  to  friction  of  the  compressor.  This  will 
amount  ordinarily  to  15^  or  20^,  and  can  be  helped  by  good  workmanship, 
but  cannot  probably  be  reduced  below  10^.  Second,  we  have  the  loss 
occasioned  by  pumping  the  air  of  the  engine  room,  rather  than  air  drawn 
from  a cooler  place.  This  loss  varies  with  the  season,  and  amounts  to  from 
M to  10^.  This  can  all  be  saved.  The  third  loss  or  series  of  losses  arises  in 
tne  compressing  cylinder.  Insufficient  supply,  difficult  discharge,  defective 
cooling  arrangements,  poor  lubrication,  and  a host  of  other  causes,  perplex 
the  designer  and  rob  the  owner  of  power.  The  fourth  loss  is  found  in  the 
pipe.  This  has  heretofore  received  by  no  means  the  consideration  that  the 
subject  demands.  The  loss  varies  with  every  different  situation,  and  is  sub- 
ject to  somewhat  complex  influences.  The  fifth  loss  is  chargeable  to  fall  of 
temperature  in  the  cylinder  of  the  air  engine.  Losses  arising  from  leaks  are 
often  serious,  but  the  remedy  is  too  evident  to  require  demonstration.  No 
leak  can  be  too  small  to  require  immediate  attention.  An  attendant  who 
is  careless  about  packings  and  hose  couplings  will  permit  losses  for  which 
no  amount  of  engineering  skill  can  compensate. 

We  can  only  realize  100^  efficiency  in  the  air  engine,  leaving  friction  out 
of  our  consideration,  when  the  expansion  of  the  air  and  the  changes  of  its 
temperature  in  the  expanding  or  air-engine  cylinder  are  precisely  the 
reverse  of  the  changes  that  have  taken  place  during  the  compression  of  the 
air  in  the  compressing  cylinder.  But  these  conditions  can  never  be  realized. 
The  air  during  compression  becomes  heated,  and  during  expansion  it 
becomes  cold.  If  the  air  immediately  after  compression,  before  the  loss  of 
any  heat,  was  used  in  an  air  engine  and  there  perfectly  expanded  back  to 
atmospheric  pressure,  it  would,  on  being  exhausted,  have  the  same  tem- 
perature it  had  before  compression,  and  its  efficiency  would  be  100^. 

But  the  loss  of  heat  after  compression  and  before  use  cannot  be  pre- 
vented, as  the  air  is  exposed  to  such  very  large  radiating  surfaces  in  the 
reservoir  and  pipes,  on  its  passage  to  the  air  engine.  The  heat,  which 
escapes  in  this  way,  did,  while  in  the  compressing  cylinder,  add  much  to 
the  resistance  of  the  air  to  compression,  and  since  it  is  sure  to  escape,  at 
some  time,  either  in  reservoir  or  pipes,  it  is  evidently  the  best  plan  to 
remove  it  as  fast  as  possible  from  the  cylinder,  and  thus  remove  one  element 
of  resistance.  Hence,  we  find  compressors  are  almost  universally  provided 
with  cooling  attachments  more  or  less  perfect  in  their  action,  the  aim  being 
to  secure  isothermal  compression,  or  compression  having  equal  temperature 
throughout.  Where  the  temperature  rises,  without  check,  during  com- 
pression, the  term  adiabatic  compression  is  employed. 

If  air  compressed  isothermally  is  used  with  perfect  expansion  and  the 
fall  of  temperature  during  expansion  be  prevented,  then  we  will  have  100^ 
efficiency.  But  air  will  grow  cold  on  being  expanded  in  an  engine,  and 
hence  we  conclude  that  warming  attachments  have  the  same  economic 
place  on  an  air  engine  that  cooling  attachments  have  on  an  air  compressor. 
In  fact,  we  find  attachments  of  this  kind  more  particularly  in  large  and 


TRANSMISSION  OF  COMPRESSED  AIR. 


199 


permanently  located  engines,  but,  for  practical  reasons,  their  use  on  most  of 
the  engines  for  mine  work  is  dispensed  with,  and  the  engines  expand  the 
air  adiabatically,  or  without  receiving  heat. 

The  practical  engineer,  therefore,  has  to  deal  with  nearly  isothermal 
compression,  and  nearly  adiabatic  expansion,  and  must  also  consider  that 
the  air  in  reservoirs  and  pipes  becomes  of  the  same  temperature  as  surround- 
ing objects.  Consideration  must  also  be  had  for  the  friction  of  the  com- 
pressor and  the  air  engine.  For  the  pressure  of  60  lb.,  which  is  that  most 
commonly  used,  the  decrease  in  resistance  to  compression  secured  by  the 
cooling  attachments,  is  almost  exactly  equaled  by  the  friction  of  the  com- 
pressor. Hence  it  is  safe,  in  calculating  the  efficiency  of  the  air  engine,  to 
consider  the  compressor  as  being  without  cooling  attachments,  and  also  as 
working  without  friction.  The  results  of  such  calculations  will  be  too  high 
efficiencies  for  light  pressures,  which  are  little  used;  about  correct  for  medium 
pressures,  which  are  commonly  employed;  and  too  low  for  higher  pressures, 
and  will  thus  have  the  advantage  of  not  being  overestimated.  This  result 
is  occasioned  by  the  fact  that,  owing  to  the  slight  heat  in  compressing  low 
pressures  of  air,  the  saving  of  power  by  the  cooling  attachments  is  not 
equal  to  the  friction  of  the  machine,  but  at  high  pressures,  on  account  of  the 
great  heat,  the  cooling  attachments  are  of  great  value  and  save  very  much 
more  power  than  friction  consumes. 

In  the  expanding  engines,  the  expansion  never  falls  as  low  as  the 
adiabatic  law  would  indicate,  owing  to  a number  of  reasons,  but  we  will 
consider  the  expansion  as  being  adiabatic,  as  an  error  in  calculations 
caused  thereby  will  be  on  the  “ safe  side”  and  the  actual  power  will  exceed 
the  calculated  power.  We  therefore  consider  the  compressor  and  engine  as 
following  the  adiabatic  law  of  compression  and  expansion,  and  as  working 
without  friction. 

With  this  view  of  the  case,  the  efficiency  of  an  air  engine,  working  with 
perfect  expansion,  stated  in  percentages  of  the  power  required  to  operate 
the  compressor,  can  be  placed  as  below  for  the  various  pressures  above  the 
atmosphere. 

Pressure  above  the  atmosphere,  2.9  lb.  94.85^  efficiency. 

Pressure  above  the  atmosphere,  14.7  lb.  81.79^  efficiency. 

Pressure  above  the  atmosphere,  29.4  lb.  72.72^  efficiency. 

Pressure  above  the  atmosphere,  44.1  lb.  66.90 efficiency. 

Pressure  above  the  atmosphere,  58.8  lb.  62.70^  efficiency. 

Pressure  above  the  atmosphere,  73.5  lb.  59.48^  efficiency. 

Pressure  above  the  atmosphere,  88.2  lb.  56.88^  efficiency. 

We  observe  that  the  efficiencies  for  the  lower  pressures  are  very  much 
greater  than  for  the  high  pressures,  and  the  conclusion  is  almost  irresistible 
that  to  secure  economical  results  we  must  design  our  air  engines  to  run 
with  light  pressures.  And,  in  fact,  the  consideration  of  tables  similar  to  the 
above,  heretofore  published  by  writers  on  this  subject,  has  led  many 
engineers  into  grave  errors. 

The  pipe  has  been  entirely  neglected.  We  notice  that  a pressure  of  2.9  lb. 
is  credited  with  an  efficiency  of  94.85/c.  It  is  clear  that  if  the  air  were 
conveyed  through  a pipe,  and  the  length  of  the  pipe  and  the  veloeity  of  flow 
were  such  that  2.9  lb.  pressure  was  lost  in  friction,  then  its  efficiency,  instead 
of  being  94.85f  would  be  absolutely  zero.  It  is,  therefore,  the  power  that 
we  can  get  from  the  air,  after  it  has  passed  the  pipe  and  lost  a part  of  its 
pressure  by  friction,  which  we  must  consider  when  we  state  the  efficiency 
of  our  entire  apparatus. 

Our  table  of  efficiencies  with  a loss  of  2.9  lb.  in  the  pipe,  now  gives  us  dif- 
ferent values  for  the  efficiencies  at  the  various  pressures. 

Pressure  above  the  atmosphere,  2.9  lb.  00.00^  efficiency. 

Pressure  above  the  atmosphere,  14.7  lb.  70.44^  efficiency. 

Pressure  above  the  atmosphere,  29.4  lb.  68.81?^  efficiency. 

Pressure  above  the  atmosphere,  44.1  lb.  64.87^  efficiency. 

Pressure  above  the  atmosphere,  58.8  lb.  61.48^  efficiency. 

Pressure  above  the  atmosphere,  73.5  lb.  58.62^  efficiency. 

Pressure  above  the  atmosphere,  88.2  lb.  56.23^  efficiency. 

It  will  be  noticed  that  the  light  pressures  have  lost  most  by  the  pipe 
friction,  2.9  lb.  having  lost  lOO/ei  14.7  lb.  IK,  and  88.2  lb.  only  a trifle  over  ^ of 
\<fo.  We  see  that  now  14.7  lb.  is  apparently  the  economical  pressure  to  use. 
But  a further  careful  a iialvsis  of  the  subject  shows,  that  when  the  loss  in  the 
pipe  is  2.9  lb.,  then  20.5  lb.  is  the  most  economical  pressure  to  use,  and  that 


200 


COMPRESSED  AIR. 


the  efficiency  is  71^.  But  2.9  lb.  is  a very  small  loss  between  compressor  and 
air  engine,  and  cases  are  extremely  exceptional  where  the  friction  of  valves, 

Sipes,  elbows,  ports,  etc.  does  not  far  exceed  this.  Yet,  with  these  con- 
itions,  which  are  very  difficult  to  fill,  we  see  that  20.5  lb.  is  the  lightest 
pressure  that  should  probably  ever  be  used  for  conveying  power,  and  that 
71^  is  an  efficiency  scarcely  to  be  obtained. 

Continuing  our  investigation  and  taking  examples  where  the  pipe  friction 
amounts  to  5.8  lb.,  we  find  the  following  efficiencies  to  correspond  to  the 
stated  pressure: 

Pressure  above  the  atmosphere,  14.7  lb.  57.14^  efficiency. 

Pressure  above  the  atmosphere,  29.4  lb.  64.49^  efficiency. 

Pressure  above  the  atmosphere,  44.1  lb.  62.71^  efficiency. 

Pressure  above  the  atmosphere,  58.8  lb.  60.12^  efficiency. 

Pressure  above  the  atmosphere,  73.5  lb.  57.73^  efficiency. 

Pressure  above  the  atmosphere,  88.2  lb.  55.59^  efficiency. 


We  again  notice  that  as  friction  increases,  or  in  other  words,  when  we 
begin  to  use  more  air  and  make  greater  demands  on  the  carrying  capacity 
of  the  pipe,  then  we  must  increase  pressure  very  considerably  to  attain  the 
most  economical  results.  If  the  demands  are  such  as  to  increase  the  friction 
and  loss  in  pipe  to  14.7  lb.,  the  air  of  14.7  lb.  pressure  at  the  compressor  is 
entirely  useless  at  the  air  engine. 

The  table  will  stand  thus: 


Pressure  above  the  atmosphere,  14.7  lb. 
Pressure  above  the  atmosphere,  29.4  lb. 
Pressure  above  the  atmosphere,  44.1  lb. 
Pressure  above  the  atmosphere,  58.8  lb. 
Pressure  above  the  atmosphere,  73.5  lb. 
Pressure  above  the  atmosphere,  88.2  lb. 


00.00^  efficiency. 
48.53?^  efficiency. 
55.13^  efficiency. 
55M^  efficiency. 
54.74^  efficiency. 
53.44^  efficiency. 


It  is  to  be  noticed  that  88.2  lb.  pressure  has  lost  only  about  3|^  of  its 
efficiency  by  reason  of  as  high  a friction  as  14.7  lb.,  while  the  efficiency  of 
the  lower  pressures  has  been  greatly  affected. 

As  the  friction  increases  we  see  that  the  most  efficient,  and,  consequently, 
most  economical,  pressure  increases.  In  fact,  for  any  given  friction  in  a 
pipe,  the  pressure  at  the  compressor  must  not  be  carried  below  a certain 
limit.  The  following  table  gives  the  lowest  pressures  that  should  be  used  at 
the  compressor,  with  varying  amounts  of  friction  in  the  pipe: 


2.9  lb.  friction.  20.5  lb.  at  compressor.  70.92^  efficiency. 

^ 5.8  lb.  friction.  29.4  lb.  at  compressor.  64.49^  efficiency. 

8.8  lb.  friction.  38.2  lb.  at  compressor.  60.64^  efficiency. 

11.7  lb.  friction.  47.0  lb.  at  compressor.  57.87^  efficiency. 

14.7  lb.  friction.  52.8  lb.  at  compressor.  55.73^  efficiency. 

17.6  lb.  friction.  61.7  lb.  at  compressor.  53.98?^  efficiency. 

20.5  lb.  friction.  70.5  lb.  at  compressor.  52.52^  efficiency. 

23.5  lb.  friction.  76.4  lb.  at  compressor.  51.26^^  efficiency. 

26.4  lb.  friction.  82.3  lb.  at  compressor.  50.17?^  efficiency. 

29.4  lb.  friction.  88.2  lb.  at  compressor.  49.19^  efficiency. 

So  long  as  the  friction  of  the  pipe  equals  the  amounts  given  above,  an 

efficiency  greater  than  the  corresponding  sums  stated  in  the  table  cannot  be 
expected.  If  we  should  have  a case  that  corresponded  to  any  of  these  cited 
in  the  table,  we  could  only  increase  efficiency  by  reducing  the  friction. 

An  increase  in  the  size  of  pipe  will  reduce  friction  by  reason  of  the  lower 
velocity  of  flow  required  for  the  same  amount  of  air.  But  many  situations 
will  not  admit  of  large  pipes  being  employed,  owing  to  considerations  of 
economy  outside  of  the  question  of  fuel  or  prime  motor  capacity. 

An  increase  of  pressure  will  decrease  the  bulk  of  air  passing  the  pipe,  and 
in  that  proportion  will  decrease  its  velocity.  This  will  decrease  the  loss  by 
friction,  and,  as  far  as  that  goes,  we  have  a gain.  But  we  subject  ourselves 
to  a new  loss,  and  that  is  the  diminishing  efficiencies  of  increasing  pressures. 
Yet  as  each  cubic  foot  of  air  is  at  a higher  pressure,  and,  therefore,  carries 
more  power,  we  will  not  need  as  many  cubic  feet  as  before  for  the  same 
work.  It  is  obvious  that  with  so  many  sources  of  gain  or  loss  the  question 
of  selecting  the  proper  pressure  is  not  to  be  decided  hastily. 

As  an  illustration  of  the  combined  effect  of  these  different  elements,  we 
will  suppose  a very  common  case. 

Compressor  102  revolutions,  pressure  52.8  lb.,  loss  in  pipe  14.7  lb.,  machine 
in  mine  running  at  38.2  lb.,  efficiency  55.73^. 


FRICTION  OF  AIR  IN  PIPES. 


201 


So  long  as;tfie  friction  of  the  pipe  amounts  to  14.7  lb.,  we  have  seen  that 
52.8  lb.  is  the  best  pressure  and  55.73^  the  greatest  efficiency.  We  will 
reduce  the  friction  by  reducing  the  bulk  of  air  passing  through  the  pipe.  We 
reduce  the  cylinder  of  the  air  engine  so  that  it  requires  47  lb.  pressure  to  do 
the  same  work  as  before.  We  find  now  that  the  friction  of  pipe  drops  to 
1 1 .7  lb.  The  pressure  on  the  compressor  rises  to  58.8  lb.,  its  number  of  revolu- 
tions falls  to  100,  and  the  resulting  efficiency  is  57.22/c. 

Another  change  of  pressure  on  compressor  to  64.7  lb.  would  decrease  its 
revolutions  to  93,  friction  to  8.8  lb.,  and  efficiency  would  rise  to  57.94/c.  Still 
again  increasing  the  pressure  to  73.5  lb.,  we  have  only  84  revolutions  of  com- 
pressor, 5.8  lb.  loss  in  pipe,  and  efficiency  of  57.73/c.  In  this  last  case  the 
efficiency  begins  to  fall  off  a little,  and  higher  pressures  would  now 
show  less  efficiency;  but,  in  comparison  with  the  first  example,  we  find  we 
are  doing  the  same  work  in  the  mine  with  a trifle  less  power  and  with  a 
decrease  of  nearly  20^  in  the  speed  of  the  compressor. 

Other  common  examples  can  be  shown  where  an  increase  of  pressure 
would  result  in  wonderful  increase  in  efficiency;  and  economy.  There  are 
many  cases  where  light  pressures  and  high  velocity  in  the  pipe  will  convey 
a given  power  with  greater  economy  than  higher  air  pressures  and  lower 
speed  of  flow  through  the  pipe.  But  these  cases  arise  mostly  when  the 
higher  air  pressures  become  very  much  greater  than  are  at  present  in  com- 
mon use. 

Therefore,  in  estimating  the  efficiency  of  the  complete  outfit,  we  find  that 
the  pipe  and  the  pressure  are  very  important  elements,  and  must  be  deter- 
mined with  care  and  skill  to  secure  the  most  satisfactory  results.  As  the 
volume  and  power  of  air  vary  with  its  pressure,  the  size  and  consequent 
cost  of  compressor  for  a certain  work  would  also  be  affected  by  the  pressure. 
To  plan  an  outfit  for  a mine,  due  regard  must  be  had  to  cost  of  fuel  or  prime 
.motor  power,  and  also  to  cost  of  compressor,  pipes,  and  machinery,  as  the 
saving  in  one  is  often  secured  by  a sacrifice  in  the  other. 

Next  to  determining  the  size  of  pipe,  the  skilful  engineer  has  need  of 
further  care  in  the  proper  position  of  reservoirs,  branches,  drains,  and  other 
attachments,  as  only  by  the  exercise  of  good  judgment  in  this  can  satis- 
factory working  be  secured. 

The  fact  that,  on  account  of  the  diminished  density  of  the  atmosphere  at 
high  altitudes,  air  compressors  do  not  give  the  same  results  as  at  sea  level, 
should  also  be  taken  into  consideration  when  a compressor  is  to  be  installed 
in  a mountainous  region. 

Friction  of  Air  in  Pipes.— Air  in  its  passage  through  pipes  is  subject  to 
friction  in  the  same  manner  as  water  or  any  other  fluid.  The  pressure  at 
the  compressor  must  be  greater  than  at  the  point  of  consumption  in  order 
to  overcome  this  resistance.  The  power  that  is  needed  to  produce  the  extra 
pressure  representing  the  friction  of  the  pipe  is  lost,  as  there  can  be  no  use- 
ful return  for  it.  The  friction  is  affected  by  very  many  circumstances,  but 
chiefly  to  be  noted  is  the  fact  that  it  increases  in  direct  proportion  to  the 
length  of  the  pipe  and  also  as  the  square  of  the  velocity  of  the  flow  of  air. 
The  pressure  of  the  air  does  not  affect  it. 

The  losses  by  friction  may  be  quite  serious  if  the  piping  system  is  poorly 
designed,  and,  on  the  other  hand,  extravagant  expenditure  in  pipe  may 
result  from  a timid  overrating  of  the  evils  of  friction.  A thorough  knowl- 
edge of  the  laws  governing  the  whole  matter,  as  well  as  a ripe  experience,  is 
necessary  to  secure  true  economy  and  mechanical  success. 

The  loss  of  power  in  pipe  friction  is  not  always  the  most  serious  result. 
When  a number  of  machines  are  in  use  in  a mine,  and  the  pipes  are  so  small 
as  to  cause  a considerable  loss  of  pressure  by  friction,  then  there  will  be 
sudden  and  violent  fluctuations  in  pressure  whenever  a machine  is  started 
or  stopped.  Breakages  will  be  of  common  occurrence,  as  the  changes  are  too 
quick  to  be  entirely  guarded  against  by  the  attendant.  Perfectly  even  pres- 
sure at  the  compressor  is  no  safeguard  against  this  class  of  accidents.  The 
trouble  arises  in  the  pipe,  and  the  remedy  must  be  applied  there.  A system 
of  reservoirs  and  governing  valves  will  regulate  these  matters  and  allow 
successful  work  to  be  done  with  pipes,  which  would  otherwise  be  entirely 
inadmissible. 

The  ordinary  formulas  for  calculating  the  volume  of  air  transmitted 
through  a pipe  do  not  take  into  account  the  increase  of  volume  due  to 
reduction  of  pressure,  i.  e.,  loss  of  head.  To  transmit  a given  volume  of  air 
at  a uniform  velocity  and  loss  of  pressure,  it  would  be  necessary  to  construct 
the  pipe  with  a gradually  increasing  area.  This,  of  course,  is  impracticable, 


202 


COMPRESSED  AIR. 


and  in  pipe  of  uniform  section  both  volume  and  velocity  must  increase  as 
the  pressure  is  reduced  by  friction.  The  loss  of  head  in  properly  propor- 
tioned pipes  is  so  small,  however,  that  in  practice  the  increase  in  volume  is 
usually  neglected. 

Loss  OF  Pressure  in  Pounds  per  Square  Inch,  by  Flow  of  Air  in  Pipes. 

Calculated  for  pipes  1,000  ft.  long;  for  other  lengths,  the  loss  varies  directly 
as  the  length. 


Velocity  of  Air 
at  Entrance 
to  Pipe. 

1"  Pipe. 

2"  Pipe. 

2i"  Pipe. 

Meters  per  Second. 

Feet  per  Second. 

Loss  of  Pressure. 
Pounds. 

Cubic  Feet  of  Free  Air 
Passed  per  Minute  When  j 
Compressed  to  60  Lb. 
Above  the  Atmosphere. 

Cubic  Feet  of  Free  Air 
Passed  per  Minute  When 
Compressed  to  80  Lb.  | 
Above  the  Atmosphere. 

Loss  of  Pressure. 
Pounds. 

Cubic  Feet  of  Free  Air 

Compressed  to  60  Lb. 

Cubic  Feet  of  Free  Air 

Compressed  to  80  Lb. 

Loss  of  Pressure. 

Pounds. 

Cubic  Feet  of  Free  Air 

Compressed  to  60  Lb. 

Cubic  Feet  of  Free  Air 

Compressed  to  80  Lb. 

1 

3.28 

.1435 

6 

7 

.0794 

23 

29 

.0574 

32 

41 

2 

6.56 

.6405 

12 

15 

.3050 

46 

59 

.2562 

65 

82 

3 

9.84 

1.4545 

18 

22 

.7216 

69 

88 

.5818 

97 

124 

4 

13.12 

2.5620 

24 

29 

1.2566 

93 

117 

1.0248 

130 

165 

5 

16.40 

• 3.9345 

29 

37 

1.9642 

116 

146 

1.5738 

163 

207 

6 

19.68 

5.4225 

35 

44 

2.7120 

139 

175 

2.1690 

195 

247 

8 

26.24 

10.2480 

47 

59 

5.0264 

185 

234 

4.0992 

260 

330 

10 

32.80 

15.7380 

59 

74 

7.8568 

232 

294 

6.2952 

326 

413 

3"  Pipe. 

4"  Pipe. 

5"  Pipe. 

1 

3.28 

.0463 

48 

60 

.0347 

86 

109 

.0287 

134 

169 

2 

6.56 

.2092 

96 

121 

.1525 

172 

217 

.1281 

268 

239 

3 

9.84 

.4880 

144 

182 

.3608 

258 

326 

.2909 

402 

509 

4 

13.12 

.8381 

193 

243 

.6283 

343 

436 

.5124 

537 

678 

5 

16.40 

1.3176 

241 

304 

.9821 

429 

544 

.7869 

671 

844 

6 

19.68 

1.8080 

289 

364 

1.3560 

515 

653 

1.0845 

805 

1,017 

8 

26.24 

3.3525 

386 

486 

2.5132 

687 

871 

2.0496 

1,073 

1,357 

10 

32.80 

5.2704 

480 

607 

3.9284 

859 

1,088 

3.1476 

1,342 

1,696 

6"  Pipe. 

8"  Pipe. 

10"  Pipe. 

1 

3.28 

.0232 

193 

244 

.0173 

343 

434 

.0143 

537 

680 

2 

6.56 

.1046 

386 

488 

.0762 

687 

864 

.0640 

1,073 

1,359 

3 

9.84 

.2440 

579 

633 

.1805 

1,030 

1,303 

.1455 

1,610 

2,039 

4 

13.12 

.4190 

772 

977 

.3141 

1,373 

1,736 

.2562 

2,146 

2,719 

5 

16.40 

.6588 

965 

1,221 

.4910 

1,717 

2,171 

.3934 

2,683 

3.399 

6 

19.68 

.9040 

1,158 

1,466 

.6780 

2,060 

2,605 

.5423 

3,220 

4,079 

8 

26.24 

1.6762 

1,544 

1,954 

1.2556 

2,747 

3,473 

1.0248 

4,293 

5,438 

10 

32.80 

2.6352 

1,931 

2,443 

1.9642 

3,434 

4,342 

1.5738 

5,367 

6,798 

The  resistance  is  not  varied  by  the  pressure,  only  so  far  as  changes  in 
pressure  vary  the  velocity.  It  increases  about  as  the  square  of  the  velocity, 
and  directly  as  the  length. 

Elbows,  short  turns,  and  leaks  in  pipes  all  tend  to  reduce  the  pressure  in 
addition  to  the  losses  given  in  the  table. 


ELECTRICITY. 


203 


Table  of  Loss  by  Friction  in  Elbows. 


An  elbow  with  a radius  of  one-half  the  diameter  of  the  pipe  is  as  short 
as  can  be  made. 


Radius  of  elbow,  5 diams. 
Radius  of  elbow,  3 diams. 
Radius  of  elbow,  2 diams. 
Radius  of  elbow,  li  diams. 
Radius  of  elbow,  li  diams. 
Radius  of  elbow,  1 diam. 
Radius  of  elbow,  f diam. 
Radius  of  elbow,  i diam. 


Equivalent  length  of  straight  pipe,  7.85  diams. 
Equivalent  length  of  straight  pipe,  8.24  diams. 
Equivalent  length  of  straight  pipe,  9.03  diams. 
Equivalent  length  of  straight  pipe,  10.36  diams. 
Equivalent  length  of  straight  pipe,  12.72  diams. 
Equivalent  length  of  straight  pipe,  17.51  diams. 
Equivalent  length  of  straight  pipe,  35.09  diams. 
Equivalent  length  of  straight  pipe,  121.20  diams. 


ELECTRICITY. 


PRACTICAL  UNITS. 

In  electrical  work  it  is  necessary  to  have  units  in  terms  of  which  to 
express  the  different  quantities  entering  into  calculations.  The  four  most 
important  of  these  are  used  to  express  strength  of  current;  electrical  pressure, 
or  electromotive  force;  resistance;  power. 

The  strength  of  current  flowing  in  a wire  may  be  measured  in  several 
ways.  If  a compass  needle  be  held  under  or  over  a wire,  it  will  be  deflected 
and  will  tend  to  stand  at  right  angles  to  the  wire.  The  stronger  the  current, 
the  greater  the  deflection  of  the  needle.  If  the  wire  carrying  the  current  be 
cut  and  the  ends  dipped  into  a solution  of  silver  nitrate,  silver  will  be 
deposited  on  the  end  of  the  wire  toward  which  the  current  is  flowing,  and 
the  amount  of  silver  deposited  in  a given  time  will  be  directly  proponional 
to  the  average  strength  of  current  flowing  during  that  time.  When  the 
current  flowing  in  a wire  is  spoken  of,  the  strength  of  the  current  is  meant. 

Unit  Strength  of  Current.— The  unit  used  to  express  the  strength  of  a cur- 
rent is  called  the  ampere.  If  a current  of  1 ampere  be  sent  through  a bath 
of  silver  nitrate,  .001118  gram  of  silver  will  be  deposited  per  second.  The 
expression  of  the  flow  of  current  through  a wire  as  so  many  amperes  is 
analogous  to  the  expression  of  the  flow  of  water  through  a pipe  as  so  many 
gallons  per  second. 

Electromotive  Force. — In  order  that  a current  may  flow  through  a wire, 
there  must  be  an  electrical  pressure  of  some  kind  to  cause  the  flow.  In 
hydraulics,  there  must  always  be  a head  or  pressure  before  water  can  be 
made  to  flow  through  a pipe.  It  is  also  evident  that  there  may  be  a pressure 
or  head  without  there  being  any  flow  of  water,  because  the  opening  in  the 
pipe  might  be  closed;  the  pressure  would,  however,  exist,  and,  as  soon  as 
the  valve  closing  the  pipe  was  opened,  the  current  would  flow.  In  the 
same  way,  an  electrical  pressure  or  electromotive  force  (usually  written 
E.  M.  F.)  may  exist  in  a circuit,  but  no  current  can  flow  until  the  circuit  is 
closed  or  until  the  wire  is  connected  so  that  there  will  be  a path  for  the 
current. 

Unit  Electromotive  Force  (E.  M.  F.).— The  practical  unit  of  electromotive 
force  is  the  volt.  It  is  the  unit  of  electrical  pressure,  and  fulfils  somewhat 
the  same  purpose  as  “pounds  per  square  inch”  in  hydraulic  and  steam 
engineering.  The  E.  M.  F.  furnished  by  an  ordihary  cell  of  a battery  usually 
varies  from  .7  to  2 volts.  A Daniell  cell  gives  an  E.  M.  F.  of  1.072  volts.  A 
pressure  of  500  volts  is  generally  used  for  street-railway  work,  and,  for  incan- 
descent lighting,  110  volts  is  common. 

Resistance.— All  conductors  offer  more  or  less  resistance  to  the  flow  of  a 
current  of  electricity,  just  as  water  encounters  friction  in  passing  through  a 
pipe.  The  amount  of  this  resistance  depends  on  the  length  of  the  wire,  the 
diameter  of  the  wire,  and  the  material  of  which  the  wire  is  composed.  The 
resistance  of  all  metals  also  increases  with  the  temperature. 

Unit  of  Resistance. — The  practical  unit  of  resistance  is  the  ohm.  A con- 
ductor has  a resistance  of  1 ohm  when  the  pressure  required  to  set  up 
1 ampere  through  it  is  1 volt.  In  other  words,  the  drop,  or  fall,  in  pressure 
through  a resistance  of  1 ohm,  when  a current  of  1 ampere  is  flowing, 
is  1 volt.  1,000  ft.  of  copper  wire  .1  in.  in  diameter  has  a resistance  of 
nearly  1 ohm  at  ordinary  temperatures. 


204 


ELECTRICITY. 


Ohm’s  Law.— The  law  governing  the  flow  of  current  in  an  electric  circuit 
was  first  stated  hy  Dr.  G.  S.  Ohm,  and  is  known  as  Ohm's  law.  This  law  has 
since  stood  the  test  of  exhaustive  experiment,  and  has  been  found  correct. 
Ohm’s  law  may  be  briefly  stated  as  follows : The  strength  of  the  current  in 
any  circuit  is  directly  proportional  to  the  electromotive  force  in  the  circuity  and 
inversely  proportional  to  the  resistance  of  the  circuit. 

This  means  that  if  the  resistance  of  a circuit  were  fixed,  and  the  E.  M.  F. 
varied,  the  current  would  be  doubled  if  the  E.  M.F.  were  doubled.  Also,  if 
the  E.  M.  F.  were  fixed,  and  the  resistance  doubled,  the  current  would  be 
halved. 

Let  E = electromotive  force  in  volts; 

R = resistance  in  ohms; 

C = current  in  amperes. 

Then,  C = oi  R = ^,  ot  E = C R. 


The  last  two  forms  are  useful  in  many  cases  where  the  usual  form 
E 

(7  = -5  is  not  directly  applicable. 

-it 

Example.— A dynamo  D which  generates  110  volts,  is  connected  to  a coil 
of  wire  C,  Fig.  1,  which  has  a resistance  of  20  ohms;  what  current  will 
flow,  supposing  the  resistance  of  the  rest  of  the  circuit  to  be  negligible? 

We  have  E = 110  volts;  R = 20  ohms;  hence,  C = ^ = 5.5  amperes. 


A problem  might  also  be  given  as  follows:  The  resistance  of  the  coil  C is 

. 6 ohms;  what  E.  M.  F.  must  the  dynamo  gen- 

^ 5 erate  in  order  to  set  up  a current  of  15  amjieres 
^ ^ through  it  ? The  third  form  of  the  law  given 
above  is  more  convenient  in  this  case. 


n )B-iiO  roits|g® 


E = G-R;  E = 15  X 6 = 90  volts. 

In  case  the  current  and  E.  M.  F.  are  known, 
the  resistance  of  the  circuit  may  be  calculated 
Fig.  1.  by  using  the  second  form  of  the  law  given  abox  e. 

For  example,  if  the  current  in  the  above  case 
were  8 amperes  and  the  E.  M.  F.  of  the  dynamo  110  volts,  the  resistance  of 
the  circuit  must  be 


E = ^;  E = = 13.75  ohms. 

U o 


Electrical  Power.— The  electrical  power  expended  in  any  circuit  is  found 
by  multiplying  the  current  flowing  in  the  circuit  by  the  pressure  required 
to  force  the  current  through  the  circuit.  In  other  words,  W = E C]  where 
W is  the  power  expended,  E is  the  E.  M.  F.,  and  C is  the  current.  When  E 
is  expressed  in  volts  and  C in  amperes,  then  W is  expressed  in  watts.  The 
watt  is  the  unit  of  electrical  power,  and  is  equal  to  the  power  developed 
when  1 ampere  flows  under  a pressure  of  1 volt.  The  watt  is  equal  to  yi, 
horsepower.  We  have,  then,  the  following  general  relations: 

Let  E = electromotive  force  in  volts; 

C = current  in  amperes; 

R = resistance  in  ohms; 

W = power  in  watts; 

H.  P.  = horsepower. 

Then,  W = E C,  but  E = C R;  hence,  W = C^  R.  That  is,  the  i)ower  in 
watts  expended  in  any  conductor  of  which  the  resistance  is  i?,  and  through 
which  a current  C is  flowing,  is  equal  to  the  product  of  the  squares  of  the 
current  and  the  resistance.  The  energy  used  in  forcing  a current  through 
the  wire  reappears  in  the  form  of  heat;  hence,  we  may  say  that  the  heating 
effect  of  a current  flowing  in  a conductor  is  proportional  to  the  square  of  the 
current.  From  the  preceding,  we  also  have 


H.  P.  = 


746  746* 


This  relation  is  very  useful  for  calculating  power  in  terms  of  electrical 
units.  The  watt  is  too  small  a unit  for  convenient  use  in  many  cases,  so 
that  the  kilowatt,  or  1,000  watts,  is  frequently  used.  This  is  sometimes 
abbreviated  to  K.W. 


CISCUITS. 


205 


The  Unit  of  Work  Is  the  Watt -Hour.— This  is  the  total  work  done  when  1 watt 
is  expended  for  1 hour.  For  example,  if  a current  of  1 ampere  were  made  flow 
for  1 hour  through  a resistance  of  1 ohm,  the  total  amount  of  work  done  would 
he  1 watt-hour.  A kilowatt-hour  is  the  total  work  done  when  1 kilowatt  is 
expended  for  1 hour.  It  is  about  equivalent  to  Ij  horsepower  for  1 hour. 


ELECTRICAL  EXPRESSIONS  AND  THEIR  EQUIVALENTS. 

{Arranged  for  Convenient  Reference  by  C.  W.  Hunt.) 


One 

Watt 


f A rate  of  doing  work. 

1.  ampere  per  sec.  at  onevolt. 
.7373  foot-pound  per  second. 

I 44.238  foot-pounds  per  minute. 

\ 2,654.28  foot-pounds  per  hour. 
.5027  mile-pound  per  hour. 
.00134  horsepower. 

. ri®  horsepower. 


One 

Kilowatt 


A rate  of  doing  work. 

737.3  foot-pounds  per  second. 
44,238.  foot-pounds  per  minute. 
502.7  mile-pounds  per  hour. 
1.34  horsepower. 


One 

Horse- 

power 


A rate  of  doing  work. 

550.  foot-pounds  per  second. 

33,000.  foot-pounds  per  minute. 

375.  mile-pounds  per  hour. 

746.  watts. 

.746  kilowatt. 


One 

Watt- 

Hour 


One 

Horse- 

power- 

Hour 


One 

Ampere- 

Hour 


1A  quantity  of  work. 

2,654.28  foot-pounds. 

.503  mile-pound. 

1.  ampere  hour  X one  volt« 

.00134  horsepower-hour, 
horsepower-hour. 

r A quantity  of  work. 

1,980,000.  foot-pounds. 

< 375.  mile-pounds. 

I 746.  watt-hour. 

L .746  kilowatt-hour. 

{A  quantity  of  current. 

One  ampere  flowing  for  one  hour, 
irrespective  of  the  voltage. 
Watt-hour  -r  volts. 


r Force  moving  in  a circle. 

Torque  ^ A force  of  one  pound  at  a radius  of 
L one  foot. 


CIRCUITS. 

The  path  through  which  a current  flows  is  generally  spoken  of  as  an 
electric  circuit.  This  path  may  be  made  up  of  a number  of  different  parts. 
For  example,  the  line  wires  may  constitute  part  of  the  circuit,  and  the 
remainder  may  be  composed  of  lamps,  motors,  resistances,  etc.  In  practice, 


the  two  kinds  of  circuits  most  commonly  met  with  are  (1)  those  in  which  the 
different  parts  of  the  circuit  are  connected  in  series;  (2)  those  in  which 
the  different  parts  of  the  circuit  are  connected  in  multiple  or  parallel. 

1.  Series  Circuits.— In  this  kind  of  circuit,  all  the  component  parts  are  con- 
nected in  tandem,  so  that  the  current  flowing  through  one  part  also  flows 


206 


ELECTRICITY. 


through  the  other  parts.  Fig.  2 (a)  represents  such  a circuit  made  up  of  a 
different  number  of  parts.  The  current  leaves  the  dynamo  D at  the  + side 
and  flows  through  the  arc  lamps  a'aaa,  thence  through  the  incandescent 
lamps  1 1 1,  thence  through  the  motor  m and  resistance  r,  back  to  the  dynamo, 
thus  making  a complete  circuit.  All  these  different  parts  are  here  connected 
in  series,  so  that  the  current  flowing  through  each  of  the  parts  must  be  the 
same  unless  leakage  takes  place  across  from  one  side  of  the  circuit  to  the 
other,  and  this  would  be  impossible  if  the  lines  were  properly  insulated. 
The  pressure  furnished  by  the  dynamo  must  evidently  be  the  sum  of  the 
pressures  required  to  force  the  current  through  the  different  parts.  The 
most  common  use  of  this  system  is  in  connection  with  arc  lamps.  These 
lamps  are  usually  connected’  in  series,  as  shown  in  Fig.  2 (5).  The  objections 
to  this  system  of  distribution  for  general  work  are  that  the  breaking  of  the 
circuit  at  any  point  cuts  off  the  current  from  all  parts  of  the  circuit;  also, 
the  pressure  generated  by  the  dynamo  has  to  be  very  high  if  many  pieces  of 
apparatus  are  connected  in  series.  In  such  a system,  the  dynamo  is  pro- 
vided with  an  automatic  regulator  that  increases  or  decreases  the  voltage  of 
the  machine,  so  that  the  current  in  the  circuit  is  kept  constant,  no  matter 
how  many  lamps  or  other  devices  are  in  operation.  For  this  reason,  such 
circuits  are  often  spoken  of  as  constant-current  circuits. 

2.  Parallel  Circuits.— In  this  type  of  circuit,  the  different  pieces  of  appa- 
ratus are  connected  side  by  side,  or  in  parallel,  across  the  main  wires  from 
the  dynamo,  as  shown  in  Fig.  2 (c).  In  this  case,  the  dynamo  D supplies 
current  through  the  mains  to  the  arc  lamps  a,  incandescent  lamps  Z,  and 
motor  m.  This  system  is  more  widely  used,  and  it  will  be  seen  at  once  from 
the  figure  that  the  breaking  of  the  circuit  through  any  one  piece  of  apparatus 
will  not  prevent  the  current  from  flowing  through  the  other  parts.  Incan- 
descent lamps  are  connected  in  this  way  almost  exclusively.  The  lamps  are 
connected  directly  across  the  mains,  as  shown  in  Fig.  2 (d).  Street  cars  and 
mining  locomotives  are  operated  in  the  same  way,  the  trolley  wire  consti- 
tuting one  main  and  the  track  the  other,  as  shown  in  Fig.  2 (e) . By  adopting 
this  system,  any  car  can  move  independently  of  the  others,  and  the  current 
may  be  turned  off  and  on  at  will.  In  all  these  systems  of  parallel  distribu- 
tion, the  pressure  generated  by  the  dynamo  is  maintained  constant,  no  matter 
what  current  the  dynamo  may  be  delivering.  For  example,  in  the  lamp 
system.  Fig.  2 (d),  the  dynamo  would  maintain  a constant  E.  M.  F.  of  110 
volts.  Each  lamp  has  a fixed  resistance,  and  will  take  a certain  current 

amperes^  when  connected  across  the  mains.  As  the  lamps  are  turned 

on,  the  current  delivered  by  the  dynamo  increases,  the  pressure  remaining 
constant.  In  street-railway  work,  the  pressure  between  trolley  and  track  is 
kept  in  the  neighborhood  of  500  volts,  the  current  varying  with  the  number 
of  cars  in  operation.  In  mine-haulage  plants,  the  pressure  is  usually  250  or 
500  volts,  the  former  being  generally  preferred  as  being  less  dangerous. 
Lamps  may  also  be  connected  in  series  multiple,  as  shown  in  Fig.  2 {e). 
Here  the  two  125-volt  lamps  ll  are  connected  in  series  across  the  250-volt 
circuit.  Such  an  arrangement  is  frequently  used  in  mines  when  lamps  are 
operated  from  the  haulage  circuit. 

Such  circuits  as  those  just  described  are  called  constant-potential  or  con- 
stant-pressure circuits,  to  aistinguish  them  from  the  constant-current  circuit 
mentioned  previously. 


RESISTANCES  IN  SERIES  AND  MULTIPLE. 

Resistances  in  Lines.— If  two  or  more  resistances  are  connected  in  series. 
Fig.  2 (/),  their  total  combined  resistance  is  equal  to  the  sum  of  their  sepa- 
rate resistances.  If  R equal  total  combined  resistance,  and  jRi,  R^,  R^  are  the 
separate  resistances  connected  in  series,  then,  JB  = 

Example.— If  the  separate  resistances  were  R\  = 10  olims,  Ro  = 1 ohm, 
and  Rz  = 30  ohms,  then  these  three  combined  would  be  equivalent  to  a 
single  resistance  of  10  + 1 + 30  = 41  ohms. 

Resistances  in  Parallel.— If  a number  of  resistances  are  connected  in 
parallel,  the  reciprocal  of  their  total  combined  resistance  is  equal  to  the 
sum  of  the  reciprocals  of  the  separate  resistances.  In  Fig.  2 {g),  three, resist- 
ances are  shown  connected  in  parallel.  It  is  evident  that  the  total  resistance 
of  such  a combination  must  be  lower  than  that  of  the  lowest  resistance 
entering  into  the  combination.  If  the  resistances  in  this  case  were  all  equal, 


ELECTRIC  WIRING, 


207 


the  resistance  of  the  three  combined  would  be  one-third  the  resistance  of 
one  of  them,  because  a current  passing  through  the  three  combined  could 
split  up  between  three  equal  paths,  instead  of  having  only  one  path  to  pass 
through.  If  R represents  the  combined  resistance,  and  Ri,  R2,  and  R^  the 
separate  resistances,  the  following  relation  is  true: 

R Ri  R2  Rq 


from  which 


R = 


R\  Ro  Rs 

E2  R3  + Ri  R3  + Ri  R2 


13  R 

If  the  three  resistances  were  all  equal,  we  would  have  = -77-,  ori^  = 

R Ri  o 

Example. — Three  resistances  of  3,  10,  and  5 ohms  are  connected  in  par- 
allel. What  is  their  combined  resistance?  We  have 


150  150  , , 

50  + 15  + 30  95  1-580  ms. 


Shunt.— When  one  circuit  B,  Fig.  2 (h),  is  connected  across  another  A,  so 
as  to  form,  as  it  were,  a by-pass,  or  side  track,  for  the  current,  such  a circuit 
is  called  a shunt,  or  it  is  said  to  be  in  shunt  with  the  other  circuit. 


ELECTRIC  WIRING  (CONDUCTORS). 

Materials.— Practically  all  conductors  used  in  electric  lighting  or  power 
work  are  of  copper,  this  metal  being  used  on  account  of  its  low  resistance. 
Iron  wire  is  used  to  some  extent  for  conductors  in  telegraph  lines,  and  steel 
is  largely  used  as  the  return  conductor  in  electric-railway  or  haulage  plants 
where  the  current  is  led  back  to  the  power  station  through  the  rails.  The 
resistance  of  iron  or  steel  varies  from  six  to  seven  times  that  of  copper, 
depending  on  the  quality  of  the  metal.  Aluminum  is  coming  into  use  as  a 
material  for  conductors,  and  in  future  may  play  an  important  part  in  electric 
transmission.  It  is  so  much  lighter  than  copper  that  it  is  able  to  compete 
with  it  as  a conductor,  even  though  its  cost  per  pound  is  higher  and  its 
conductivity  only  about  60;:^  that  of  copper. 

Forms  of  Conductors.— Most  of  the  conductors  used  are  in  the  form  of 
copper  wire  of  circular  cross-section.  Conductors  of  large  cross-section  are 
made  up  of  a number  of  strands  of  smaller  wire  twisted  together.  For 
electrolytic  plants,  copper-refining  plants,  etc.,  copper  bars  of  rectangular 
cross-section  are  frequently  used. 

Wire  Gauge.— The  gauge  most  generally  used  in  America  to  designate 
the  different  sizes  of  copper  wire  is  the  American,  or  Brown  & Sharpe 
(B.  &.S.).  The  sizes  as  given  by  this  gauge  range  from  No.  0000,  the 
largest,  .460  in.  diameter,  to  No.  40,  the  finest,  .003  in.  diameter.  Wire 
drawn  to  the  sizes  given  by  this  gauge  is  always  more  readily  obtained 
than  sizes  according  to  other  gauges;  hence,  in  selecting  line  wire  for 
any  purpose  it  is  always  desirable,  if  possible,  to  give  the  size  required  as 
a wire  of  the  B.  & S.  gauge.  A wire  can  usually  be  selected  from  this  gauge, 
which  will  be  very  nearly  that  required  for  any  specified  case. 

Estimation  of  Cross-Section  of  Wires.— The  diameter  of  round  wires  is 
usually  given  in  the  tables  in  decimals  of  an  inch,  and  the  area  of  cross- 
section  is  given  in  terms  of  a unit  called  a circular  mil.  This  is  done  simply 
for  convenience  in  calculation,  as  it  makes  calculations  of  the  cross-section 
much  simpler  than  if  the  square  inch  were  used  as  the  unit  area.  A mil 
is  YoW  of  an  inch,  or  .001  in.  A circular  mil  is  the  area  (in  decimals  of  a 
square  inch)  of  a circle,  the  diameter  of  which  is  in.,  or  1 mil.  The 

circular  mil  is  therefore  equal  to  (.001)2  = .0000007854  sq.  in. 

If  the  diameter  of  the  conductor  were  1 in.,  its  area  would  be  .7854  sq.  in., 

and  the  number  of  circular  mils  in  its  area  would  be  = 1,000,000; 

.0000007854 

but  1 in.  = 1,000  mils,  and  (1,000)2  = 1,000,000;  hence  the  following  is  true: 
CM  = (P\  or  the  area  of  cross-section  of  a wire  in  circular  mils  is  equal  to  the 
square  of  its  diameter  expressed  in  mils. 

Example.— A wire  has  a diameter  of  .101  in.  What  is  its  area  in  circular 
mils? 

.101  in.  = 101  mils.  Hence,  CM  = (101)2  = 10, 201. 


vid( 

imb 

)luir 

*ROP 

6 

50 

0)  o3 

w 

0000 

000 

00 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 


ELECTRICITY. 


^ table  gives  the  dimensions,  weight,  and  resistance  of  pure 
he  weights  given  are,  of  course,  for  bare  wire.  The  first 
le  B.  & S.  gauge  number,  the  second  the  diameter  in  mils. 
1 inches  would  be  the  number  as  given  in  this  column, 
).  The  third  column  gives  the  area  in  circular  mils,  the 
column  being  equal  to  the  squares  of  those  in  the  second 
ife  carrying  capacity  is  also  given. 


Copper  Wire.  American,  or  Brown  & Sharpe,  Gauge. 


»h<n* 

111 

. 

.go 

. 

<X)  02 

We 

Poi 

Per 

1,000  Ft. 

ight. 

inds. 

Per 

Mile. 

1 

Resistance  per 

1,000  Ft. 

International 

Ohms.  68°  F. 

Current  Capacity 
(Amperes). 
National  Board 
Fire  Underwriters. 

Weath- 

er-Proof. 

Rubber- 

Covered. 

211,600.0 

640.50 

3,381.4 

.0489 

312 

210 

167,805.0 

508.00 

2,682.2 

.0617 

262 

177 

133,079.4 

402.80 

2,126.8 

.0778 

220 

150 

105,534.5 

319.50 

1,686.9 

.0981 

185 

127 

83,694.2 

253.30 

1,337.2 

.1237 

156 

107 

66,373.0 

200.90 

1,060.6 

.1560 

131 

90 

52,634.0 

159.30 

841.1 

.1967 

110 

76 

41,742.0 

126.40 

667.4 

.2480 

92 

65 

33,102.0 

100.20 

529.1 

.3128 

77 

54 

26,250.5 

79.46 

419.5 

.3944 

65 

46 

20,816.0 

63.02 

332.7 

.4973 

16,509.0 

49.98 

263.9 

.6271 

46 

33 

13,094.0 

39.63 

209.2 

.7908 

10,381.0 

31.43 

165.9 

.9972 

32 

24 

8,234.0 

24.93 

131.6 

1.257 

6,529.9 

19.77 

104.4 

1.586 

23 

17 

5,178.4 

15.68 

82.8 

1.999 

4,106.8 

12.43 

76.2 

2.521 

16 

12 

3,256.7 

9.86 

52.0 

3.179 

2,582.9 

7.82 

41.3 

4.009 

8 

6 

2,048.2 

6.20 

32.7 

5.055 

1,624.3 

4.92 

25.9 

6.374 

5 

3 

1,288.1 

3.90 

20.6 

8.038 

1,021.5 

3.09 

16.3 

10.14 

810.1 

2.45 

12.9 

12.78 

642.4 

1.94 

10.3 

16.12 

509.4 

1.54 

8.1 

20.32 

404.0 

1.22 

6.4 

25.63 

320.4 

.96 

5.1 

32.31 

254.1 

.76 

4.0 

40.75 

201.5 

.61 

3.2 

51.38 

159.7 

.48 

2.5 

64.79 

126.7 

.38 

2.0 

81.7 

100.5 

.30 

1.6 

103.0 

79.70 

.24 

1.27 

129.9 

63.21 

.19 

1.01 

163.8 

50.13 

.15 

.801 

206.6 

39.75 

.12 

.635 

260.5 

31.52 

.095 

.504 

328.4 

25.00 

.075 

.400 

414.2 

19.83 

.060 

.317 

522.2 

15.72 

.047 

.251 

658.5 

12.47 

.038 

.199 

830.4 

9.89 

.030 

.158 

1,047.0 

ELECTRIC  WIRING, 


209 


The  following  table  gives  a comparison  of  the  properties  of  aluminum 
and  copper: 

Comparison  of  Properties  of  Aluminum  and  Copper. 


Aluminum. 

Copper. 

Conductivity  (for  equal  sizes) 

.54  to  .63 

1 

Weight  (for  equal  sizes) 

.33 

1 

Weight  (for  equal  length  and  resistance).... 

.48 

1 

Price  (per  pound)  aluminum,  29  cents;  cop- 
per, 16  cents  (bare  wire) 

1.81 

1 

Price  (equal  length  and  resistance,  bare 
line  wire) 

.868 

1 

Temperature  coefficient  per  degree  F 

.002138 

.002155 

Resistance  of  mil-foot  (20°  C.) 

18.73 

10.5 

Specific  gravity 

2.5  to  2.68 

8.89  to  8.93 

Breaking  strength  (equal  sizes) 

1 

1 

In  case  a conductor  larger  than  that  given  in  the  table  is  required, 
stranded  cables  are  used.  These  are  made  in  various  sizes.  The"  table 
below  gives  some  of  the  more  common  sizes,  with  their  allowable  current 
capacity. 

Carrying  Capacity  of  Cables. 


Area. 

Circular 

Mils. 

Current. 

Amperes. 

Area. 

Circular 

Mils. 

Current. 

Amperes. 

Exposed. 

Concealed. 

Exposed. 

Concealed. 

200,000 

299 

200 

1,200,000 

1,147 

715 

300,000 

405 

272 

1,300,000 

1,217 

756 

400,000 

503 

336 

1,400,000 

1,287 

796 

500,000 

595 

393 

1,500,000 

1,356 

835. 

600,000 

682 

445 

1,600.000 

1,423 

873 

700,000 

765 

494 

1,700,000 

1,489 

910 

800,000 

846 

541 

1,800,000 

1,554 

946 

900,000 

924 

586 

1,900,000 

1,618 

981 

1,000,000 

1,000 

630 

2,000,000 

1,681 

1,015 

1,100,000 

1,075 

673 

Estimation  of  Resistance.— The  resistance  of  any  conductor  is  directly  pro- 
portional to  its  length,  and  inversely  proportional  to  its  area  of  cross-sec- 
tion, or  R = K where  if  is  a constant.  If  L is  expressed  in  feet  and 

A is  expressed  in  circular  mils,  then  the  constant  K must  be  the  resistance 
of  a foot  of  the  wire  in  question  of  1 circular  mil  cross-section.  The  resist- 
ance of  1 mil-foot  of  copper  wire  at  75°  F.  is  about  10.8  ohms.  Hence, 

for  copper  wire,  we  have  R = J.  = d-  when  d is  the  diameter 

in  mils;  hence,  we  also  have  R = — ^ — . 

This  formula  is  easily  remembered,  and  is  very  convenient  for  estimating 
the  resistance  of  any  length  of  wire  of  given  diameter  when  a wire  table  is 
not  at  hand,  or  when  the  diameter  of  the  given  wire  does  not  correspond  to 
anything  given  in  the  table. 

Example.— Find  the  resistance  of  1 mile  of  copper  wire  .20  in.  in  diameter, 
1 mile  = 5,280  ft.  .20  in.  = 200  mils.  Area  of  cross-section  = (200)2  = 
-1  TT  10.8  X L 10.8  X 5,280  , ^ 

40,000  circular  mils.  Hence,  R = — — = - — — = 1.42  ohms. 

’ a2  40,000 


210 


ELECTRICITY. 


CALCULATION  OF  WIRES  FOR  ELECTRIC  TRANSMISSION. 

Direct-Current  Circuits.— No  matter  how  large  a wire  may  be,  some  energy 
must  always  be  expended  in  forcing  a current  through  it,  because  no  con- 
ductor can  be  entirely  devoid  of  resistance.  It  is  true  that  the  loss  may  be 
made  as  small  as  we  please  by  using  a very  large  conductor,  but,  in  practice, 
this  would  not  pay,  because  the  interest  on  the  cost  of  the  copper  would 
more  than  counterbalance  the  gain  in  the  efficiency  of  transmission.  In 
starting  out,  then,  to  estimate  the  size  of  wire  to  transmit  a given  amount 
of  power  over  a given  distance,  one  of  the  first  things  to  be  decided  is  the 
amount  of  power  that  may  be  allowed  for  loss  in  the  line,  because  it  is  evi- 
dent that  the  greater  the  power  lost,  the  higher  may  be  the  line  resistance, 
and  hence  the  smaller  the  wire.  The  pressure  required  to  force  a current 
C through  a wire  of  resistance  Ris  C X R-  This  pressure  is  generally  spoken 
of  as  the  drop,  for  the  reason  that  the  pressure  necessary  to  set  up  the  current 
through  the  line  is  lost,  and,  consequently,  the  pressure  falls  off  or  drops 
from  the  dynamo  to  the  receiving  end  of  the  line.  In  all  cases,  the  pressure 
at  the  end  of  the  line,  or  point  where  the  power  is  delivered,  is  equal  to  the 
pressure  at  the  dynamo  less  the  drop  in  the  line,  and,  conversely,  the  pres- 
sure that  must  be  maintained  by  the  dynamo  in  order  to  obtain  a given 
pressure  at  the  end  will  be  equal  to  the  pressure  at  the  receiving  end  plus 
the  drop  in  the  line.  To  illustrate  the  above,  take  the  case  shown  in  Fig.  3, 
where  a dynamo  D supplies  current  to  a motor  M situated  1 mile  distant. 
In  order  that  the  motor  may  operate  properly,  the  pressure  at  its  terminals 
must  be  kept  constant  at,  say,  500  volts.  It  is  evident,  then,  that  the  pressure 
between  a and  b (the  dynamo  terminals)  must  be  more  than  500  volts,  by  the 
drop  or  pressure  necessary  to  force  the  current  through  the  line.  If  the 
motor  is  taking  very  little  current,  i.  e.,  if  it  is  running  on  a very  light  load, 
the  current  will  be  small,  and  hence  the  drop  in  the  line  will  be  small.  In 
order,  then,  that  the  pressure  at  the  motor  may  remain  constant,  or  nearly 
so,  the  pressure  at  the  dynamo  must  automatically  increase  as  the  load 
increases.  The  way  in  which  this  is  done  will  be  explained  later;  for  the 
present,  we  are  concerned  only  with  the  calculation  of  the  line.  The  line 

must  evidently  be  designed 
with  regard  to  the  maximum 
current  it  has  to  carry.  We 
will  suppose,  for  the  sake  of 
illustration,  that  the  motor 
takes  50  amperes  at  full  load 
and  that  the  line  wire  is  of 
such  size  that  it  has  a resist- 
ance of  .2  ohm  per  mile.  The 
current  has  to  pass  through  2 
miles  of  wire  (because  it  has 
to  flow  out  through  1 mile  and 
back  through  1 mile),  and 
hence  encounters  a resistance 
of  .4  ohm.  The  drop  in  the 
line  will  then  be  .4  X 50  = 20  volts,  and  in  order  to  obtain  a pressure  of 
500  volts  at  the  motor,  the  pressure  at  the  dynamo  would  have  to  be  520 
volts.  The  loss  of  power  in  the  line  would  be  current  X drop  = 50  X 20  = 
1,000  watts,  or  about  1}  horsepower.  The  drop  in  an  electrical  transmission 
line  is  analogous  to  the  loss  in  pressure  due  to  the  friction  encountered 
by  water  flowing  through  a pipe  line. 

If,  in  the  illustration  just  given,  a size  of  wire  were  used  such  that  its 
resistance  would  be  .1  ohm  per  mile,  it  is  evident  that  the  loss  in  the  line 
would  be  halved,  but  the  weight  of  copper  required  doubled,  because  the 
wire  would  have  to  be  double  the  cross-section.  The  question  as  to  whether 
it  would  pay  better  to  invest  more  money  in  the  line  or  to  put  up  with  the 
larger  loss  is  something  that  must  be  determined  in  each  case  by  the  relative 
cost  of  power  and  copper. 

In  many  cases,  the  loss  allowed  in  the  line  is  about  10^!^  of  the  power  to  be 
delivered,  though  sometimes  the  loss  may  be  allowed  to  run  as  high  as  15^ 
or  25^.  This  applies  only  to  transmission  lines.  For  local  electric-light  or 
power-distributing  systems,  the  amount  of  drop  allowed  is  usually  about  2^ 
for  the  former  and  5^  for  the  latter. 

The  problem  of  calculating  line  wires  usually  presents  itself  in  the 
following  form:  Given,  a certain  amount  of  power  to  transmit  over  a known 


CALCULATION  OF  WIRE. 


211 


distance  with  a certain  allowable  loss,  to  determine  the  cross-section  of  the 
wire  required. 

Let  P = power  to  be  delivered,  expressed  in  watts;  P will  be  equal 
to  horsepower  delivered  at  end  of  line  multiplied  by  746; 

^ = allowable  percentage  of  loss  in  line,  i.  e.,  percentage  of 
power  delivered  that  may  be  lost  in  transmission; 

E = voltage  at  end  of  line  where  power  is  delivered; 

C = current  at  full  load; 

L = length  of  wire  through  which  current  flows. 

The  cross-section  of  the  copper  conductor  will  then  be  given  by  the 
following  formula: 

. 10.8  X P X P X 100  . 

^ = • (1) 

A will  be  expressed  in  circular  mils,  and  the  corresponding  size  of  wire 
may  be  found  by  consulting  the  wire  table.  It  should  be  noticed,  particu- 
larly, that  in  this  formula,  L is  the  average  length  of  conductor  through 
which  the  current  C flows.  The  application  of  distance  of  transmission  in 
the  formula  will  be  understood  from  what  follows. 

Example. — A mine  pump,  driven  by  an  electric  motor,  is  situated  2 miles 
from  the  power  station.  The  electrical  input  of  the  motor  at  full  load  is 
50  H.  P.,  and  the  voltage  at  its  terminals  is  to  be  500.  Estimate  the  size  of 
line  wire  necessary  to  supply  the  motor,  the  allowable  loss  in  the  line  being 
15^  of  the  power  delivered. 

The  actual  length  of  line  through  which  the  current  will  flow  will  be 
4 miles,  because  the  current  has  to  flow  out  to  the  motor  and  back  again. 
W e have 


watts 


50  X 746 
500 


= 74.6  amperes. 


Applying  formula  (1),  we  have 


10.8  X 2 X 2 X 5,280  X 74.6  X 100 
500  X 15 


226,880  circular  mils,  nearly. 


By  consulting  the  wire  table  it  is  found  that  this  calls  for  a wire  a little 
larger  than  No.  0000,  which  has  a cross-section  of  211,600  circular  mils; 
No.  0000  wire  would  probably  be  used  in  this  case,  as  it  is  near  enough  to  the 
calculated  size  for  all  practical  purposes.  In  case  the  calculated  size  comes 
out  larger  than  any  size  given  in  the  table,  a number  of  wires  may  be  used 
in  multiple  to  make  up  the  required  cross-section,  or,  what  is 'better,  a 
stranded  cable  may  be  used.  These  heavy  stranded  cables  may  now  be 
Obtained  in  different  sizes,  up  to  2,000,000  circular  mils  cross-section. 

It  is  evident  that,  in  the  above  examples,  if  it  were  allowable  to  waste 
twice  as  much  pgwer  in  the  line,  or  what  is  equivalent  to  having  a line  drop 
of  150  volts  instead  of  75  volts,  the  cross-section  of  wire  required  would  have 
been  one-half  of  that  found  above.  Such  a large  amount  of  loss  would, 
however,  be  objectionable  unless  power  was  very  cheap.  A large  drop  in 
the  line  is  in  any  case  objectionable,  because  the  voltage  at  the  receiving 
end  of  the  circuit  will  fall  off  greatly  unless,  the  voltage  at  the  generating 
station  is  raised,  as  the  load  comes  on,  in  order  to  compensate  for  the  line 
drop.  Most  of  the  uses  to  which  electricity  is  put,  in  mines  or  other  places, 
requires  that  the  pressure  at  the  point  where  the  power  is  utilized  shall  be 
kept  approximately  constant.  For  example,  in  the  case  of  incandescent 
lights,  the  lamps  will  fall  off  greatly  in  brightness  if  the  pressure  decreases 
even  by  a comparatively  slight  amount.  Also,  if  motors  are  being  operated, 
the  speed  will  vary  considerably  if  the  pressure  is  not  kept  constant,  and  it 
may  be  stated’,  in  general,  that  a large  line  loss  tends  to  poor  regulation  at 
the  end  of  the  circuit  where  power  is  delivered. 

From  the  above  considerations,  it  will  be  seen  that,  in  the  majority  of 
cases,  the  size  of  wire  to  be  used  under  given  conditions  is  determined  by 
the  allowable  amount  of  drop.  In  some  cases,  however,  especiallv  if  the 
current  is  to  be  used  near  at  hand,  the  size  of  wire  so  determined  might  not 
be  large  enough  to  carrj^  the  current  without  overheating.  Of  course,  in 
such  cases,  the  safe  carrying  capacity  of  the  wire  determines  the  size  to  be 
used,  and  the  drop  will  be  correspondingly  less. 

The  amount  of  current  that  a given  wire  can  carry  without  overheating 
depends  very  largely  on  the  location  of  the  wire.  For  example,  a wire 
strung  in  the  open  air  will  carry  a greater  current,  with  a given  temperature 
rise,  than  the  same  wire  would  if  boxed  up  in  a molding  or  conduit.  The 


212 


ELECTRICITY. 


table  on  page  209  gives  the  approximate  safe  carrying  capacity  of  wires 
when  strung  in  the  air. 

In  order  to  keep  down  the  size  of  wire  required  to  transmit  a given 
amount  of  power  over  a given  distance,  with  a certain  allowable  loss,  the 
current  must  be  kept  as  small  as  possible.  Now,  for  a given  amount  of 
power,  the  current  can  only  be  made  small  by  increasing  the  pressure, 
because  the  number  of  watts,  or  power  delivered,  is  equal  to  the  product  of 
the  current  and  the  pressure.  As  a matter  of  fact,  if  the  pressure  in  any 
given  case  be  doubled,  the  amount  of  copper  required  will  be  only  one- 
fourth  as  great;  in  other  words,  for  a given  amount  of  power  transmitted, 
the  weight  of  copper  required  decreases  as  the  square  of  the  voltage.  It  is 
at  once  seen,  then,  that  if  any  considerable  amount  of  power  is  to  be  trans- 
mitted over  long  distances,  a high  line  pressure  must  be  used  or  else  the  cost 
of  copper  becomes  prohibitory.  The  use  of  high  pressures  in  power  trans- 
mission will  be  taken  up  in  connection  with  alternating  currents. 

Insulated  Wires. — For  most  overhead  line  work  using  modern  voltages, 
w'eather-proof  insulated  wire  is  used.  This  wire  is  covered  with  two  or  three 
braids  of  cotton,  and  treated  with  insulating  compound.  For  inside  work, 
and  in  places  where  a better  quality  of  insulation  is  required,  rubber-covered 
wires  are  used.  The  following  table  gives  the  approximate  weight  of 
weather-proof  line  wire.  The  cost  of  the  wire  per  pound  varies  considerably, 
owing  to  the  variations  in  the  price  of  copper;  about  18  cents  per  pound 
may  be  taken  as  an  approximate  figure  in  making  calculations. 


Weather-Proof  Line  Wire  (Roebling’s). 


Number. 

B.  &S. 
Gauge. 

Double  Braid. 

Triple  Braid. 

Outside 
Diameter. 
32ds  Inch. 

Weight. 

Pounds. 

Outside 
Diameter. 
32ds  Inch. 

Weight. 

Pounds. 

Per 

1,000  Ft. 

Per 

Mile. 

Per 

1,000  Ft. 

Per 

Mile. 

0000 

20 

716 

3,781 

24 

775 

4,092 

000 

18 

575 

3,036 

22 

630 

3,326 

00 

17 

465 

2,455 

18 

490 

2,58/ 

0 

16 

375 

1,980 

17 

400 

2,112 

1 

15 

285 

1,505 

16 

306 

1,616 

2 

14 

245 

1,294 

15 

268 

1,415 

3 

13 

190 

1,003 

14 

.210 

1,109 

4 

11 

152 

803 

12 

164 

866 

5 

10 

120 

634 

11 

145 

766 

6 

9 

98 

518 

10 

112 

591 

8 

8 

66 

349 

9 

78 

412 

10 

7 

45 

238 

8 

55 

290 

12 

6 

30 

158 

7 

35 

185 

14 

5 

20 

106 

6 

26 

137 

16 

4 

14 

74 

5 

20 

106 

18 

3 

10 

53 

4 

16 

85 

For  high-tension  lines,  it  is  customary  to  use  bare  wires  and  insulate 
them  thoroughly  on  special  porcelain  insulators.  The  ordinary  weather- 
proof wire  insulation  is  of  little  or  no  use  as  a protection  when  these  high 
pressures  are  used,  and  it  only  makes  the  line  more  dangerous  because  of 
the  appearance  of  false  security  that  it  gives.  In  many  cases,  it  is  also 
better  to  use  bare  feeders  for  mine-haulage  plants,  because  the  ordinary 
insulation  soon  becomes  defective  in  a mine,  and  a wire  in  this  condition  is 
really  more  dangerous  than  a bare  wire,  because  the  latter  is  known  to  be 
dangerous  and  will  be  left  alone.  

CURRENT  ESTIMATES. 

Before  calculating  the  size  of  wire  required  for  any  given  case,  it  is 
necessary  to  know  the  current,  and  the  method  of  getting*  at  this  will  depend 
on  what  the  current  is  to  be  used  for. 


INCANDESCENT  LAMPS. 


213 


Fig.  4. 


Incandescent  Lamps. — These  are  usually  operated  on  110-volt  circuits,  Fig.  4, 
or  on  the  three-wire  system,  as  shown  in  Fig.  5.  In  the  three-wire  system, 
two  110-volt  dynamos  are  connected  in  series  so  that  the  voltage  across  the 
outside  wires  is  220.  The  neutral 
wire  a a connects  to  the  point  h 
where  the  machines  are  connected 
together.  The  wire  a a merely 
serves  to  carry  the  difference  in 
the  currents  on  the  two  sides  of 
the  system,  in  case  more  lamps 
should  be  burning  on  one  side 
than  on  the  other.  The  outside 
wires  for  such  a system  are  calcu- 
lated as  if  the  lights  were  operated 

two  in  series  across  220  volts.  The  middle  wire  is  usually  made  equal  in  size 
to  the  outer  wires.  An  ordinary  16  c.  p.  incandescent  lamp  requires  about 
55  watts  for  its  operation;  a 32  c.  p.  lamp  requires  about  110  watts. 

Hence,  in  the  case  of 
ordinary  parallel  dis- 
tribution, as  shown 
in  Fig.  4,  the  dy- 
namo will  deliver 
about  i ampere  for 
each  16  c.  p.  lamp 
operated,  and  1 am- 
pere for  each  32  c.  p. 
lamp.  In  the  case  of 
the  three-wire  sys- 
tem, each  pair  of  16 
c.  p.  lamps  will  take 
i ampere,  and  the 
total  number  of  amperes  in  the  outside  wires  will  be  one-fourth  the  num- 
ber of  lamps  operated. 

Example.— A certain  part  of  a mine  is  to  be  illuminated  by  fifty  16  c.  p. 
lamps  and  ten  32  c.  p.  lamps.  This  portion  of  the  mine  is  1,000  ft.  from  the 
dynamo  room,  and  the  allowable  drop  in  pressure  is  b<fo.  The  lamps  are  to 
be  run  on  a 110-volt  system.  Find  the  size  of  wire  required. 


Fifty  16  c.  p.  lamps  require 25  amperes 

Ten  32  c.  p.  lamps  require lb  amperes 

Total  current 35  amperes 

We  have,  then. 


. , .,  10.8X1,000  X 2 X 35X100 

circular  mils  = w r = 137,454  circular  mils, 

110  X 5 

or  about  a No.  00  B.  & S.  wire. 

Example. — Take  the  same  case  as  in  the  last  example,  but  suppose  the 
lights  to  be  operated  on  the  three-wire  system.  There  will  then  be  twenty- 
five  16  c.  p.  lamps  and  five  32  c.  p.  lamps  on  each  side  of  the  circuit,  and 
the  total  current  in  the  outside  wires  will  be  17.5  amperes.  The  voltage 
between  the  outside  wires  will  be  220,  and  we  will  have 

, 10.8  X 1,000  X 2 X 17.5  X 100  , ., 

circular  mils  = ^ ^ = 34,363  circular  mils, 

220  X 5 

or  about  a No.  5 B.  & S.  wire. 

If  we  make  the  central  wire  also  of  this  size,  it  is  seen  that  this  system 
would  require  three-eighths  the  amount  of  copper  called  for  by  the  plain 
110-volt  system.  There  is  the  disadvantage  that  two  dynamos  are  needed. 

Note. — The  length  to  be  used  in  the  wiring  formula  is  the  average  dis- 
tance traversed  by  the  current  in  the  conductor.  For  example,  if,  as  in 
Fig.  6 (a),  the  lamps  were  all  grouped  or  bunched  at  the  end  of  the  line,  the 
length  used  in  the  formula  would  be  twice  that  from  G to  A,  because 
the  whole  current  has  to  flow  out  to  A through  one  main  and  back  through  the 
other.  In  other  words,  the  whole  current  here  passes  through  the  whole 
length  of  the  line.  In  case  the  load  is  uniformly  distributed  all  along  the 
line,  as  shown  in  Fig.  6 (5),  it  is  evident  that  the  current  decreases  step  by 
step  from  the  dynamo  to  the  end.  In  such  a case,  the  length  or  distance  to 
be  used  in  the  formula  is  one-half  that  used  in  the  former  case,  or  simply 
the  distance  from  the  dynamo  to  the  end,  instead  of  twicq  this  distance, 


214 


ELECTRICITY. 


Arc  Lamps.— Arc  lamps  are  frequently  run  on  constant-potential  circuits, 
and  usually  consume  from  400  to  500  watts.  There  are  so  many  types  of 
these  lamps  that  it  is  difficult  to  give  any  current  estimates  that  will  be  gen- 
erally applicable.  Enclosed  arc  lamps  usually  take  from  3 to  5 amperes 
when  run  on  110-volt  circuits. 

Motors.— Practically  all  the  motors  used  in  mining  work  are  run  on  the 
constant-potential  system,  either  at  250  or  500  volts.  The  efficiency  of  ordi- 
nary motors  will  vary  from  70^  to  95^0  or  higher,  depending  on  the  size.  The 
efficiency  is  greater  with  the  larger  machines,  and,  for  the  ordinary  run  of 
motors,  it  will  probably  lie  between  80^  and  90fc.  By  efficiency  is  here  meant 
the  ratio  of  the  useful  output  at  the  pulley  or  pinion  of  the  motor  to  the 
total  input.  The  accompanying  table  gives  the  efficiency  of  motors  of 
ordinary  size: 

Approximate  Motor  Efficiency. 
f to  1|  H.  P.,  inclusive  = 75^  efficiency 
3 to  5 H.  P.,  inclusive  = W efficiency 
to  10  H.  P.,  inclusive  = 85^  efficiency 
15  H.  P.  and  upwards  = 90fo  efficiency 
If  the  required  output  in  horsepower  is  known,  the  input  will  be 
jj.  H.P.X746 
efficiency  ’ 

W 

and  the  current  required  at  full  load  will  be  (7  = where  E is  the  voltage 
between  the  mains  at  the  motor. 

, Conductors  for  Electric-Haulage  Plants.— In  electric-haulage  plants,  the  rails 
take  the  place  of  one  of  the  conductors,  so  that,  in  calculating  the  size  of 
feeders  required,  only  the  overhead  conductors  are  taken  into  account.  It 
is  a difficult  matter  to  assign  any  definite  value  to  the  resistance  of  the  track 
circuit,  as  it  depends  very  largely  on  the  quality  of  the  rail  bonding  at  the 


joints.  If  this  bonding  is  well  done,  the  resistance  of  the  return  circuit 
should  be  very  low,  because  the  cross-section  of  the  rails  is  comparatively 
large.  For  calculating  the  supply  feeders,  we  may  use  the  approximate 
formula, 


circular  mils  = 


14XXX  CXIOO 
EXio  drop 


In  this  case,  L is  the  average  length  of  feeder  over  which  the  power  is  to 
be  transmitted.  It  will  be  noticed  that  the  constant  10.8  appearing  in  the 
previous  formulas  has  here  been  increased  to  14.  This  has  been  done  to  allow, 
approximately,  for  the  track  resistance,  but  this  constant  might  vary  con- 
siderably, depending  on  the  quality  of  the  rail  bonding.  If  the  load  is  all 
bunched  at  the  end  of  the  feeder,  Xis  the  actual  length  of  the  feeder  in  feet. 
If  the  load  is  uniformly  distributed  all  along  the  line,  as  it  would  be  if  a 
number  of  locomotives  were  continually  mo\dng  along  the  line,  the  dis- 
tance L in  the  above  formula  would  be  taken  as  one-h^f  that  used  in  the 
case  where  the  load  was  bunched  at  the  end.  In  other  words,  the  whole 
current  C would  only  flow  through  an  average  of  one-half  the  length  of  the 
line. 


DYNAMOS  AND  MOTORS. 


215 


Example.— In  Fig.  7,  a & represents  a section  of  track  4^000  ft.  long.  From 
the  dynamo  c to  the  beginning  of  the  section,  the  distance  is  1,200  ft.  The 
trolley  wire  is  No.  00  B.  & S.,  and  is  fed  from  the  feeder  at  regular  intervals. 
Two  mining  locomotives  are  operated,  each  of  which  takes  an  average  cur- 
rent of  75  amperes.  The  total  allowable  drop  to  the  end  of  the  line  is  to  be 
bio  of  the  terminal  voltage,  which  is  500  volts.  Calculate  the  size  of  feeder 
required,  assuming  that  the  constant  14,  in  the  formula,  takes  account  of  the 
resistance  of  the  return  circuit. 

Since  the  locomotives  are  moving  from  place  to  place,  the  center  of  dis- 
tribution for  the  load  may  be  taken  at  the  center  of  the  4,000  ft.  The 


-4000- 


■H 


Fig.  7. 


Trolley 


distance  L will  then  be  1,200  + 2,000  = 3,200  ft.  The  total  current  will  be 
150  amperes;  hence,  we  have 


500X5 


This  would  require  either  a stranded  cable  or  the  use  of  two  No.  00  wires 
in  parallel  from  c to  a.  From  a to  5 we  have  the  No.  00  trolley  wire  in 
parallel  with  the  feeder;  hence,  the  section  of  feeder  ah  may  be  a single 
No.  00  wire.  In  many  cases,  the  drop  is  allowed  to  run  as  high  as  10/p, 
because  the  loads  are  usually  heavier,  and  the  distances  longer,  than  in  the 
example  given  above.  


DYNAMOS  AND  MOTORS. 

A dynamo  is  a machine  for  converting  mechanical  energy  into  electrical 
energy  by  moving  conductors  relatively  to  a magnetic  held. 

An  electric  motor  is  a machine  for  converting  electrical  energy  into 
mechanical  energy  by  the  relative  motion  between  conductors  carrying  a 
current  and  a magnetic  held. 

In  the  case  of  a dynamo,  a number  of  conductors  are  made  to  move 
across  a magnetic  held  by  means  of  a steam  engine  or  other  prime  mover, 
and  the  result  is  that  an  E.  M.  F.  is  set  up  in  the  conductors,  and  this  E.  M.  F. 
will  set  up  a current  if  the  circuit  is  closed. 

In  the  case  of  a motor,  a number  of  conductors  are  arranged  so  that  they 
are  free  to  move  across  a magnetic  held,  and  a current  is  sent  through  these 
conductors  from  some  source  of  electric  current.  The  current  howing 
through  these  conductors  reacts  on  the  magnetic  held  and  causes  the 
conductors  to  move,  thus  converting  the  electrical  energy  delivered  to  the 
motor  into  mechanical  energy. 

As  far  as  mechanical  construction  goes,  dynamos  and  motors  are  almost 
identical,  and  the  operation  of  the  motor  is  exactly  the  reverse  to  that  of  the 
dynamo. 

Dynamos  and  motors  may  be  divided  into  two  general  classes:  (a)  Dyna- 
mos and  motors  for  direct  current,  (6)  dynamos  and  motors  for  alternating 
current. 


DIRECT-CURRENT  DYNAMOS. 

Principle  of  Action.— Direct-current  dynamos  are  those  that  furnish  a 
current  that  always  hows  in  the  same  direction.  This  kind  of  dynamo  is 
largely  used  for  incandescent  lighting,  and  also  for  the  operation  of  street 
railways. 

A dynamo  generates  an  E.  M.  F.  by  the  motion  of  conductors  across  a 
magnetic  held;  hence,  at  the  outset,  it  is  seen  that  there  must  be  at  least  two 
essential  parts  to  a dynamo;  namely,  a magnet  of  some  kind  to  set  up  a 
magnetic  held,  and  a series  of  conductors  arranged  so  that  they  may  be 
moved  or  revolved  in  the  magnetic  held.  The  hrst  part  is  known  as  the 


216 


DYNAMOS  AND  MOTORS. 


field  magnet,  or  very  often,  simply  as  the  field.  The  second  part  is  known  as 
the  armature.  The  field  is  supplied  by  means  of  a powerful  electromagnet 
which  is  magnetized  by  the  current  in  the  field  coils.  Fig.  8 shows  a typical 
six-pole  magnet  of  this  kind;  B,  B are  the  magnetizing  coils,  which,  when  a 
current  is  sent  through  them,  form  powerful  magnetic  poles  at  N,  S.  The 
framework  A of  such  a field  magnet  is  usually  made  of  cast  iron  or  cast  steel. 

These  field  magnets  may 
have  any  number  of  poles, 
but  machines  of  ordinary 
size  are  usually  provided 
with  from  two  to  eight  poles. 

The  armature  usually  con- 
sists of  a number  of  turns  of 
insulated  copper  wire, 
arranged  around  the  periph- 
ery of  a ring  or  drum  built 
up  of  soft  iron  sheets.  Fig.  9 
shows  the  construction  of  a 
typical  armature  of  the  ring 
type.  The  winding  is 
divided  into  a number  of 
sections,  and  the  terminals 
connected  to  the  commutator. 

This  commutator  consists 
of  a number  of  copper  bars, 
insulated  from  each  other  by 
means  of  mica,  the  bundle  of 
bars  being  clamped  firmly 
into  place  and  turned  up  to 
form  a true  cylindrical  sur- 
face. The  sections  in  the 
commutator  correspond  with 
those  in  the  armature,  and 
the  use  and  operation  of  the 
commutator  will  be  described  later.  The  winding  on  the  ring  is  endless, 
i.  e.,  it  consists  of  a number  of  coils  or  sections  c,  the  end  of  one  section 


Fig.  8. 


COMPLETE  ARMATURE.. 


^anduetor 

fnsutaticn. 


"•Binding- ufiresr 

Fig.  9. 


being  joined  to  the  beginning  of  the  next,  thus  forming  an  endless  coil,  as 
shown  in  Fig.  10.  The  construction  of  such  a ring  armature  would  be  as 
shown  in  Fig.  9. 


DIRECT-CVRRENT  DYNAMOS. 


217 


Suppose  the  ring  shown  in  Fig.  10  with  its  endless  winding  to  be  rotated 
between  the  poles  of  a 2-pole  field  magnet.  We  will  then  have  the  condi- 
tion of  affairs  as  indicated  in  Fig.  10.  The  magnetic  lines  will  flow  from  the 
N pole  of  the  field  magnet  across  through  the  iron  core  of  the  armature  and 
enter  the  S pole  on  the  other  side.  Since  all  the  conductors  on  the  right- 
hand  face  of  the  ring  are  moving  upwards,  they  will  have  an  E.  M.  F.  gen- 
erated in  them  in  one  direction,  while  the  E.  M.  F.  in  the  conductors  on  the 
left  side  will  have  an  E.  M.  F.  in  the  opposite  direction,  because  all  the 
conductors  on  this  side  are 
moving  downwards,  or  in 
the  opposite  direction,  to 
those  on  the  other  side. 

These  two  opposing  E.  M. 

F.’s  will  meet  at  a,  as 
shown  by  the  arrowheads, 
and  will  neutralize  each 
other  so  that  no  current 
will  flow  through  the 
windings  of  the  armature. 

Suppose,  however,  that 
taps  are  connected  at  the 
points  a and  a',  as  shown 
by  the  dotted  lines,  and 
these  taps  connected  to 
two  rings  r,  r',  mounted  so 
as  to  revolve  with  the 
armature.  By  allowing 
brushes  b,  b'  to  press  on  Fig.  10. 

these  rings,  we  can  make 

connection  with  an  outside  circuit  d,  which  may  consist  of  a number  of 
lamps  or  any  other  device  through  which  we  wish  to  send  a current.  By 
putting  in  the  taps  at  a and  a',  we  have  allowed  the  two  opposing  E.  M.  F.’s 
to  set  up  a current  through  the  common  connections  to  the  rings,  and 
thence  through  the  outside  circuit.  Current  now  flows  in  each  half  of  the 
armature  winding,  unites  at  a,  flows  out  by  means  of  ring  r'  and  brush  b', 
thence  through  the  outside  circuit  d to  brush  b and  ring  r,  from  whence  it 
passes  to  a',  and  thus  completes  the  circuit.  When  the  ring  makes  a half 
revolution  from  the  position  shown  in  the  figure,  it  is  seen  that  the  current 
in  the  ouside  circuit  will  flow  in  the  opposite  direction.  In  fact,  an  arrange- 
ment of  this  kind  would  deliver  a current  that  would  be  periodically  revers- 
ing in  the  outside  circuit,  or 
it  would  be  what  is  known  as 
an  alternating  current. 

Instead  of  simply  bringing 
out  two  terminals  to  rings, 
suppose  the  winding  to  be 
tapped  at  a fairly  large  number 
of  .points,  and  connections 
brought  down  to  a number  of 
insulated  strips,  as  shown  in 
Fig.  11.  If  the  armature  be 
now  revolved,  it  is  seen  that 
the  brushes  will  come  in  contact 
with  successive  bars  and  keep 
the  outside  circuit  in  such  re- 
lation to  the  armature  winding 
that  the  current  will  always 
flow  through  it  in  the  same 
direction . Moreover,  if  the  num- 
Fig.  11.  her  of  divisions  in  the  armature 

be  large,  the  current  will  fluc- 
tuate very  little,  being  nearly  as  steady  as  that  obtained  from  a battery. 
The  arrangement  made  up  of  insulated  bars  is  called  the  commutator, 
because  it  commutes  or  changes  the  relation  of  the  outside  circuit  to  the 
armature  winding  so  that  the  current  in  the  outside  circuit  always  flows 
in  the  same  direction.  All  practical  machines  used  for  the  generation 
of  direct  current  must  be  provided  with  such  a commutator.  When  alter- 
nating currents  are  used  it  is  only  necessary  to  use  plain  collector  rings,  as 


218 


DYNAMOS  AND  MOTORS, 


shown  in  Fig.  10.  The  foregoing  brief  description  will  give  a general  idea 
as  to  the  construction  of  an  ordinary  direct-current  dynamo  or  motor. 
Drum-wound  armatures  are  more  frequently  used  than  the  ring  type  shown, 
but  the  action  is  the  same  in  either  case.  , ^ ^ ^ ^ ^ 

Factors  Determining  E.  M.  F.  Generated.— A dynamo  should  be  looked  upon 
as  a machine  for  maintaining  an  electrical  pressure  rather  than  as  a machine 
for  generating  a current.  A pump  does  not  manufacture  water— it  merely 
maintains  a head  or  pressure  that  causes  water  to  flow  wherever  an  outlet  is 
provided  for  it  to  flow  through.  In  the  same  way,  a dynamo  maintains  a 
pressure,  and  this  pressure  will  set  up  a current  whenever  the  circuit  is 
closed,  so  that  the  current  can  flow.  The  important  thing  to  consider, 
therefore,  is  the  E.  M.  F.  that  the  dynamo  is  capable  of  generating. 

The  E.  M.  F.  generated  by  an  armature  depends  on  the  total  number  ol 
magnetic  lines  cut  through  per  second  by  the  armature  conductors.  This 
means  that,  in  the  first  place,  the  faster  the  armature  runs,  the  higher  will  be 
the  E.  M.  F.;  in  the  second  place,  the  greater  number  of  conductors  or  turns 
there  are  on  the  armature,  the  higher  will  be  the  E.  M.  F.;  and  in  trm  tmrd 
place,  the  stronger  the  magnetic  field,  the  higher  will  be  the  E.  M.  F.  The 
E.  M.  F.  in  terms  of  these  quantities  may  be  written 

nCN 

100,000,000’ 

where  n = speed  in  revolutions  per  second; 

C = number  of  conductors  on  face  of  the  armature; 

N = number  of  magnetic  lines  flowing  from  one  pole. 

The  constant  100,000,000  is  necessary  to  reduce  the  result  to  volts.  This 
equation  enables  us  to  make  calculations  relating  to  any  two-pole  dynamo, 
and  with  slight  modification  it  is  applicable  to  machines  with  field  magnets 


having  a number  of  poles.  It  will  not  be  necessary  to  consider  this  formula 
further  here,  as  the  main  thing  to  fix  in  mind  is  that  the  E.  M.  F.  is  propor- 
tional to  the  three  quantities:  speed,  number  of  conductors,  and  strength  of 
field. 

Field  Excitation  of  Dynamos.— In  the  earliest  form  of  dynamo,  the  magnetic 
field  in  which  the  armature  rotated  was  set  up  by  means  of  permanent 
magnets.  Permanent  magnets  are,  however,  very  weak  compared  with 
electromagnets,  which  are  excited  by  means  of  current  flowing  around 
coils  of  wire  wound  on  a soft-iron  core,  as  shown  in  Fig.  13.  As  soon  as  the 
current  ceases  flowing  around  the  coils  of  an  electromagnet,  the  magnetism 
almost  wholly  disappears,  but  a small  amount,  known  as  the  residual  magnet- 
ism remains.*  It  is  to  this  residual  magnetism  that  the  dynamo  owes  its 
ability  to  start  up  of  its  own  accord  and  excite  its  own  field  magnets. 
When  the  armature  is  first  started  to  revolve,  a very  feeble  E.  M.  F.  is  gener- 
ated in  it,  but  the  armature  is  connected  to  the  field  coils  in  such  a way 
that  this  small  E.  M.  F.  is  able  to  force  a small  current  through  the  field 
coils,  and  thus  set  up  a larger  amount  of  magnetism  in  the  field.  This  in 
turn  increases  the  E.  M.  F.  in  the  armature,  and  the  building-up  process  goes 
on  rapidly  until  the  dynamo  generates  its  full  pressure.  There  are  three 
different  methods  in  use  for  supplying  the  field  coils  with  current,  and  con- 
tinuous-current dynamos  are  divided  into  three  classes,  according  to  the 
method  used  for  exciting  their  fields.  These  three  classes  are:  (a)  Series- 
wound  dynamos;  (&j  shunt- wound  dynamos;  (c)  compound-wound  dynamos^ 


SHUNT-WOUND  DYNAMOS. 


219 


(a)  Series-Wound  Dynamos. — In  this  class  of  machine,  the  field  coils  are 
connected  in  series  with  the  armature,  and  all  the  current  that  passes 
through  the  armature  also  passes  through  the  field  and  the  outside  circuit. 
This  arrangement  is  shown  in  Fig.  12,  where  N 
and  represent  the  poles  of  the  magnet,  -f  B 
and  — B the  brushes,  and  R e the  outside  cir- 
cuit, which  may  consist  of  lamps,  motors,  or 
any  other  device  in  which  it  is  desired  to 
utilize  the  current.  It  will  be  noticed  that  with 
an  arrangement  of  this  kind,  the  E.  M.  F.  will 
increase  as  the  current  increases,  because  the 
field  will  become  stronger  and  the  speed  is  sup- 
posed to  remain  constant.  This  will  be  true  up 
to  the  point  where  the  field  carries  all  the  mag- 
netism it  is  capable  of,  or,  in  other  words,  until 
it  becomes  saturated.  After  this  point  is 
reached,  the  E.  M.  F.  will  increase  very  little 
with  increase  of  current.  In  most  of  the 
work  connected  with  lighting  or  power  trans- 
mission, it  is  desirable  to  have  the  voltage 

remain  nearly  constant.  For  this  reason,  therefore,  the  series  method  of 
excitation  has  not  been  very  largely  used  for  dynamos.  The  only  style 
of  generator  to  which  it  has  been  applied  at  all  generally  is  the  arc-light 
dynamo,  and  these  machines  are  provided  with  an  automatic  regulator  of 
some  kind  to  vary  the  voltage  as  desired.  The  series  field  winding  has, 
however,  been  largely  used  in  connection  with  the  motors  operated  on 
constant-pressure  circuits,  as  will  be  taken  up  later  in  connection  with 
motors. 


{h)  Shunt-Wound  Dynamos.— This  style  of  machine  has  not  been  used 
largely  of  late  years,  although  it  was  formerly  very  common.  Its  use  is  at 
present  confined  more  particularly  to  machines  of  small  size.  In  this 
method  of  excitation,  the  field  is  connected  as  a shunt  or  by-pass  to  the 
armature;  i.  e.,  the  field  winding  is  connected  in  parallel  with  the  armature. 
This  winding  consists  of  a large  number  of  turns  of  fine  wire,  so  that  its 
resistance  is  high  and  only  a small  part  of  the  total  current  flows  through  it. 
Fig.  13  shows  the  connections  for  this  kind  of  field  excitation.  An  adjust- 
able resistance  r is  usually  inserted  in  the  field  circuit,  and  by  cutting  this 
resistance  in  or  out,  the  field  may  be  weakened  or  strengthened  and  the 
voltage  varied  accordingly.  With  this  type  of  machine,  the  current 
through  the  field  does  not  vary  greatly  from  no  load  to  full  load,  and  il 
the  dynamo  is  well  designed,  the  pressure  at  the  brushes  will  keep  approxi- 
mately constant.  The  pressure  will,  however,  always  fall  off  more  or  less, 
on  account  of  the  drpp  in  the  armature,  due  to  its  resistance,  and  also  upon 
the  tendency  that  the  current  in  the  armature  has  of  weakening  the  field. 
The  shunt  winding  is  used  quite  largely  for  motors. 

(c)  Compound-Wound  Dynamos.— The  compound-wound  dynamo  is  the  one 
most  largely  used  for  direct-current  power  and  light  distribution,  and  it  is  so 
called  because  the  winding  used  for  exciting  the  field  is  a combination  of  the 
series  and  shunt  windings  previously  described.  The  series  winding 
serves  the  purpose  of  keeping  up  the  field  strength  while  the  load  is 
increased,  and  thus  keeps  the  pressure  constant,  or  even  makes  it  rise  with 
increased  load,  if  so  desired.  When  the  series  winding  is  so  adjusted  that 
the  pressure  rises  as  the  load  is  increased,  the  machine  is  said  to  be  overcom- 
pounded. Fig.  14  shows  the  connections  for  such  a machine.  It  will  be  seen 
that  the  shunt  winding  is  connected  as  before,  a field  resistance  or  rheostat, 
not  shown  in  the  figure,  being  inserted  for  the  purpose  of  adjusting  the  volt- 
age. One  brush  connects  directly  to  one  terminal  of  the  machine  + T,  while 
the  other  brush  connects  to  one  end  of  the  series  winding  on  the  field.  The 
other  end  of  the  series  winding  forms  the  other  terminal  — T,  to  which  the 
outside  circuit  Reis  connected.  It  is  thus  seen  that  the  shunt  coil  supplies 
a certain  amount  of  initial  magnetization  that  is  augmented  by  the  magnet- 
ism supplied  by  the  series  coils.  Of  course,  care  must  be  taken  to  see  that 
the  current  in  the  series  coils  circulates  around  the  field  in  the  same  direc- 
tion as  that  in  the  shunt  coils,  otherwise  the  effect  would  be  to  make  the 
E.  M.  F.  fall  off  with  increasing  load  instead  of  keeping  it  up.  This  is  the  style 
of  dynamo  used  almost  exclusively  for  electric  haulage  plants,  as  well  as 
plants  for  direct-current  illuminating  purposes. 


220 


DYNAMOS  AND  MOTORS, 


DIRECT-CURRENT  MOTORS. 

Direct-current  motors  are  in  general  almost  identical,  so  far  as  construc- 
tion goes,  with  direct-current  dynamos.  Motors  are  often  required  to  oper- 
ate under  very  trying  conditions,  as  for  example,  in  mine  haulage  or  pump- 
ing plants  or  on  the  ordinary  street  car.  For  this  reason,  their  mechanical 
construction  often  differs  somewhat  from  that  of  the  dynamo,  the  design 
being  modified  in  such  a way  as  to  enclose  the  working  parts  as  completely 
as  possible,  and  thus  protect  them  from  dirt  and  injury.  The  two  kinds  of 
motors  most  commonly  used  are  the  series  and  shunt  varieties.  Compound- 
wound  motors  are  only  used  for  a few  special  kinds  of  work.  Practically  all 
of  the  motors  in  use*  are  operated  from  constant-pressure  mains;  i.  e.,  lhe 
pressure  at  the  terminals  of  the  motor  is  practically  constant,  no  matter 
what  load  it  may  be  carrying.  We  will  here  consider  constant-potential 
motors  only. 

Principles  of  Operation. — If  the  fields  of  an  ordinary  constant-potential 
dynamo  are  excited  and  a current  supplied  to  the  armature  from  some  out- 
side source,  such  as  another  dynamo  D,  Fig.  15,  so  that  the  current  enters 

at  -\-B,  and  passing  through 
the  winding  in  the  direc- 
tion indicated  by  the 
arrowheads, leaves  at  brush 
— B,  it  will  be  found  that 
all  of  the  conductors  under 
the  /S  pole  face,  5,  c,  d,  c,  /, 
and  g,  will  tend  to  move 
downwards,  and  all  those 
under  the  N pole  face,  j,  k, 
I,  m,  n,  and  o,  will  tend  to 
move  upwards,  as  indicated 
by  the  small  arrows. 

These  forces  combine  to 
produce  a tendency  of  the 
armature  to  rotate  about 
its  axis  as  indicated  by  the 
large  arrows,  which*  ten- 
dency is  called  the  torque 
of  the  motor. 

The  amount  of  this 
torque — which  is  usually 
expressed  in  pound-feel; 
that  is,  a certain  number  of  pounds  acting  at  a radius  of  a certain  number 
(usually  1)  of  feet— depends  on  (1)  the  strength  of  the  field,  (2)  the  number 
of  conductors,  (3)  their  mean  distance  from  the  axis  of  the  armature,  and 
(4)  the  amperes  in  each  conductor.  In  any  given  machine,  the  second  and 
third  conditions  are  constant,  so  that  the  torque  depends  on  the  strength  of 
the  field  and  the  current. 

If  the  armature  is  stationary,  the  E.  M.  F.  required  to  send  the  current 
through  the  winding  is  only  that  necessary  to  overcome  the  drop,  which  is 
due  to  the  resistance  of  the  ‘winding.  If  the  torque  exerted  by  this  current 
is  greater  than  the  opposition  to  motion,  so  that  it  causes  the  armature  to 
revolve,  the  motion  of  the  conductors  through  the  field  generates  in  them 
an  E.  M.  F.  that  is  opposed  to  the  E.  M.  F.  that  is  sending  the  current  through  the 
armature. 

This  opposing  E.  M.  F.,  or  counter  E.  M.  F.  as  it  is  called,  then  diminishes 
the  effect  of  the  applied  E.  M.  F.,  so  that  the  current  is  reduced,  reducing 
the  torque.  Should  the  torque  still  be  greater  than  the  opposition  to 
motion,  the  speed  of  the  armature  will  continue  to  increase,  increasing  the 
counter  E.  M.  F.,  and  thereby  further  reducing  the  current  and  the  cor- 
responding torque,  until  the  torque  just  balances  the  opposition  to  the  motion, 
when  the  speed  will  remain  constant. 

At  all  times,  the  drop  of  potential  through  the  armature  is  equal  to  the 
difference  between  the  counter  and  the  applied  E.  M.  F.*s,  and  as  the  product  of 
this  drop  and  the  current  represents  energy  wasted,  it  is  desirable  to  make  it 
as  low  as  possible.  In  good  motors  of  about  10  H.  P.  output,  the  drop  in 
the  armature  is  seldom  more  than  about  5^  of  the  applied  E.  M.  F.,  and  is 
less  in  larger  machines. 

This  being  the  case,  it  is  evident  that  if  the  armature  is  at  rest,  so  that  it 


DIRECT-CURRENT  MOTORS. 


221 


has  no  counter  E.  M.  F.,  and  is  connected  directly  to  the  mains,  a very  large 
current  will  flow  through  it,  which  would  be  liable  to  damage  the  armature. 
On  this  account  an  external  resistance,  called  a starting  resistance,  is  con- 
nected in  series  with  the  armature  when  it  is  to  be  started.  This  resistance 
is  made  great  enough  to  prevent  more  than  about  the  normal  current  from 
flowing  through  the  armature  when  it  is  at  rest;  as  the  armature  speeds  up 
and  develops  some  counter  E.  M.  F.,  this  resistance  is  gradually  cut  out. 
until  the  armature  is  connected  directly  to  the  mains,  and  is  running  at 
normal  speed. 

The  energy  represented  by  the  product  of  drop  in  the  armature  and  the 
current  is  wasted;  that  represented  by  the  product  of  the  current  and  the 
rest  of  the  E.  M.  F.,  that  is,  the  counter  E.  M.  F.,  is  the  energy  required  to 
keep  the  armature  in  motion. 

Aside  from  the  comparatively  small  amount  of  current  required  to  furnish 
the  torque  necessary  for  overcoming  the  frictional  losses  in  the  motor  itself, 
which  are  practically  constant,  the  amount  of  current  taken  from  the  mains 
is  directly  proportional  to,  and  varies  automatically  with,  the  amount  of  the 
external  load;  for,  if  this  external  load  is  increased,  the  current  which  has 
been  flowing  in  the  armature  cannot  furnish  sufficient  torque  for  this 
increased  load,  so  that  the  machine  slows  down.  This  decreases  the  counter 
E.  M.  F.,  which  immediately  allows  more  current  to  flow  through  the  arma- 
ture, increasing  the  torque  to  the  proper  amount.  If  the  external  load 
is  decreased,  the  current  flowing  furnishes  an  excess  of  torque,  which 
causes  the  speed  to  increase,  increasing  the  counter  E.  M.  F.,  and  de- 
creasing the  current  until  it  again  furnishes  only  the  required  amount 
of  torque. 

Since  the  counter  E.  M.  F.  is  very  nearly  equal  to  the  applied,  it  is  only 
necessary  for  it  to  vary  a small  amount  to  vary  the  current  within  wide 
limits.  For  example,  if  the  resistance  of  a certain  armature  is  1 ohm,  and  it 
is  supplied  with  current  at  a constant  potential  of  250  volts,  then,  when  a 
current  of  10  amperes  is  flowing  through  it,  the  drop  is  10  X 1 = 10  volts, 
and  the  counter  E.  M.  F.  is  250  — 10  = 240  volts.  Now,  if  the  current  is 
reduced  to  1 ampere,  the  drop  is  1 X 1 = 1 volt,  and  the  counter  E.  M.  F.  is 

9 

250  — 1 = 249  volts;  that  is,  the  counter  E.  M.  F.  only  varies  or  3.75^, 

240 

9 

while  the  current  varies  — , or  90^. 

As  stated  before,  the  field  magnets  of  constant-potential  motors  are 
usually  either  shunt-wound  or  series-wound. 

If  shunt-wound,  and  supplied  from  a constant-potential  circuit,  the  mag- 
netizing force  of  the  field  coils  is  constant,  giving  a practically  constant 
field.  This  being  the  case,  the  counter  E.  M.  F.  is  directly  proportional  to 
the  speed,  so  that  variations  of  the  load  make  only  slight  variation  in 
the  speed.  A shunt- wound  motor  is  then  (practically)  a constant^speed 
motor. 

With  series-wound  motors,  the  strength  of  the  field  varies  with  the  cur- 
rent; if  the  load  on  such  a motor  is  reduced,  the  excess  of  torque  makes  the 
armature  speed  up,  but  as  the  resulting  decrease  of  the  current  decreases 
the  field  strength,  the  armature  must  speed  up  to  a much  greater  extent,  in 
order  to  increase  the  counter  E.  M.  F.  to  the  right  degree,  than  would  be 
necessary  if  the  field  were  constant.  If  the  load  is  increased,  the  increase 
in  the  current  so  increases  the  field  strength  that  the  speed  must  decrease 
considerably,  in  order  to  decrease  the  counter  E.  M.  F.  by  the  right  amount. 
The  speed  of  a series-wound  motor,  then,  varies  largely  with  variations  in 
the  load. 

An  advantage  of  the  series  motor  is  that  if  a torque  greater  than  the 
normal  is  required,  it  can  be  obtained  with  less  current  than  with  a shunt 
motor,  since  the  increased  current  increases  the  field  strength,  and  the 
torque  is  proportional  to  both  these  factors. 

It  would  not  be  practicable  to  make  the  field  strength  of  a shunt  motor 
as  great  as  is  possible  to  get  with  a series  motor,  since  it  would  require  a 
very  large  magnetizing  force,  and  with  the  shunt  winding,  this  extra 
magnetizing  force  would  have  to  be  expended  all  the  time,  whether  the 
strong  field  was  required  or  not,  which  would  be  very  wasteful;  in  the 
series  motor,  however,  this  extra  magnetizing  force  is  only  expended  whil^ 
It  is  needed. 


222 


DYNAMOS  AND  MOTORS, 


A disadvantage  of  the  series  winding  is  that  if  all  the  load  is  taken  off, 
the  current  required  to  drive  the  motor  is  very  small,  making  a weak  field, 
which  requires  such  a high  speed  to  generate  the  proper  counter  E.  M.  F. 
that  the  armature  is  liable  to  be  damaged.  In  other  words,  the  motor  will 
race,  or  run  away,  if  the  load  is  all  removed.  This  cannot  occur  with  the 
shunt  motor  as  long  as  the  field  circuit  remains  unbroken. 

On  account  of  the  above  features,  shunt  motors  are  used  to  drive 
machinery  that  requires  a' nearly  constant  speed  with  varying  loads,  or 
which  would  be  damaged  if  the  speed  should  become  excessive,  such  as 
ordinary  machinery  in  shops  and  factories,  pumps,  etc.  Series  motors  are 
used  on  street  cars,  to  operate  hoists,  etc.,  where,  on  account  of  the  gearing 
used,  the  load  cannot  be  entirely  thrown  off,  and  the  torque  required  at 
starting  and  getting  quickly  up  to  speed  is  much  greater  than  the  normal 
amount. 

Speed  Regulation  of  Motors. — The  torque  of  a motor  depends  on  the  current; 
that  is,  for  a given  current,  the  torque  will  be  the  same  whatever  may  be 
the  speed,  provided  the  field  strength  remains  the  same.  The  speed  at 
which  the  armature  runs  is  a matter  of  E.  M.  F.  only;  that  is,  with  a given 
current  the  speed  will  be  proportional  to  the  applied  E.  M.  F.,  or,  more 
strictly,  the  counter  E.  M.  F.,  other  conditions  remaining  the  same. 

It  has  been  shown  that  the  torque  will  automatically  regulate  itself  for 
changes  in  the  load.  The  speed,  however,  may  be  varied  by  varying  the 
applied  E.  M.  F.  or  the  strength  of  the  field.  A change  in  speed  may  or 
may  not  result  in  a change  in  the  torque  required,  depending  on  the 
character  of  the  work  done  by  the  motor. 

The  simplest  way  to  vary  the  applied  E.  M.  F.  is  to  insert  a resistance,  in 
series  with  the  armature,  similar  to  the  starting  resistance.  By  varying 
this  resistance,  the  applied  E.  M.  F.  at  the  terminals  of  the  motor  is  also 
varied,  although  the  E.  M.  F.  of  the  mains  remains  constant.  It  is  evident 


-250  VoltSr- 


—250  Volts— 


—500  Volts- 
Fig.  16. 


that  the  energy  represented  by  the  product  of  the  current  and  the  drop 
through  the  resistance  is  converted  into  heat,  and  is  thereby  wasted; 
therefore,  for  great  variations  in  speed,  this  method  is  not  economical, 
though  often  very  convenient. 

The  applied  E.  M.  F.  may  also  be  varied  by  varying  the  E.  M.  F.  of  the 
generator  supplying  the  current,  but  this  can  only  be  done  where  a single 
generator  is  supplying  a single  motor,  or  several  motors,  whose  speed  must 
all  be  varied  at  the  same  time;  so  that  this  method  is  only  used  in  special 
cases. 

If  the  strength  of  the  field  is  changed,  the  speed  necessary  to  give  a cer- 
tain counter  E.  M.  F.  will  also  be  changed,  which  gives  a convenient 
method  of  varying  the  speed.  If  the  strength  of  the  field  is  lessened,  the 
speed  will  increase,  and  if  the  field  is  strengthened,  the  speed  will  decrease. 
With  shunt  motors,  the  field  may  be  weakened  by  inserting  a suitable 
resistance  in  the  field  circuit,  as  in  shunt  dynamos;  with  series  motors  the 
same  result  may  be  obtained  by  cutting  out  some  of  the  turns  of  the  field 
coils  or  by  placing  a suitable  resistance  in  parallel  with  the  field  coils. 

This  method  of  regulation  is  also  of  limited  range,  since  it  is  not  econom- 
ical to  maintain  the  strength  of  the  field  much  above  or  below  a certain 
density.  The  resistance  method  described  above  being  rather  more  simple, 
it  is  generally  used.  For  special  cases,  such  as  street-railroad  work,  various 
special  combinations  of  the  above  methods  of  regulation  are  used. 

One  of  the  most  common  of  these  is  known  as  the  series-parallel  method, 
and  is  the  method  of  regulation  generally  used  at  present  for  operating 
street  cars.  This  method  is  equivalent  to  the  method  of  cutting  down  the 
speed  by  reducing  the  E.  M.  F.  applied  to  the  motor,  and  is  only  applicable 
where  at  least  two  motors  are  used.  It  is  also  used,  to  some  extent,  in 
haulage  plants.  When  a low  speed  is  desired,  or  when  the  car  is  to  be 
startea  up,  the  motors  are  thrown  in  series,  as  shown  in  Fig.  16,  thus  making 
the  voltage  across  eacli  motor  equal  to  one-half  the  voltage  between  the 
lines,  and  cutting  down  the  speed  accordingly.  When  a high  speed  is 


CONNECTIONS  FOE  MOTORS. 


223 


desired,  the  motors  are  thrown  in  multiple,  as  shown  in  Fig.  17,  and  each 
motor  runs  at  full  speed  because  it  gets  the  full  line  pressure.  In  practice, 
starting  resistances  are  used  in  connection  with  the  above  to  make  the 
starting  smooth,  but  the  two  running  positions  are  as  shown,  the  motors 
being  connected  in  series  in  the  one  case,  and  in  parallel  in  the  other. 

Connections  for  Continuous-Current  Motors. — Fig.  18  shows  the  manner  in 
which  a shunt  motor  is  connected  to  the  terminals  -f  and  — of  the  circuit. 
It  will  be  seen  that  the  current 
through  the  shunt  field  does  not  /7WW\ 

pass  through  the  resistance  E UUUU 

which  is  connected  in  the  arma-  

tiire  circuit.  This  is  necessary,  Trolley  Ground 

since  to  keep  the  field  strength  — ^000^^—^^ 

constant,  the  full  difference  of 

potential  must  be  maintained  be-  SO(i  Vott» *■ 

tween  the  terminals  of  the  field  Fig.  17. 

coil,  which  would  not  be  the  case 

if  the  rheostat  were  included  in  the  field  current,  for  then  the  difference  of 
potential  would  be  only  that  existing  between  the  brushes  + B and  — B. 
As  on  starting  the  motor  this  difference  of  potential  is  small,  only  a small 
current  would  flow  through  the  field  coils,  which  would  generate  such  a 
weak  field  that  an  excessive  current  would  be  required  to  furnish  the 
necessary  torque  for  starting  the  motor. 

When  connected  as  shown,  however,  the  field  is  brought  up  to  its  full 
strength  before  any  current  passes  through  the  armature;  so  this  difficulty 
does  not  arise. 

Since  in  a series  motor  the  same  current  flows  through  both  armature  and 
field  coils,  the  starting  resistance  may  be  placed  in  any  part  of  the  circuit. 
The  diagram  in  Fig.  19  illustrates  one  method  of  connecting  a series  motor 
to  the  line  terminals  + and  — ; here  the  starting  or  regulating  resistance  E 
is  placed  between  the  — line  terminal  and  the  brush  —B  of  the  motor. 

To  reverse  the  direction  of  rotation  of  a motor  it  is  necessary  to  reverse 
either  the  direction  of  the  field  or  the  direction  of  the  current  through  the 
armature.  It  is  usual  to  reverse  the  direction  of  the  current  in  the  arma- 
ture. a switch  being  used  to  make  the  necessary  changes  in  the  connections. 

Fig.  20  shows  the  connections  of  one  form  of  reversing  switch.  Two 
metal  bars  B and  Bi  are  pivoted  at  the  points  T and  T] ; one  is  extended 
and  supplied  with  a handle  H,  and  the  two  bars  are  joined  together  by  a 
link  L of  some  insulating  material,  such  as  fiber.  Three  contact  pieces  a,  h, 
and  c are  arranged  on  the  base  of  the  switch  so  that  the  free  ends  of  the 


bars  B and  Bi  may  rest  either  on  a and  5,  as  shown  by  the  full  lines,  or  on  6 
and  c,  as  shown  by  the  dotted  lines.  The  line  is  connected  to  the  terminals 
T and  T^,  and  the  motor  armature  between  a and  b,  or  vice  versa,  a and  c 
being  connected  together. 

When  the  switch  is  in  the  position  shown  by  the  full  lines,  T is  connected 
to  a by  the  bar  B,  and  Ti  to  b by  the  bar  B],  If  the  switch  is  thrown  by 
means  of  the  handle  H into  the  position  indicated  by  the  dotted  lines, 
Tis  connected  to  b by  the  bar  B,  and  21  to  a by  the  bar  Bi  and  the  connection 


224 


DYNAMOS  AND  MOTORS. 


between  c and  a.  The  direction  of  the  current  through  the  motor 
armature,  or  whatever  circuit  is  connected  bet>veen  a and  &,  is  thus  reversed. 

In  order  to  reverse  only  the  current  in  the  armature,  the  reversing  switch 
must  be  placed  in  the  armature  circuit  only.  Fig.  21  represents  the  connec- 
tion for  a reversing-shunt  motor  (a)  and  a reversing- 
series  motor  (6);  -}-  and  — are  the  line  terminals;  R, 
the  starting  resistance;  B and  the  brushes  of  the 
motor,  and  F,  the  field  coil  of  the  motor.  Some  man- 
ufacturers combine  the  starting  resistance  and  revers- 
ing switch  in  one  piece  of  apparatus. 

In  connecting  up  motors,  some  form  of  main  switch 
is  used  to  entirely  disconnect  the  motor  from  the  line 
when  it  is  not  in  use. 

To  prevent  an  excessive  current  from  fiowing 
through  the  motor  circuit  from  any  cause,  short  strips 
of  an  easily  melted  metal,  known  as  fuses,  mounted  on 
suitable  terminals,  known  as  fuse  boxes,  are  placed  in 
the  circuit.  These  fuses  are  made  of  such  a sectional 
area  that  a current  greater  than  the  normal  heats 
them  to  such  an  extent  that  they  melt,  thereby  breaking  the  circuit  and 
preventing  damage  to  the  motor  from  an  excessive  current.  The  length 
of  fuse  should  be  proportioned  to  the  voltage  of  the  circuit,  a high  voltage 
requiring  longer  fuses  than  a low  voltage,  in  order  to  prevent  an  arc  being 
maintained  across  the  terminals  when  the  fuse  melts. 

If  desired,  measuring  instruments  (ammeter  and  voltmeter)  may  be 
connected  in  the  motor  circuit,  so  that  the  condition  of  the  load  on  the 
motor  may  be  observed  while  it  is  in  operation.  All  these  appliances, 
regulating  resistance,  reversing  switch,  fuses,  instruments,  etc.,  are  placed 


inside  the  main  switch;  that  is,  the  current  must  pass  through  the  main 
switch  before  coming  to  any  of  these  appliances,  so  that  opening  the  main 
swit(!li  entirely  disconnects  them  from  the  circuit,  when  they  may  be 
handled  without  fear  of  shocks. 


ALTERNATING-CURRENT  DYNAMOS. 

An  alternating-current  dynamo  is  one  that  generates  a current 
that  periodically  reverses  its  direction  of  flow.  It  was  shown  in 
connection  with  Fig.  10  that  an  armature  provided  simply  with  collector 
rings  produced  an  alternating  current  in  the  outside  circuit.  This 
current  may  be  represented  by  a curve  such  as  that  shown  in  Fig.  22. 
The  complete  set  of  values  that  the 
current  or  E.  M.  F.  passes  through 
repeatedly  is  known  as  a cycle.  For 
example,  the  values  passed  through 
during  the  interval  of  time  represented 
by  the  distance  a c would  constitute  a 
cycle.  The  set  of  values  passed 
through  during  the  interval  ab  is 
known  as  an  alternation.  An  alternation  is,  therefore,  half  a cycle.  The 
number  of  cycles  passed  through  per  second  is  known  as  XhQ  frequency  of  the 
current,  or  E.  M.  F. 

Alternating-current  dynamos  are  now  largely  used  both  for  lighting  and 
power  transmission,  especially  when  the  transmission  is  over  long  distances. 
The  reason  that  the  alternating  current  is  specially  suitable  for  long-distance 


Fig.  22. 


ALTERNATORS. 


225 


work  is  that  it  may  be  readily  transformed  from  one  pressure  to  another. 
We  have  already  seen  that  in  order  to  keep  down  the  amount  of  copper  in 
the  line,  a high  line  pressure  must  be  used.  Pressures  much  over  500  or  600 
volts  cannot  be  readily  generated  with  direct-current  machines,  owing  to  the 
troubles  that  are  likely  to  arise  due  to  sparking  at  the  commutator.  On  the 
other  hand,  an  alternator  requires  no  commutator  or  even  collecting  rings, 
if  the  armature  is  made  stationary  and  the  field  revolving,  as  is  frequently 
done.  Alternators  are  now  built  that  generate  as  high  as  8,000  or  10,000  volts 
directly.  If  a still  higher  pressure  is  required  on  the  line,  it  can  be  easily 
obtained  by  the  use  of  transformers,  to  be  explained  later.  It  is  thus  seen 
that  where  power  is  to  be  carried  over  long  distances,  the  alternating  current 
is  indispensable. 

Alternating-current  dynamos,  like  direct-current  machines,  consist  of 
two  main  parts,  i.  e.,  the  field  and  armature.  Either  of  these  parts  may 
be  the  revolving  member, 
and  in  many  modern  ma- 
chines the  armature,  or  the 
part  in  which  the  current 
is  induced,  is  the  revolving 
member.  Fig.  23  shows  a 
typical  alternator  of  the 
belt-driven  type,  having  a 
revolving  armature.  It  is 
not  unlike  a direct-current 
machine  as  regards  its  gen- 
eral appearance.  The 
number  of  poles  is  usually 
large,  in  order  to  secure 
the  required  frequency 
without  running  the  ma- 
chine at  a high  rate  of 
speed.  The  frequencies 
met  with  in  practice  vary 
all  the  way  from  25  to  150. 

The  higher  frequencies 
are,  however,  passing  out 
of  use,  and  at  present  a Fig.  23. 

frequency  of  60  is  very 

common.  This  frequency  is  well  adapted  both  for  power  and  lighting  pur- 
poses. When  machines  are  used  almost  entirely  for  lighting  work,  frequen- 
cies of  125  or  higher  may  be  used.  The  frequency  of  any  machine  may  be 
readily  determined  when  the  number  of  poles  and  the  speed  is  known,  as 
follows: 


_ number  of  poles  , , rev.  per  min. 

Frequency  = X 60 ' 


For  example,  if  an  eight-pole  alternator  were  run  at  a speed  of  900  R.  P.  M., 
the  frequency  would  be 

8 900 

/ = X = 60  cycles  per  second.  - 


Alternators  may  be  divided  into  the  two  following  classes:  (a)  Single- 
phase alternators;  (6)  Multiphase  alternators. 

(a)  Single-Phase  Alternators.— These  machines  are  so  called  because  they 
generate  a single  alternating  current  (as  represented  by  the  curve  shown  in 
Fig.  22).  The  armature  is  provided , with  a single  winding  and  the  two 
terminals  are  brought  out  to  collector  rings,  as  previously  described.  Single- 
phase machines  have  been  largely  used  in  the  past  for  lighting  work,  bul 
they  are  gradually  being  replaced  by  multiphase  machines,  because  the 
single-phase  machines  are  not  well  suited  for  the  operation  of  alternating- 
current  motors. 

(5)  Multiphase  Alternators.— These  machines  are  so  called  because  they 
deliver  two  or  more  alternating  currents  that  differ  in  phase;  i.  e.,  when  one 
current  is,  say,  at  its  maximum  value,  the  other  currents  are  at  some  other 
value.  This  is  accomplished  by  providing  the  armature  with  two  or  more 
distinct  windings  which  are  displaced  relatively  to  each  other  on  the 
armature.  One  set  of  windings,  therefore,  comes  under  the  poles  at  a later 
instant  than  the  winding  ahead  of  it,  and  the  current  in  its  winding  comes 


226 


DYNAMOS  AND  MOTORS. 


to  its  maximum  value  at  a later  instant  than  the  current  in  the  first  wind- 
ing.  In  practice,  the  two  types  of  multiphase  alternator  most  commonly 
used  are  (1)  two-phase  alternators,  (2)  three-phase  alternators. 

Two-phase  alternators  are  machines  that  deliver  two  alternating  currents 
that  differ  in  phase  by  one-quarter  of  a complete  cycle;  i.  e.,  when  the 
current  in  one  circuit  is  at  its  maximum  value,  the  current  in  the  other 
circuit  is  passing  through  its  zero  value.  By  tapping  four  equidistant  points 
of  a regular  ring  armature,  as  shown  in  Fig.  24,  and  connecting  these  points 
to  four  collector  rings,  a simple  two-pole  two-phase  alternator  is  obtained. 
One  circuit  connects  to  rings  1 and  I',  the  other  circuit  connects  to  rings 
2 and  2\  It  is  easily  seen  from  the  figure  that  when  the  part  of  the  winding 
connected  to  one  pair  of  rings  is  in  its  position  of  maximum  action,  the 
E.  M.  F.  in  the  other  coils  is  zero,  thus  giving  two  currents  in  the  two 
different  circuits  that  differ  in  phase  by  one-quarter  of  a cycle  or  one-half 
an  alternation. 

Three-phase  alternators  are  machines  that  deliver  three  currents  that  differ 
in  phase  by  one-third  of  a complete  cycle;  i.  e.,  when  one  current  is  flowing 
in  one  direction  in  one  circuit,  the  currents  in  the  other  two  circuits  are  one- 
half  as  great,  and  are  flowing  in  the  opposite  direction.  By  tapping  three 
equidistant  points  of  a ring  winding,  as  shown  in  Fig.  25,  a simple  three- 
phase  two-pole  alternator  is  obtained.  Three  mains  lead  from  the  collecting 
rings. 

In  order  to  have  three  distinct  circuits,  it  would  ordinarily  be  necessary 
to  have  six  collecting  rings  and  six  circuits;  but  this  is  not  necessary  in  a 
three-phase  machine  if  the  load  is  balanced  in  the  three  different  circuits, 
because  one  wire  can  be  made  to  act  alternately  for  the  return  of  the  other 
two. 

Uses  of  Multiphase  Alternators.— Multiphase  alternators  are  coming  largely 
into  use,  because,  by  using  them,  alternating-current  motors  can  be  readily 
operated.  By  using  multiphase  machines,  motors  can  be  operated  that  will 


start  from  rest  under  load,  whereas  with  single-phase  machines  the  motor 
has  to  be  brought  up  to  speed  from  some  outside  source  of  power  before  it  can 
be  made  to  run.  For  this  reason,  such  machines  are  used  for  the  operation 
of  modern  power-transmission  plants.  As  far  as  the  general  appearance  of 
three-phase  machines  goes,  they  are  similar  to  ordinary  single-phase  alter- 
nators, the  only  difference  being  in  the  armature  winding  and  the  larger 
number  of  collector  rings.  The  multiphase  alternator  is  also  adapted  for 
the  operation  of  lights,  so  that  by  using  these  machines,  both  lights  and 
motors  may  be  operated  from  the*  same  plant.  They  are  well  adapted  for 
power-transmission  purposes  in  mines,  especially  for  the  operation  of  pump- 
ing and  hoisting  machinery,  because  the  motors  operated  by  them  are  very 
simple  in  construction  and  therefore  not  liable  to  get  out  of  order. 


ALTERNATING-CURRENT  MOTORS. 

Alternating-current  motors  may  be  divided  into  two  general  classes: 
(a)  Synchronous  motors;  (5)  Induction  motors. 

(rt)  Synchronous  motors  are  almost  identical,  so  far  as  construction  goes, 
with  the  corresponding  alternator.  For  example,  a two-phase  synchronous 
motor  would  be  constructed  in  the  same  way  as  a two-phase  alternator. 


AL  TERN  A TING-  C UR  RENT  MO  TORS. 


227 


They  are  called  synchronous  motors  because  they  always  run  in  synchro- 
nism, or  in  step,  with  the  alternator  driving  them.  This  means  that  the 
motor  runs  ,at  the  same  frequency  as  the  alternator,  and  if  the  motor  had 
the  same  number  of  poles  as  the 
alternator,  it  would  run  at  the  same 
speed,  no  matter  what  load  it  might 
be  carrying.  This  type  of  motor  has 
many  good  points,  and  is  especially 
well  suited  to  cases  where  the 
amounts  of  power  to  be  transmitted 
are  comparatively  large  and  where 
the  motor  does  not  have  to  be 
started  and  stopped  frequently. 

Multiphase  synchronous  motors  will 
start  up  from  rest  and  will  run  up  to 
synchronous  speed  without  aid  from 
any  outside  source.  They  will  not, 
however,  start  with  a 'strong  starting 
torque  or  effort,  and  will  not,  there- 
fore, start  up  under  load,  and  can- 
not be  used  in  places  where  a strong 
starting  effort  is  required.  For  this 
reason  synchronous  motors  are  not 
suitable  for  intermittent  work. 

(6)  Induction  motors  are  so  called 
because  the  current  is  induced  in  the 
armature  instead  of  being  led  into  it  from  some  outside  source.  Fig.  26  shows 
a typical  induction  motor.  There  are  two  essential  parts  in  these  machines, 
viz.,  the  field,  into  which  multiphase  currents  are  led  from  the  line,  and  the 
armature,  in  which  currents  are  induced  by  the  magnetism  set  up  by  the 
field.  Either  of  these  parts  may  be  the  stationary  or  revolving  member,  but 
in  most  cases  the  field,  or  part  that  is  connected  to  the  line,  is  stationary. 
Fig.  27  shows  the  construction  of  the  stationary  member  or  field.  This  con- 
sists of  a number  of  iron  laminations,  built  up  to  form  a core  and  provided 
with  slots  around  the  inner  periphery.  The  form-wound  coils  constituting 
the  field  winding  are  placed  in  these  slots  and  connected  to  the  mains.  This 
winding  is  arranged  in  the  same  way  as  the  armature  winding  of  a multi- 
phase alternator.  When  the  alternating  currents  differing  in  phase  are  sent 
through  the  winding,  magnetic  poles  are  formed  at  equidistant  points  around 

the  periphery  of  the  field,  and 
the  constant  changing  of  the 
currents  causes  these  poles  to 
shift  around  the  ring,  thus  set- 
ting up  what  is  known  as  a 
revolving  magnetic  field.  This 
armature,  Fig.  28,  consists  of  a 
laminated  iron  core  provided 
with  a number  of  slots,  in  each 
of  which  is  placed  a heavy 
copper  bar  b.  The  ends  of 
these  bars  are  all  connected 
together  by  two  heavy  short- 
circuiting  rings  r,  r running 
around  each  end  of  the  arma- 
ture. The  bars  and  end  rings 
thus  form  a number  of  closed 
circuits.  When  such  an  arma- 
ture is  placed  in  the  revolv- 
ing field,  the  magnetism  will 
cut  across  the  armature  con- 
ductors, inducing  E.  M.  F.’s 
in  them,  and  since  the  conduc- 
tors are  joined  up  into  closed 
circuits,  currents  will  flow  in 
^ ^ , them.  These  currents  will 

react  on  the  field,  and  the  armature  will  be  forced  to  revolve.  Such  an 
armature  will  not  run  exactly  in  synchronism,  because  if  it  did,  it  would 
revolve  just  as  fast  as  the  magnetic  field,  and  there  would  be  no  cutting  of 


228 


DYNAMOS  AND  MO  TOES, 


lines  of  force.  The  speed  drops  slightly  from  no  load  to  fhll  load,  but  if  the 
motor  is  well  designed,  this  falling  off  in  speed  is  slight. 

Induction  motors  possess  many  advantages  for  mine  work.  One  of  the 
chief  of  these  is  the  absence  of  the  commutator  or  any  kind  of  sliding  con- 


Fig.  28. 


vide  the  armature  with  a winding  simih 
the  terminals  to  collecting  rings,  so  that 
armature  circuit. 


tacts  whatever.  Such  motors  can 
therefore  operate  with  absolutely 
no  sparking— a desirable  feature 
for  mine  work.  The  motors  are 
also  very  simple  in  construction, 
and  are  therefore  not  liable  to 
get  out  of  order.  They  have  an 
additional  advantage  over  the  syn- 
chronous motor  in  that  they  start 
up  with  a strong  starting  effort, 
and,  in  fact,  behave  in*  most  re- 
spects like  any  good  shunt-wound 
direct-current  motor.  They  are 
used  quite  ' successfully  for  all 
kinds  of  stationary  work,  such  as 
pumping,  hoisting,  etc.,  but  so  far 
have  not  been  used  to  any  great 
extent  for  haulage  purposes. 
When  these  motors  are  used  for 
purposes  where  a variable  speed  is 
required,  it  is  customary  to  pro- 
• to  that  of  the  field  and  bring  out 
resistance  may  be  inserted  in  the 


TRANSFORMERS. 

Reference  has  already  been  made  to  the  use  of  transformers  for  changing 
an  alternating  current  from  a higher  to  a lower  pressure,  or  vice  versa,  with 
a corresponding  change  in  current.  Transformers  used  for  raising  the  volt- 
age are  known  as  step-up  transformers;  those  used  for  lowering  the  pressure 
are  known  as  step-down  transformers. 

The  transformer  consists  of  a laminated  iron  core  upon  which  two  coils 
of  wire  are  wound.  These  coils  are  entirely  distinct,  having  no  connection 
with  each  other.  One  of  these  coils,  called  the  primary,  is  connected  to  the 
mains;  the  other  coil,  called  the  secondary,  is  connected  to  the  circuit  to 
which  current  is  delivered.  Fig.  29  shows  the  arrangement  of  coils  and  core 
for  a common  type  of  transformer.  The  secondary 
coil  is  wound  in  two  parts  S,  S',  and  the  primary  coil, 
also  in  two  parts  P,  P', 
is  placed  over  the  sec- 
ondary. C is  the  core, 
built  up  of  thin  iron 
plates.  Fig.  30  shows  a 
weather-proof  cast-iron 
case  for  this  transformer. 

When  a current  is  sent 
through  the  primary  it 
sets  up  a magnetism  in 
the  core  which  rapidly 
alte mates  with  the 
changes  in  the  current. 

This  changing  magnet- 
ism sets  up  an  alterna- 
ting E.  M.  F.  in  the  sec- 
ondary, and  this  second- 
ary E.  M.  F.  depends 
upon  the  number  of  turns  in  the  secondary  coil.  If  the  secondary  turns  are 
greater  than  the  primary,  the  secondary  E.  M.  F.  will  be  higher  than  that 
of  the  primary.  The  relation  between  the  primary  E.  M.  F.  and  secondary 
E.  M.  F.  is  given  by  the  following: 


Fig.  29. 


Fig.  30. 


Secondary  E.  M.  F.  = primary  E.  M.  F.  X 


secondary  turns^ 
primary  turns  ' 


BATTERIES. 


229 


j -r^  nr  T-.  primary  E.  M.  F. 

or,  secondary  E.  M.  F.  = - — ^ — - — 7 . 

primary  turns 

secondary  turns 


The  ratio 


primary  turns  . , 

• IS  known  as  the 


secondary  turns 
ratio  of  transformation  of  the  transformer. 
For  example,  if  a transformer  had  1,200  pri- 
mary turns  and  60 


secondary  turns,  its 
ratio  of  transforma- 
tion would  be  20  to  1, 
and  the  secondary 

voltage  would  be  one-twentieth  that  of  the  primary. 
Transformers  are  made  for  a number  of  different 
ratios  of  transformation,  the  more  common  ones 
being  10  to  1 or  20  to  1.  Of  course,  a transformer 
never  gives  out  quite  as  much  power  from  the  sec- 
ondary as  it  takes  in  from  the  primary  mains, 
because  there  is  always  some  loss  in  the  iron  core 
and  in  the  wire  making  up  the  coils.  The  efficiency 


1000  v-~* 

p 

lonnnnnnnnnr 


Fig.  33. 


-‘joo  r — • 

Fig.  31, 


■1000  V- 

p' 

WifffirBTnrmNi 

rminnn 

s' 

-100  V- 


of  transformers  is,  however,  high,  reaching  as  high  as  97^  or  98^  in  the 
larger  sizes.  Transformers  are  always  connected  in  parallel  across  the 
mains,  and  if  they  are  well  designed,  will  furnish  a very  nearly  constant 
secondary  pressure  at  all  loads,  when  furnished  with  a constant  primary 
pressure.  Fig.  31  shows  transformers  connected  on  a single-phase  circuit. 
Fig.  32  shows  the  connection  for  a two-phase  circuit,  and  Fig.  33  shows 
one  method  of  connection  for  a three-phase  circuit. 


ELECTRIC  SIGNALING. 


BATTERIES. 

Batteries  are  used  for  various  purposes  in  connection  with  mining  work, 
principally  for  the  operation  of  bells  and  signals. 

The  LeclancM  cell  is  one  that  is  widely  used  for 
bell  and  telephone  work.  It  is  made  in  two  or 
three  different  forms, 
one  of  the  most  com- 
mon of  these  being  as 
shown  in  Fig.  34  (a). 

The  zinc  element  of 
this  battery  is  in  the 
form  of  a rod  Z,  and 
weighs  about  3 oz.  The 
other  electrode  is  a car- 
bon plate  placed  in  a 
porous  cup  and  sur- 
rounded with  black 
oxide  of  manganese, 
mixed  with  crushed 
coke  or  carbon.  The 
electrolyte  used  in 
the  battery  is  a satura- 
ted solution  of  sal 


Pig  34. 


230 


ELECTRIC  SIGNALING. 


ammoniac.  The  E.  M.  F.  of  this  cell  is  about  1.48  volts  when  the  cell  is  in 
good  condition.  In  another  form  of  the  cell,  known  as  the  Gonda  type,  the 
black  oxide  of  manganese  is  pressed  into  the  form  of  bricks  and  clamped 
against  each  side  of  the  carbon  plate  by  means  of  rubber  bands.  This  cell 
will  do  good  work  if  it  is  only  used  intermittently,  i.  e.,  on  circuits  w'here 
the  insulation  is  good  and  where  there  is  no  leakage  causing  the  cell  to  give 


out  current  continuously.  If  current  is  taken  from  it  for  any  length  of 
time,  it  soon  runs  down,  but  will  recuperate  if  allowed  to  stand. 

In  cases  where  the  insulation  is  apt  to  be  poor,  as  it  often  is  in  mines, 
it  is  best  to  use  a battery  that  will  stand  a continuous  delivery  of  current  and 
that  will  at  the  same  time  operate  all  right  on  intermittent  work  or  on  work 
where  the  circuit  is  open  most  of  the  time.  For  work  of  this  kind,  cells  of 
the  Edison-Lalande  or  Gordon  type  are  excellent.  Fig.  34  (&)  shows  the 
Edison-Lalande  cell.  The  elements  consist  of  two  zinc  plates  Z,  hung  on 
each  side  of  a plate  of  compressed  cupric  oxide  C.  The  electrolyte  is  a satu- 
rated solution  of  caustic  potash,  and  this  should  be  kept  covered  with  a 
layer  of  heavy  paraffin  oil,  to  prevent  the  action  of  the  air  on  the  solution. 
The  voltage  of  the  cell  is  only  .7  volt,  but  its  internal  resistance  is  very  low 
and  its  current  capacity  correspondingly  large.  The  electrolyte  used  in  the 
Gordon  cell  is  also  caustic-potash  solution,  and  the  two  cells  are  much  the 
same,  so  far  as  their  general  characteristics  are  concerned.  The  table  on 
page  231  gives  data  relating  to  a number  of  different  types  of  cell. 


BELL  WIRING. 

The  simple  bell  circuit  is  shown  in  Fig.  35,  where  p is  the  push  button,  b 
the  bell,  and  c,  c the  cells  of  the  battery  connected  up  in  series.  When  two 
or  more  bells  are  to  be  rung  from  one  push  button,  they  may  be  joined  up 


in  parallel  across  the  battery  wires,  as  in  Fig.  37  at  a and  6,  or  they  may  be 
arranged  in  series,  as  in  Fig.  36.  The  battery  B is  indicated  in  each  diagram 
by  short  parallel  lines,  this  being  the  conventional  method.  In  the  parallel 
arrangement  of  the  bells,  they  are  independent  of  each  other,  and  the 
failure  of  one  to  ring  would  not  affect  the  others;  but  in  the  series  grouping, 
all  but  one  bell  must  be  changed  to  a single-stroke  action,  so  that  eacn 
impulse  of  current  will  produce  only  one  movement  of  the  hammer.  The 
current  is  then  interrupted  by  the  vibrator  in  the  remaining  bell,  the  result 


BATTERIES. 


231 


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232 


ELECTRIC  SIGNALING. 


being  that  each  bell  will  ring  with  full  power.  The  only  change  necessary 
to  produce  this  effect  is  to  cut  out  the  circuit-breaker  on  all  but  one  bell  by 

connecting 
the  ends  of 
the  magnet 
wires  directly 
to  the  bell 
terminals. 

When  it  is 
desired  to 

Fig.  39.  ring  a bell 

from  one  of 


a ' 


Fig.  40. 


Fig.  41. 


Fig.  42. 


two  places  some  distance  apart,  the 
wires  may  be  run  as  shown  in  Fig. 
38.  The  pushes  p,  p'  are  located  at 
the  required  points,  and  the  battery 
and  bell  are  put  in  series  with  each 
other  across  the  wires  joining  the 
pushes. 

A single  wire  may  be  used  to  ring 
signal  bells  at  each  end  of  a line,  the 
connections  being  given  in  Fig.  39. 
Two  batteries  are  required,  B and 
B',  and  a key  and  bell  at  each  sta- 
tion. Ihe  keys  k'  are  of  the 
double-contact  type,  making  connections 
normally  between  bell  h or  b'  and  line 
wire  L.  When  one  key,  as  k,  is  depressed, 
a current  from  B flows  along  the  wire 
through  the  upper  contact  of  k'  to  bell  h' 
and  back  through  ground  plates  G',  G. 

When  a bell  is  intended  for  use  as  an 
alarm  apparatus,  a constant-ringing 
attachment  may  be  introduced,  which 
closes  the  bell  circuit  through  an  extra 
wire  as  soon  as  the  trip  at  door  or  window^ 
is  disturbed.  In  the  diagram.  Fig.  40,  the 
main  circuit,  when  the  push  p is  depressed, 
is  through  the  automatic  drop  d by  way  of 
the  terminals  a,  b to  the  bell  and  battery. 
This  current  releases  a pivoted  arm  which, 
on  falling,  completes  the  circuit  betw'een 
b and  c,  establishing  a new  path  for  the 
current  by  way  of  e,  independent  of  the 
push  p. 

For  operating  electric  bells,  any  good 
type  of  open-circuit  battery  may  be  used. 
The  Leclanche  cell  is  largely  used  for  this 
purpose,  also  several  types  of  dry  cells. 

Annunciator  System.— The  wiring  dia- 
gram for  a simple  annunciator  system  is 
shown  in  Fig.  42.  The  pushes  1,  2,  3,  etc. 
are  located  in  various  places,  one  side  being  con- 
nected to  the  battery  wire  b,  and  the  other  to  the 
leading  wire  I in  communication  with  the  annun- 
ciator drop  corresponding  to  that  place.  A bat- 
tery of  tw^o  or  three  Leclanche  cells  is  placed 
at  'B  in  any  convenient  location.  The  size  of 
wire  used  throughout  may  be  No.  18  annuncia- 
tor wure. 

A return-call  system  is  illustrated  in  Fig.  41,  in 
which  there  is  one  battery  wire  5,  one  return 
wire  r,  and  one  leading  wire  etc.  for  each 

glace.  The  upper  portion  of  the  annunciator 
oard  is  provided  with  the  usual  drops,  and  below 
these  are  the  return-call  pushes.  These  are 
double-contact  buttons,  held  normally  against 
the  upper  contact  by  a spring.  When  in  this 


BELL  WIRING. 


233 


position,  the  closing  of  the  circuit  by  the  push  button  in  any  room,  such  as 
No.  4,  rings  the  office  bell  and  releases  No.  4 drop,  the  path  of  the  current  in 


Fig.  43. 


this  case  being  from  push  4 to  a-c-d-e-f-g-B-h-h 
back  to  the  push  button.  On  the  return  sig- 
nal being  made  by  pressing  the  button  at  the 
lower  part  of  the  annunciator  board,  the 
office-bell  circuit  is  broken  at  d,  and  a new 
circuit  formed  through  k as  follows:  From 
the  battery  B to  g-m-r-n-o-a-c-k-p  to  battery, 
the  room  bell  being  in  this  circuit.  A gen- 
eral fire-alarm  may  be  added  to  this  system, 
consisting  of  an  automatic  clockwork  appa- 
ratus for  closing  all  the  room-bell  circuits  at 
once,  or  as  many  at  a time  as  a battery  can 
ring.  When  this  system  is  installed,  the  bat- 
tery wire  should  be  either  No.  14  or  No.  16. 
Four  or  five  Leclanche  cells  are  usually  re- 
quired in  this  case. 

It  will  be  seen  that  the  connections  are 
so  arranged  that  the  room  bell  will  ring  when 
the  push  in  that  room  is  pressed.  If  this  be 
not  desired,  a double-contact  push  may  be 
substituted,  so  that  the  room-bell  circuit  is 
broken  at  the  same  time  that  the  circuit  is 
made  through  the  annunciator.  This  double 
push  should  be  so  connected  that  the  circuit 
is  nmmally  complete  through  the  bell,  the 
leading  wire  being  connected  to  the  tongue, 
and  the  battery  wire  being  connected  to  the 
second  contact  point,  which  is  normally  out 
of  circuit. 

Telephones  are  also  used  for  signaling  and 
communicating  purposes.  It  has  been  found 
that  a first-class  long-distance  bridging  tele- 
phone is  the  best  type  to  use.  Bridging  tele- 
phones are  so  called  because  they  are  bridged 
or  connected  in  parallel  across  the  line,  and 
are  not  connected  in  series.  If  one  telephone 
should  get  out  of  order,  the  others  are  not 
likely  to  be  disabled.  Fig.  43  shows  a com- 
plete bell  annunciator  and  telephone  outfit, 


lac.  LJEVKI. 


8JfD.  LEVEL 


aBD.  LEVEL 


'1 


234 


ELECTRIC  SIGNALING. 


Hoisting  Engine  House, 


as  installed  in  one  of  the  anthracite 
coal  mines  of  the  D.,  L.  & W.  R.  R.  Co. 
It  will  be  noticed  that  bridging  instru- 
ments are  used  and  that  each  bell  in 
the  shaft  is  provided  with  a return- 
call  button.  This  bell  wiring  should 
be  put  up  in  a substantial  manner, 
and  it  is  best,  if  possible,  to  run  all  the 
wires  down  the  shaft  in  the  shape  of  a 
lead-covered  cable. 

Another  shaft-signaling  apparatus 
is  shown  in  Fig.  44,  as  used  at  the 
West  Vulcan  mines,  Mich.  Fig.  45 


Fig.  44. 


shows  a form  of  waterproof  push  but- 
ton used  at  the  same  mine.  Fig.  46 
shows  the  arrangement  of  flash  signals 
as  used  in  Montana.  This  consists  of 
a switch  cut  into  this  main  circuit  at 


PROSPECTING. 


235 


each  level  of  the  mines.  By  pulling  out  the  handle  bar 
of  the  switch,  the  lights  on  this  circuit  can  all  be  flashed 
at  once,  and  by  a properly  arranged  code  of  flash  sig- 
nals, the  system  can  be  used  for  communicating  between 
the  surface  to  any  part 
of  the  mine,  and  between 
different  portions  of  the 
mine. 

A system  of  signaling 
by  which  signals  can  be 
sent  to  the  engine  room 
from  any  point  along  the 
haulage  road  is  shown  in 
Fig.  47.  The  conductors  a and  6,  leading  from  the  battery 
run  parallel  to  each  other  along  the  roadside,  and  about 
6 in.  apart.  A short  iron  rod,  placed  across  the  wires  a,  h, 
signals  to  the  engineer,  or  by  simply  bringing  the  two  wires 
together  a signal  may  be  sent. 

When  the  engineer  hauls  from  different  roads,  the  signal- 
ing system  should  be  supplemented  with  indicators,  so  that 
when  the  bell  rings  the  indicator  would  show  from  which 
point  the  signal  came,  and  in  case  several  signals  were 
given  at  the  same  time,  the  engineer  should  not  heed  any 
until  the  indicator  shows  that  a complete  signal  came 
from  one  place. 

A system  of  signaling  for  showing  whether  or  not  a 
section  of  track  is  occupied  by  another  motor  is  shown 


r.o/tev 


Fig.  48. 


V/OO' 


\200 


[^<300* 


^00* 


in'  Fig.  48.  White  lights  indicate  a clear  track  and  dark- 
ness an  occupied  section.  A single-center  hinge,  double-  — 
handle  switeh  at  each  signal  station  is  used  and  a touch  of  Fig.  46. 
the  handle  throws  the  switch  in  the  desired  direction.  The 
switches  are  placed  in  the  roof,  4i  ft.  above  rails  within  easy  reach  of  motor- 
man.  Fig.  48  shows  the  connections.  Each  switch  is  provided  with  a spring 
(not  shown  in  the  figure)  which,  drawing  across  the  center  hinge,  when  the 
handles  are  in  their  central  position,  insures  a perfeet  contact  when  the 
switch  is  inclined  toward  either  the  trolley  or  rail-terminal  plug. 


PROSPECTING. 


The  prospector  should  have  a general  knowledge  of  the  mineral-bearing 
strata,  and  should  know  from  the  nature  of  the  ledges  exposed  whether  to 
expect  to  find  mineral  or  not.  He  should  also  possess  such  a knowledge  of  the 
use  of  tools  as  will  enable  him  to  construct  simple  structures,  and  a sufficient 
experience  in  blacksmithing  to  enable  him  to  sharpen  picks  and  drills,  or 
to  set  a horseshoe,  if  necessary. 

Outfit  Necessary.— The  character  of  the  prospecting  being  carried  on  will 
have  considerable  effect  on  the  outfit  necessary,  which  should  always  be  as 
simple  as  possible.  In  general,  when  operating  in  a settled  country,  the 
outfit  is  as  follows:  A compass  and  clinometer  for  determining  the  dip  and 
strike  of  the  various  measures  encountered;  a pick  and  shovel  for  excavating, 
and,  where  rock  is  liable  to  be  encountered,  a set  of  drills,  hammer,  spoon 
for  cleaning  the  holes,  tamping  stick,  powder  and  fuse,  or  dynamite  fuse 
and  cap;  a blowpipe  outfit;  a small  magnifying  glass;  an  aneroid  barometer 
for  determining  elevations,  and  a small  hand  pick;  the  latter  should  weigh 
about  If  lb.,  and  should  have  a piek  on  one  end  and  a square-faced  ham- 
mer on  the  other,  the  handle  bein^  from  12  to  14  in.  long. 

If  the  region  under  consideration  has  been  settled  for  some  time,  there 
will  probably  be  geological,  county,  railroad,  or  other  maps  available. 


236 


PROSPECTING. 


These  may  not  be  accurate  as  to  detail,  but  will  be  of  great  assistance  in  the 
work  on  account  of  the  fact  that  they  give  the  course  of  the  railroads, 
streams,  etc. 

When  operating  in  a mountainous  region,  away  from  a settled  country, 
and  especially  when  searching  for  precious  metals,  the  following  materials, 
in  addition  to  that  already  mentioned,  may  be  required:  A donkey  or  pony 
packed  with  a couple  of  heavy  blankets,  an  A tent,  cooking  utensils,  etc.;  a 
supply  of  flour,  sugar,  bacon,  salt,  baking  powder,  and  coffee,  suflicient  for 
at  least  a month.  It  is  also  well  to  take  some  fruit,  but  all  fruit  containing 
stones  or  pits  should  be  avoided,  as  they  are  only  dead  weight,  and  every 
pound  counts.  For  the  same  reason,  canned  goods  should  be  avoided,  on 
account  of  the  large  amount  of  water  they  contain.  A healthy  man  will 
require  about  3 lb.  of  solid  food  per  day.  Many  prefer  to  vary  the  diet  by 
taking  rice,  corn  meal,  beans,  etc.,  in  place  of  a portion  of  the  flour. 

The  additional  tools  necessary  are  an  ax,  a pan  for  washing  gold  ore, 
making  concentrating  tests,  etc.,  and,  in  some  cases,  an  assay  furnace 
and  outfit  packed  upon  another  animal.  Where  game  is  abundant,  a shot- 
gun or  rifle  will  be  found  useful  for  supplying  fresh  meat.  In  regions 
abounding  in  swamps  it  becomes  necessary  to  operate  from  canoes,  or  to 
take  men  for  porters  or  packers,  who  carry  the  outfit  on  their  backs  or 
heads.  These  men  will  carry  from  60  to  125  lb. 

Plan  of  Operations.— When  the  presence  of  mineral  is  suspected  in  a tract 
of  land,  a thorough  examination  of  the  surface  and  a study  of  the  exposed 
rocks,  in  place,  may  result  in  its  immediate  discovery,  or  in  positive  proof 
of  its  absence;  or  it  may  result  in  still  further  increasing  the  doubt  of,  or  the 
belief  that,  it  does  exist.  The  first  procedure  in  prospecting  a tract  of  land 
is  to  thoroughly  traverse  it,  ana  note  carefully  any  stains  or  traces  of  smut, 
and  all  outcrops  of  every  description;  and,  whenever  possible,  take  the  dip 
and  the  course  of  the  outcrop  with  a pocket  compass.  Any  fossils  should 
also  be  carefully  noted,  to  assist  in  determining  the  geological  age  of  the 
region.  These  outcrops  are  frequently  more  readily  found  along  roads  or 
streams  than  any  other  place  on  the  tract.  In  traveling  along  the  streams, 
the  prospector  should  pay  particular  attention  to  its  bed  and  banks,  to  see 
whether  there  are  any  small  particles  of  mineral  in  the  bed  of  the  stream, 
or  any  stains  or  smut  exposed  along  the  washed  banks.  If  small  pieces  of 
mineral  are  found  in  the  stream,  a search  up  it  and  its  tributaries  will  show 
where  the  outcrop  from  which  the  find  came  is  located.  When  the  ravines 
and  valleys  are  so  filled  with  wash  that  no  exposures  are  visible,  and  nothing 
is  gained  by  a careful  examination  of  them,  the  prospector  must  rely  on 
topographical  features  to  guide  him. 

Any  gold  present  in  the  vein  material  usually  remains  in  the  float  as  free 
or  metallic  gold,  but  other  valuable  metals  are  often  leached  out.  The  fact 
that  the  float  itself  may  be  barren  does  not  indicate  that  it  may  not  have 
come  from  a very  rich  deposit,  and  hence  it  will  often  pay  to  follow  barren 
float,  since  the  outcrop  of  the  vein  itself  is  often  either  entirely  barren,  low 
grade,  or  of  a different  nature  from  the  deeper  deposits.  In  cases  where 
there  are  no  outcrops  or  any  other  surface  indications,  it  would  become 
necessary  to  sink  shafts  or  test  pits,  or  to  proceed  by  drilling. 

The  absence  of  any  indication  of  mineral  in  the  soil  may  not  prove  that 
there  is  not  an  outcrop  near  at  hand,  for  the  soil  is  frequently  brought  from 
a distance,  and  bears  no  relation  to  the  material  underlying  it.  In  like 
manner,  glacial  soil  often  contains  debris  transported  from  deposits  many 
miles  away;  but  such  occurrences  can  usually  be  distinguished  by  the  gen- 
eral character  of  the  associated  wash  material. 

Frequently,  the  weathered  outcrop  of  a deposit  has  been  overturned  or 
dragged  back  upon  itself,  so  as  to  indicate  the  presence  of  a very  thick 
deposit.  For  this  reason,  any  openings  made  to  determine  the  character  of 
the  material  should  be  continued  until  the  coal  or  other  mineral  is  of  a firm 
character,  and  both  floor  and  roof  are  well  exposed.  Sometimes,  in  the  case 
of  steeply  pitching  coal  beds,  the  surface  may  be  overturned  for  a consider- 
able depth,  so  that  it  is  difficult  to  tell  which  is  the  roof  and  which  is  the 
floor.  Usually,  if  Stigmariae  are  found  in  the  rocks  of  one  wall,  it  is  supposed 
that  this  wall  is  the  floor  of  the  seam,  while  if  SigillariaQ,  fern  leaves,  etc.  are 
found  in  the  wall  rock,  it  is  probably  the  roof  of  the  deposit.  These  indi- 
cations are  not  positive  proof,  for  both  of  these  fossils  may  occur  in  either 
the  top  or  bottom  wall  of  a coal  deposit,  though  they  are  usually  found  in 
the  positions  noted.  Coal,  clay,  gypsum,  salt,  etc.  usually  occur  in  unaltered 
deposits,  i.  e.,  in  rocks  that  have  riot  undergone  metamorphism. 


PROSPECTING. 


237 


The  accompanying  table  gives  the  names  of  the  various  geological  periods, 
both  as  they  occur  in  America  and  their  foreign  equivalents,  together  with 
the  name  of  the  principal  form  of  life  during  each  period.  The  various 
terms  employed  in  geology  are  defined  in  the  glossary. 


238 


PROSPECTING, 


Metals  and  metallic  ores  usually  occur  in  rocks  that  have  undergone 
more  or  less  metamorphism.  This  change  may  have  been  accomjmnied  by 
heat  and  volcanic  disturbances  sufficient  to  render  the  rocks  thoroughly 
crystalline,  or  it  may  simply  have  been  the  converting  of  limestone  into 
dolomite. 

The  prospector  for  metals  usually  avoids  regions  in  which  the  rocks  have 
been  wholly  unaltered;  while,  on  the  other  hand,  a region  covered  by 
extensive  flows  of  basalt  is  generally  barren.  As  the  vein  filling  of  most 
metal-bearing  deposits  has  been  deposited  from  circulating  water,  it  stands 
to  reason  that  porous  rock  formations  are  more  favorable  to  the  occurrence 
of  metallic  ores  than  are  hard,  dense,  rock  formations.  As  a rule,  ore 
deposits  are  more  common  at  the  junction  of  two  dissimilar  rock  formations, 
as,  for  instance,  the  contact  between  limestone  and  porphyry. 

When  a prospector  is  operating  in  any  particular  region,  it  is  best  to 
study  carefully  the  conditions  of  that  region  before  proceeding,  as  such 
factors  as  lack  of  rain,  frozen  ground,  etc.  may  have  played  an  important 
part  in  determining  the  character  of  placer  or  fragmentary  deposits,  and 
the  outcrop  and  surface  appearance  of  other  deposits.  Experience  obtained 
in  one  region  is  frequently  very  misleading  when  applied  in  another. 

Coal  or  Bedded  Materials.— The  presence  of  the  outcrop  of  any  bed  may 
Often  be  located  by  a terrace  caused  by  the  difference  in  the  hardness  of  the 
strata;  but  as  any  soft  material  overlaying  a hard  material  will  form  a ter- 
race, it  is  necessary  to  have  some  means  of  distinguishing  a coal  or  ore 
terrace  from  one  caused  by  worthless  material.  Usually,  the  outcrop  of  a 
coal  terrace  will  be  accompanied  by  springs  carrying  a greater  or  less  amount 
of  iron  in  solution,  which  is  deposited  as  ochery  films  upon  the  stones  and 
vegetable  matter  over  which  the  water  flows.  The  outcrops  of  beds  of  iron 
or  other  ores  are  very  frequently  marked  by  mineral  springs.  Sometimes 
the  outcrop  of  a bed  will  be  characterized  by  a marked  difference  in  the 
vegetation,  as,  for  instance,  the  outcrop  of  a bed  of  phosphate  rock  by  a 
luxuriant  line  of  vegetation,  the  outcrop  of  a mineral  bed  by  a lack  of 
vegetation,  the  outcrop  of  a coal  bed  contained  between  very  hard  rocks 
by  more  luxuriant  vegetation  than  the  surrounding  country,  etc.  Some 
indication  as  to  the  dip  and  strike  of  the  material  composing  the  bed  may 
be  obtained  by  examining  the  terrace  and  noting  the  deflections  from  a 
straight  line  caused  by  the  changes  in  contour  of  the  ground.  If  the  varia- 
tion occasioned  by  a depression  is  toward  the  foot  of  the  hill,  the  bed  dips  in 
the  same  direction  with  the  slope  of  the  ground;  but  if  the  deflection  is 
toward  the  top  of  the  hill,  the  dip  is  the  reverse  from  the  slope  of  the 
ground,  or  into  the  hill.  After  any  terrace  or  indication  of  the  outcrop  of  a 
bed  has  been  discovered,  it  will  be  necessary  to  examine  the  outcrop  by 
means  of  shafts,  tunnels,  or  trenches.  The  position  of  such  openings  will 
depend  on  the  general  character  of  the  terrace.  If  the  dip  appears  to  be 
with  the  hill,  a trench  should  be  started  below  the  terrace  and  continued  to 
and  across  it;  while  if  the  dip  appears  to  be  into  the  hill,  it  may  be  best 
to  sink  a shallow  shaft  above  the  terrace. 

Formations  Likely  to  Contain  Coal.— No  coal  beds  of  importance  have  as  yet 
been  found  below  the  Carboniferous  period,  but  coal  may  be  looked  for  in 
any  stratified  or  sedimentary  rocks  that  were  formed  after  this  period, 
although  the  bulk  of  the  best  coal  has,  up  to  the  present  time,  been  found 
in  the  Carboniferous  period.  As  a rule,  highly  metamorphic  regions  con- 
tain no  coal,  and  the  same  may  be  said  of  regions  composed  of  volcanic  or 
igneous  rocks.  An  examination  of  the  fossils  contained  in  the  rocks  of  any 
locality  will  usually  determine  whether  they  belong  to  a period  below  or 
above  the  Carboniferous,  and  hence  whether  there  is  a probability  of  the 
formations  containing  coal.  On  account  of  this  fact,  the  prospector  should 
familiarize  himself  with  the  geological  periods,  and,  by  referring  to  any 
elementary  geology,  with  the  most  common  fossils  of  the  various  periods. 
The  rocks 'most  common  in  coal  measures  are  sandstones,  limestones,  shale, 
conglomerates,  fireclays,  and,  in  some  localities,  the  coal  deposits  are 
frequently  associated  with  beds  of  iron  ore. 

Ore  deposits,  as  is  well  known,  are  generally  found  in  mountainous 
districts,  rather  than  in  the  undisturbed  horizontal  strata  of  the  plains  and 
mountain  parks— usually  deep  in  the  core  and  center  of  the  mountain 
system,  rather  than  along  their  flanking  foot-hills.  Consequently,  not  only 
are  the  prairies  and  flat  portions  of  the  mountain  i:)arks  to  be  avoided,  but 
also  the  zone  of  uptilted  strata  on  the  edges  of  prairies  and  parks,  commonly 
called  hogbacks.  These  hogbacks  are  the  natural  “habitat”  of  such 


OEE  DEPOSITS. 


239 


economic  products  as  coal,  petroleum,  building  stone,  clays,  etc.,  but  not  often 
of  the  precious  metals.  The  reason  for  this  appears  to  be  that  the  latter  are 
commonly  found  to  be  associated  with  evidences  of  more  or  less  heat.  In 
the  Rocky  Mountains  they  are  rarely  found  except  where  volcanic  eruptions 
have  at  some  time  been  active,  or  where  the  strata  have  been  changed  or 
metamorphosed  and  crystallized  by  heat. 

As  metallic  ore  bodies  occupy  fissures  and  other  openings  in  the  earth’s 
crust,  we  must  go  to  regions  where  the  greatest  disturbances  and  uplifts 
bave  occurred,  accompanied  by  the  greatest  rending  and  contortions  of  the 
rocks,  and  eruptions  of  volcanic  matter. 

As  a broad  assertion,  we  may  say  that  the  greater  part  of  any  mountain 
region  is  a prospecting  field,  with  the  exception  of  those  areas  we  have 
restricted  as  unpromising.  But  over  this  wide  area  of  more  or  less  metamor- 
phosed and  crystalline  rocks,  there  are  regions  and  localities  where  the 
precious  metals  have  already  been  found,  and  others  where  on  geological 
grounds  they  are  most  likely  yet  to  be  found,  and  those  are  generally  where 
eruptive  forces  have  been  especially  active,  where  once  molten  eruptive 
rocks  are  most  abundant,  and  the  disturbance  and  crystallizing  of  the  strata 
most  pronounced. 

Position  of  Veins  and  Ore  Deposits. — Ores,  as  a rule,  are  to  be  looked  for  at 
the  junction  of  any  two  dissimilar  rocks,  rather  than  in  the  mass  of  those 
rocks.  However,  there  are  many  exceptions  to  this,  where  the  mass  of  a 
decomposed  dike  or  sheet  of  porphyry  has  been  impregnated  by  free  gold  or 
gold-bearing  pyrites,  and  the  whole  rock  is  practically  a gold  vein.  In  this 
mass,  the  richest  gold  is  often  found  in  a network  of  little  quartz  veins  run- 
ning through  the  porphyry  mass.  Some  of  our  richest  gold  mines  are  found 
in  “rotten,”  decomposed,  oxidized  dikes  and  sheets  of  porphyry;  but  this  is 

rarely  the  case  with  lead-silver  ores, 
which  frequent  rather  the  lines  of  con- 
tact in  limestones  or  in  fissure  veins  in 
granite.  The  Cambrian  quartzites  a few 
years  ago  were  rather  avoided  by  the 
prospectors,  their  extreme  hardness  pre- 
senting great  difficulties  in  mining,  and 
from  the  fact  that  they  were  generally 
supposed  to  be  barren.  The  late  discov- 
& eries  of  very  rich  gold  deposits  in  them, 
and  of  similar  deposits  in  quartzites  of 
a later  age,  have  drawn  more  attention 
to  them.  The  gold  has  been  found  in 
a free  state  associated  with  oxide  of  iron 
in  cavernous  deposits,  and  in  close  prox- 
imity to  eruptive  rocks.  In  the  granitic 
rocks,  both  gold  and  silver  occur  in  fissure  veins  associated  with  pyrites, 
galena,  etc.  These  fissures,  occupied  by  mineralized  quartz  veins,  may  occur 
in  the  granite  or  gneiss  alone,  or  be  at  the  contact  of  these  rocks  with  a 
porphyry  dike. 

Veins  in  overflows  of  volcanic  lava  generally  fill  a fissure  having  a more 
or  less  steep  inclination,  penetrating  the  lava  sheets,  caused  probably  by 
shrinkage  of  the  molten  lava  on  cooling.  These  fissures,  in  some  cases,  are 
likely  to  be  limited  in  depth  to  the  thickness  of  the  lava  sheet.  Where,  in  a 
few  rare  cases,  the  fissure  has  been  traced  down  to  the  underlying  granite  or 
some  other  rock,  it  has  come  abruptly  to  an  end. 

Underground  Prospecting.— Frequently  a seam  or  deposit  becomes  faulted 
or  pinched  out  underground,  and  it  is  necessary  to  continue  the  search  by 
means  of  underground  prospecting.  Underground  prospecting  is,  to  a large 
extent,  similar  to  surface  prospecting,  the  underground  exposures  being 
simply  additional  faces  for  the  guidance  of  the  engineer.  In  the  case  of 
coal  beds  or  similar  seams,  if  a fault  or  dislocation  is  encountered,  the  man- 
ner of  carrying  on  the  search  will  depend  on  the  character  of  the  fault. 
Where,  sand  faults  or  washouts  are  encountered,  the  drift  or  entry  should 
be  driven  forwards  at  the  angle  of  the  seam  until  the  continuation  of  the 
formation  is  encountered,  when  a little  examination  of  the  rocks  will  indi- 
cate whether  they  are  the  underlying  or  overlying  measures.  In  the  case 
of  dislocations  or  throws,  the  continuation  of  the  vein  may  be  looked  for  by 
Schmidt’s  law  of  faults,  which  is  as  follows:  Always  follow  the  direction  of  the 
greatest  angle.  It  has  been  discovered  by  observation  that,  in  the  majority 
of  cases,  the  hanging- wall  portion  of  the  fault  has  moved  down,  and  oh  this 


240 


PROSPECTING, 


account  such  faults  are  commonly  called  normal  faults.  For  instance,  if  the 
bed  a b,  Fig.  1,  were  being  worked  from  a toward  the  fault,  upon  encoun- 
tering the  fault,  work  would  be  continued  down  on  the  farther  side  of  the 
fault  toward  d,  until  the  continuation  of  the  bed  toward  b was  encountered. 
In  like  manner,  had  the  work  been  proceeding  from  6,  the  exploration 
would  have  been  carried  up  in  the  direction  of  the  greatest  angle,  and  the 
continuation  toward  a thus  discovered.  A reverse  fault  is  one  in  which 
the  movement  has  been  in  the  opposite  direction  to  a normal  fault.  Espe- 
cially in  the  case  of  precious  metal  mines,  where  the  material  occurs  as 
perpendicular  or  steeply  pitching  veins,  faults  are  liable  to  displace  the 
deposit,  both  horizontally  and  vertically,  in  which  case  it  may  be  difficult 
to  determine  the  direction  of  the  continuation  of  the  ore  body;  but  fre- 
quently pieces  of  ore  are  dragged  into  the  fault,  and  these  serve  as  a guide 
to  the  miner,  and  indicate  the  proper  direction  for  exploration.  Where  a 
bed  or  seam  is  faulted,  its  continuation  can  frequently  be  found  by  breaking 
through  into  the  measures  beyond,  when  an  examination  of  the  formation 
will  indicate  whether  the  rocks  are  those  that  usually  occur  above  or  below 
the  desired  seam. 

Prospecting  for  Placer  Deposits.— Placers  are  fragmental  deposits  from  water 
in  which  the  heavier  minerals  have  been  concentrated  in  certain  portions, 
usually  next  the  underlying,  or  bed,  rock.  The  materials  that  are  recovered 
from  placer  deposits  are  metallic  gold,  tinstone,  monazite,  sand,  or  precious 
stones.  Placer  deposits  are  modern  or  ancient.  Modern  placers  are 
deposits  of  washed  material,  or  debris,  in  the  beds  or  along  the  banks  of 
streams  that  are  either  now  in  existence  or  existed  in  comparatively  recent 
times.  Placer  deposits  may  also  occur  in  deposits  along  the  seashore. 
Ancient  placers  are  fragmental  accumulations,  similar  to  the  modern 
placers,  which  have  been  buried  under  accumulations  of  strata  or  flows  of 
lava,  and  they  may  or  may  not  have  become  consolidated  into  rock. 

At  times,  placers  are  very  compact,  owing  to  the  presence  of  large  quanti- 
ties of  oxide  of  iron  or  calcium  carbonate,  or  similar  cementing  material. 
Often,  in  the  case  of  modern  placers,  the  streams,  or  other  sources  of  water 
that  deposited  the  material,  have  changed  their  course  so  that  the  placer 
deposit  is  now  high  up  in  the  benches  bordering  the  streams,  or,  possibly, 
even  on  the  top  of  the  present  hills.  Such  deposits  are  commonly  called 
bench  deposits,  while  those  along  the  sides  of  the  streams  below  the  high- 
water  mark  are  called  bar  deposits,  diggings,  or  placers. 

Frequently,  a large  portion  of  the  gold  or  other  valuable  material  is 
found  in  pockets  or  irregularities  in  the  bed  rock,  but  the  pot  holes  under 
waterfalls  are  frequently  barren  of  gold,  on  account  of  the  fact  that  the 
current  there  was  sufficiently  swift  to  wash  everything  out,  either  heavy  or 
light.  When  the  soil  is  saturated  with  water,  the  mass  may  partake  of  the 
nature  of  a semifluid  through  which  the  heavy  particles  of  gold  settle  until 
they  accumulate  on  the  bed  rock. 

When  prospecting  for  placers,  the  miner  examines  the  country  for  any 
indications  of  present  or  ancient  watercourses  in  which  the  deposits  of 
placer  material  have  been  formed.  He  pans  the  dirt  from  any  deposits  dis- 
covered, to  see  if  it  contains  colors  (small  particles  of  metallic  gold).  If 
colors  are  found,  more  extensive  operations  are  in  order,  and  hence  he 
sinks  to  bed  rock  and  examines  the  material  thoroughly,  to  see  if  it  contains 
a paying  quantity  of  the  valuable  mineral. 

The  form  of  placer  deposit  in  dry  or  arid  regions  differs  from  that  in 
regions  where  the  rivers  have  a continuous  flow,  on  account  of  the  fact  that 
the  deposits  are  largely  the  result  of  sudden  rushes  of  water  partaking  of  the 
nature  of  cloudbursts,  hence  the  rich  portions  in  the  placer  material  are 
very  irregular,  and  are  rarely  situated  on  bed  rock,  but  are  usually  found  on 
any  strata  that  formed  the  bottom  of  the  ravine  during  the  sudden  rush  of 
water.  During  the  rainy  season  in  arid  regions,  the  surface  soil  is  some- 
times softened  for  a few  inches,  so  that  it  becomes  practically  a mud,  and 
particles  of  gold  that  it  may  contain  tend  to  settle  to  the  bottom  of  the  soft 
portion,  thus  rendering  the  surface  barren.  This  barren  surface  may  be 
subsequently  washed  away  by  the  rain,  or  blown  away  as  dust  during  the 
dry  season.  The  repeating  of  this  process  year  after  year  results  in  the 
removal  of  considerable  of  the  original  surface  and  the  formation  of  a rich 
stratum  mst  below  the  grass  roots.  Prospectors  in  arid  regions,  who  have 
been  used  to  operating  in  an  ordinarily  well-watered  country,  are  frequently 
deceived  by  finding  this  rich  ground  so  high  up  in  the  deposit,  not  knowing 
that  it  is  no  indication  as  to  the  value  of  the  material  at  a greater  depth. 


GEMS  AND  PRECIOUS  STONES. 


241 


In  many  cases,  in  the  arid  regions  the  portion  of  the  deposit  upon  bed  rock 
is  entirely  barren.  In  like  manner,  frozen  ground  may  play  an  important 
part  in  the  formation  and  distribution  of  the  values  in  placer  deposits. 

Gems  and  precious  stones  are  prospected  for  in  a manner  similar  to  that 
employed  in  searching  for  placer  material,  and  are  usually  found  in  alluvial 
deposits,  from  which  they  are  obtained  by  washing.  In  a few  caseSj  gems 
are  found  in  the  rocks  themselves;  as,  for  instance,  diamonds  in  the  hard 
matrix  that  occurs  as  pipes  or  chimneys  in  metamorphic  rocks,  and  which, 
upon  exposure  to  the  atmosphere,  becomes  decomposed,  so  that  the  stones 
are  easily  removed.  Some  of  the  corundum  minerals  are  found  in  lime- 
stone and  metamorphic  or  crystalline  rocks.  Turquoise  usually  occurs  in 
veins,  the  outcrop  of  which  is  stained  with  carbonate  of  copper.  In  most 
cases,  it  does  not  pay  to  extract  gems  from  rock  formations  when  the  rock  is 
extremely  hard,  owing  to  the  fact  that  the  gems  are  liable  to  become  broken 
in  separating  them  from  the  rock  matrix. 

For  gem  prospecting,  the  following  outfit  has  been  recommended:  A 
shovel  and  pick;  two  sieves,  one  of  2 or  3 meshes  to  the  linear  inch,  and  the 
other  of  20  or  more  meshes  to  the  inch  (the  coarse  sieve  should  be  arranged 
to  fasten  on  top  of  the  finer  one  for  use  together);  a tub  in  which  the  sieves 
can  be  submerged  in  water;  an  oilcloth  on  which  to  sort  the  gravel;  several 
stones  and  crude  gems  as  a scale  of  hardness;  a small  pocket  magnifying 
glass,  and  a dichroscope.  In  some  cases,  a portion  of  the  outfit  is  dispensed 
with.  The  use  of  the  outfit  may  be  explained  as  follows:  The  tub  is  partially 
filled  with  water,  the  two  sieves  fastened  together,  and  a shovelful  of 
material  placed  in  the  upper  one,  when  they  are  submerged  in  water,  the 
large  stones  cleaned  and  examined,  and  all  of  the  fine  material  worked 
through  the  upper  sieve,  which  is  then  removed,  the  material  on  it  examined 
and  disposed  of.  The  material  in  the  fine  sieve  is  then  washed  until 
free  from  clay,  when  a little  jigging  motion  in  the  water  will  carry  the 
lighter  material  to  the  top.  The  sieve  is  then  quickly  inverted  and  the 
material  dumped  out  on  the  oilcloth,  thus  bringing  the  heavier  stones  to 
the  top.  The  various  pieces  should  now  be  examined  with  the  magnifying 
glass,  scale  of  hardness,  etc.,  and  the  identity  of  any  doubtful  colored  gems 
settled,  by  means  of  the  dichroscope.  Few  precious  stones  are  of  sufficient 
specific  gravity  to  be  concentrated  in  distinct  beds,  like  gold  or  tinstone,  but 
they  are  usually  fairly  well  concentrated  and  freed  from  much  of  the  lighter 
worthless  material. 

Value  of  Free  Gold  per  Ton  of  Ore.— The  accompanying  table  was  prepared 
by  Mellville  Atwood,  F.  G.  S.,  and  its  use  may  be  explained  as  follows: 
If  a 4-lb.  sample  of  quartz  be  crushed,  the  gold  separated  by  panning  and 


Value  of  Free  Gold  per  Ton  of  Ore. 
{Risdon  Iron  Works.) 


Weight, 
Washed  Gold. 
4-Lb.  Sample. 
Grains. 

Fineness, 

780. 

Value  per  Oz., 
S16.12. 

Fineness, 

830. 

Value  per  Oz., 
$17.15. 

Fineness, 

875. 

Value  per  Oz., 
$18.08. 

Fineness, 

920. 

Value  per  Oz., 
$19.01. 

5.0 

$83.97 

$89.36 

$94.20 

$99.05 

4.0 

67.18 

71.49 

75.36 

79.24 

3.0 

50.38 

53.61 

56.52 

59.43 

2.0 

33.59 

35.74 

37.68 

39.62 

1.0 

16.79 

17.87 

18.84 

19.81 

.9 

15.11 

16.08 

16.95 

17.82 

.8 

13.43 

14.29 

15.07 

15.84 

.7 

11.75 

12.51 

13.19 

13.86 

.6 

10.07 

10.73 

11.30 

11.88 

.5 

8.40 

8.93 

9.42 

9.90 

.4 

6.71 

7.14 

7.53 

7.92 

.3 

5.03 

5.36 

5.65 

5.94 

.2 

3.36 

3.57 

3.76 

3.96 

.1 

1.68 

1.78 

1.88 

1.98 

amalgamation,  the  quicksilver  volatilized  by  blowpiping  or  otherwise,  and 
the  resulting  button  weighed,  the  value  of  the  ore  per  ton  of  2,000  lb.  will 


242 


PROSPECTING. 


be  found  opposite  the  weight  of  the  button.  The  values  are  given  for  fine- 
ness of  gold  varying  from  780  to  920. 

To  determine  the  value  of  gravel,  a 6-lb.  sample  will  give  the  same 
results  as  that  obtained  from  a 4-lb.  sample  of  quartz,  on  account  of  the 
fact  that  18  cu.  ft.  of  gravel  measured  in  a bank  weigh  1 ton,  or  2,000  lb.; 
hence,  a cubic  yard  of  gravel  measured  in  a bank  weighs  3,000  lb.,  and 
for  this  reason  a sample  one  and  one-half  times  as  large  as  that  required 
for  quartz  must  be  taken.  In  case  the  gravel  is  of  low  grade,  a sample  ten 
times  as  large,  or  60  lb.,  may  be  taken,  in  which  case  the  value  opposite 
the  weight  of  the  button  will  have  to  be  divided  by  10. 

As  an  example,  in  the  use  of  the  table  we  may  suppose  that  a button 
from  4 lb.  of  ore  or  61b.  of  gravel  weighs  3.8  gr.,  and  that  the  fineness  of 
the  gold  is  830.  Opposite  3 in  the  table  we  will  find  $53.61  as  the  value  of 
the  button  in  dollars  containing  3 gr.  of  gold,  and  opposite  .8  we  will  find 
$14.29.  The  sum  of  these  is  $67.90,  the  value  of  the  ore  per  ton,  or  the  gravel 
per  cubic  yard. 


EXPLORATION  BY  DRILLING  OR  BORE  HOLES. 

Earth  Augers.— When  testing  soil  or  searching  for  placer  gold,  sand,  soft 
iron,  or  manganese  ores,  and  similar  materials  that  usually  occur  compara- 
tively near  the  surface,  hand  augers  may  be  employed  to  great  advantage. 
A good  form  of  hand  auger  consists  of  a piece  of  flat  steel  or  iron,  with  a 
steel  tip,  twisted  into  a spiral  about  1 ft.  long,  and  having  four  turns.  The 
point  is  split  and  the  tips  sharpened  and  turned  in  opposite  directions  and 
dressed  to  a standard  width,  usually  2 in.  The  auger  is  attached  to  a short 
piece  of  1"  pipe,  and  is  operated  by  joints  of  1"  pipe,  which  are  coupled 
together  with  common  pipe  couplings.  The  auger  is  turned  by  means  of  a 
double-ended  handle  having  an  eye  in  the  center  through  which  the  rod 
passes. 

The  handle  is  secured  by  means  of  a setscrew.  In  addition  to  the  auger, 
it  is  well  to  have  a straight-edged  chopping  bit  for  use  in  comparatively  hard 
seams.  This  may  be  made  from  a piece  of  If"  octagon  steel,  with  a 2"  cut- 
ting edge.  The  upper  end  of  the  steel  is  welded  on  to  a piece  of  pipe  similar 
to  that  carrying  the  auger.  When  the  chopping  bit  is  employed,  it  is 
necessary  to  have  a heavy  sinking  bar,  which  may  be  made  from  a piece  of 
solid  If"  iron  bar,  fitted  with  ordinary  1"  pipe  threads  on  the  ends.  Pros- 
pecting can  be  carried  on  to  a depth  of  from  50  to  60  ft.  with  this  outfit.  The 
number  of  men  necessary  to  operate  the  rods  varies  from  2 to  4,  depending 
on  the  depth  of  the  hole  being  drilled.  When  more  than  30  ft.  of  rods  are  in 
use,  it  is  usually  necessary  to  have  a scaffold  on  which  some  of  the  men  can 
stand  to  assist  in  withdrawing  the  rods.  When  withdrawing  the  rods, 
to  remove  the  dirt,  they  are  not  uncoupled  unless  over  40  ft.  of  rods  are  in 
use  at  one  time,  and  sometimes  as  many  as  50  or  60  ft.  are  drawn  without 
uncoupling. 

Percussion  or  churn  drills  are  frequently  employed  in  drilling  for  oil, 
w^ater,  or  gas,  and  were  formerly  much  used  in  searching  for  coal  and  ores, 
but,  owing  to  the  fact  that  they  all  reduce  the  material  passed  through  to 
small  pieces  or  mud,  and  so  do  not  produce  a fair  sample,  and  to  the  fact 
that  they  can  only  drill  perpendicular  holes,  they  are  at  present  little  used 
in  prospecting  for  either  ore  or  coal. 

The  cost  and  rate  of  drilling  by  means  of  a percussive  or  churn  drill 
varies  greatly,  being  affected  much  more  by 
the  character  of  the  strata  penetrated  than  is 
the  case  with  the  diamond  drill.  In  the  case 
of  highly  inclined  beds  of  varying  hardness, 
the  holes  frequently  run  out  of  line  and  be- 
come so  crooked  that  the  tools  w'edge.  and 
drilling  has  to  be  suspended.  For  drilling 
through  moderately  hard  formations,  usually 
encountered  in  searching  for  gas  or  w'ater, 
such  as  sandstones,  limestones,  slates,  etc.,  the 
accompanying  costs,  from  the  American  Well 
Works,  Aurora,  111.,  may  be  taken  per  foot 
for  wells  from  500  to  3^000  ft.  deep  for  the 
central  or  eastern  portion  of  the  United 
States  at  present  (1900).  This  cost  includes  the  placing  of  the  casing,  but 
not  the  casing  itself. 


Cost  of  Well-Drilling. 


Size  of  Well. 
Inches. 

Cost  per  Foot. 

6 

$1.50 

8 

2.25 

10 

3.00 

12 

5.00 

15 

8.00 

DRILLING  OR  BORE  HOLES. 


243 


When  drilling  wells  for  oil  or  gas  to  a depth  of  approximately  1,000  ft., 
using  the  ordinary  American  rig  with  a cable,  the  cost  is  sometimes  reduced 
to  as  little  as  65  cents  per  foot  for  6"  or  8"  wells.  This  is  when  operating  in 
rather  soft  and  known  formations.  From  15  to  40  ft.  per  day  of  24  hours  is 
usually  considered  a good  rate  of  drilling,  though  in  soft  materials  as  much 
as  100  ft.  may  be  drilled  in  a single  day,  and  at  other  times,  when  very  hard 
rock  is  encountered,  it  is  impossible  to  make  more  than  from  1 to  2 ft.  per 
day. 

The  diamond  drill  is  the  only  form  that  has  been  universally  successful  in 
drilling  in  any  direction  through  hard,  soft,  or  variable  material.  Even  in 
the  use  of  the  diamond  drill,  many  difficulties  present  themselves,  and 
demand  careful  study  in  adapting  the  form  of  apparatus  to  the  work  in 
hand,  and  in  rightly  interpreting  the  results  obtained  from  any  set  of 
observations. 

Note.— See  “Mines  and  Minerals”  for  articles  on  Diamond-Drilling 
Practice,  by  H.  M.  Lane,  August,  1899,  to  January,  1900,  Vol.  XX. 

Selecting  the  Machine.— It  is  not  economy  to  employ  a machine  of  large 
capacity  in  shallow  explorations,  as  the  large  machines  are  provided  with 
powerful  motors,  and  hence  do  not  work  economically  under  light  loads. 
When  a large  machine  is  operating  small  rods  on  light  work,  the  driller 
cannot  tell  the  condition  of  the  bit,  or  properly  regulate  the  feed.  The 
machine  should  possess  a motor  of  sufficient  capacity  to  carry  the  work  to 
the  required  depth,  but  where  much  drilling  is  to  be  done,  it  is  usually  best 
to  have  two  or  more  machines,  and  to  employ  the  small  ones  for  shallow 
holes,  and  the  large  ones  for  deep  holes. 

All  feed  mechanisms  employed  in  diamond  drilling  may  be  divided  into 
two  classes:  (1)  Those  that  are  an  inverse  function  of  the  hardness  of  the 
material.  This  class  includes  friction,  spring,  and  hydraulic  feeds.  (2)  Those 
in  which  the  feed  is  independent  of  the  material  being  cut,  as  in  the  case  of 
the  positive  gear-feed. 

The  first  class  is  advantageous  when  drilling  through  variable  measures 
in  search  of  fairly  firm  material,  which  does  not  occur  in  very  thin  beds  or 
seams.  On  account  of  the  fact  that  this  class  of  feed  insures  the  maximum 
amount  of  advance  of  which  the  bit  is  capable  in  the  material  being  cut,  the 
danger  is  that  the  core  from  any  thin  soft  seam  may  be  ground  up  and 
washed  away’,  without  any  indication  of  its  presence  having  been  given. 

The  second  class,  or  positive  gear-feed,  if  properly  operated,  requires 
somewhat  greater  skill,  but  if  used  in  connection  with  a thrust  register,  it 
gives  reliable  information  as  to  the  material  being  cut,  and  is  especially 
useful  when  prospecting  for  soft  deposits  of  very  valuable  material. 

Size  of  Tools.— The  size  of  tools  and  rods,  and  consequently  the  size  of  the 
core  extracted,  depends  on  the  depth  of  the  hole  and  the  character  of  the 
material  being  prospected.  When  operating  in  firm  measures,  such  as 
anthracite  coal,  hard  rock,  etc.,  it  is  best  to  employ  a rather  small  bit,  even 
when  drilling  up  to  700  ft.,  or  more,  in  depth.  For  such  work,  a core  of  from 

in.  to  lx%  in.  is  usually  extracted.  The  rate  of  drilling  with  a small  outfit 
IS  very  much  greater  than  with  a large  one,  owing  to  the  fact  that  there 
is  a small  cutting  surface  exposed,  and  the  rate  of  rotation  of  the  rods  can  be 
much  greater.  When  prospecting  for  soft  materials,  such  as  bituminous 
coal,  valuable  soft  ores,  or  for  disseminated  ores,  such  as  lead,  copper,  gold, 
silver,  etc.,  it  is  best  to  employ  a larger  outfit  and  extract  a core  2 or  3 in.  in 
diameter,  and  sometimes  even  larger,  even  though  a comparatively  small 
machine  is  used  to  operate  the  rods. 

Drift  of  diamond-drill  holes,  or  the  divergence  from  the  straight  line,  often 
becomes  a serious  matter.  This  trouble  may  be  minimized  by  keeping  the 
tools  about  the  bit  as  nearly  up  to  gauge  as  possible.  Core  barrels,  with 
spiral  water  grooves  about  them,  answer  this  purpose  very  well  if  they  are 
renewed  before  excessive  wear  has  taken  place. 

Surveying  of  diamond  drill-holes  may  be  carried  on  by  either  one  of  two 
methods,  depending  on  the  magnetic  conditions  of  the  district.  Where 
there  is  no  magnetic  disturbance,  the  system  developed  by  Mr.  E.  F. 
MacGeorge,  of  Australia,  may  be  employed.  This  consists  in  introducing 
into  the  hole,  at  various  points,  small  tubes  containing  melted  gelatine,  in 
which  are  suspended  magnetic  needles  and  small  plummets.  After  the 
gelatine  has  hardened  the  tubes  are  removed,  and  the  angles  between  the 
center  line  of  the  tube,  the  plummet,  and  the  needle  noted,  thus  furnishing 
the  data  from  which  the  course  of  the  hole  can  be  plotted.  This  method 
gives  both  the  vertical  and  the  horizontal  drift. 


244 


PROSPECTim. 


Where  there  is  magnetic  disturbances  the  needle  cannot  be  used,  but  a 
system  brought  out  by  Mr.  G.  Nolten,  of  Germany,  has  been  quite  exten- 
sively employed.  In  this  case,  tubes  partly  filled  with  hydrofluoric  acid  are 
introduced  into  the  hole,  at  various  points,  and  the  acid  allowed  to  etch  a 
ring  on  the  inside  of  the  tube.  After  the  acid  has  spent  itself  the  tubes  are 
withdrawn,  and  by  bringing  the  liquid  into  such  a position  that  it  corre- 
sponds with  the  ring  etched  on  the  inside  of  the  tube,  the  angle  of  the  hole 
at  the  point  examined  can  be  determined.  This  method  gives  a record  of 
the  vertical  drift  of  the  hole  only. 

The  value  of  ':he  record  furnished  by  the  diamond  drill  depends  largely  on 
the  character  of  the  material  sought.  The  core  extracted  is  always  of  very 
small  volume  when  compared  with  the  large  mass  of  the  formation  pros- 
pected, and  hence  will  give  a fair  average  sample  only  in  the  case  of  very 
uniform  deposits.  The  value  of  the  diamond  drill  for  prospecting  may  be 
stated  as  follows:  More  dependence  can  be  placed  on  the  record  furnished  by 
the  diamond  drill  when  prospecting  for  materials  that  occur  in  large  bodies  of 
uniform  composition  than  when  prospecting  for  materials  that  occur  in  small 
bunches  or  irregular  seams.  To  the  first  class  belong  coal,  iron  ore,  low-grade 
finely  disseminated  gold  and  silver  ores,  many  deposits  of  copper,  lead,  zinc, 
etc.,  as  well  as  salt,  gypsum,  building  stone,  etc.  To  the  latter  class  belong 
small  but  rich  bunches  of  gold,  silver  mineral,  or  rich  streaks  of  gold  telluride. 

The  arrangement  of  holes  has  considerable  effect  upon  the  results  fur- 
nished. If  the  material  sought  lies  in  beds  or  seams  (as  coal),  the  dip  of 
which  is  fairly  well  known,  it  is  best  to  drill  a series  of  holes  at  right 
angles  to  the  formation.  If  the  material  sought  occurs  in  irregular  bunches, 
l)Ockets,  or  lenses,  it  will  be  necessary  to  drill  holes  at  two  or  more  angles,  so 
as  to  divide  the  ground  into  a series  of  rectangles,  thus  rendering  it  prac- 
tically impossible  for  any  vein  or  seam  of  commercial  importance  to  exist 
without  being  discovered.  Where  the  surface  of  the  ground  is  covered  with 
drift  and  wash  material,  it  may  be  best  to  sink  a shaft  or  drill  pit  to  bed 
rock,  and  locate  the  machine  on  bed  rock.  After  this,  several  series  of  fan 
holes  may  be  drilled  at  various  angles  from  the  bottom  of  the  pit.  Owing 
to  the  upward  drift  of  diamond-drill  holes,  the  results  furnished  from  a set 
of  fan  holes  drilled  from  a single  position  would  make  a flat  bed  appear  as 
an  inverted  bowl,  or  the  top  of  a hill.  On  this  account,  it  is  best  to  drill 
sets  of  fan  holes  from  two  or  more  locations,  so  that  they  will  correct  one 
another.  If  fan  holes  from  different  positions  intersect  the  same  bed,  a care- 
ful examination  of  them  will  usually  furnish  a check  on  the  vertical  drift 
of  the  holes. 

The  cost  and  speed  of  drilling  depend  greatly  on  the  formation  being 
penetrated.  As  a rule,  it  is  more  expensive  to  sink  the  stand  pipe  than  to  do 
the  subsequent  drilling.  Stand  pipes  may  cost  S5  or  more  per  foot  to  sink, 
while  the  cost  of  drilling  in  firm  rock  varies  from  10.50  to  ^2  per  foot;  in  the 
case  of  difficult  drilling,  the  cost  may  run  over  $4  per  foot.  Where  a large 
amount  of  drilling  has  to  be  done,  a fair  average  estimate  for  shallow  holes 
up  to  700  ft.  deep  would  be  $2  per  foot,  under  such  conditions  as  exist  in 
most  mineral  districts  of  the  United  States.  The  cost  of  labor,  fuel,  etc., 
enter  into  the  problem,  and  frequently  affect  it  to  a considerable  extent. 

The  rate  of  drilling  varies  considerably,  but  in  firm  rock  an  average  of 
1 ft.  per  hour,  including  all  delays  for  changing  rods,  etc.,  would  be  a fair 
average  up  to  700  ft.  Greater  speed  than  this  could  be  made  in  soft  shales  or 
sandstones,  and  somewhat  less  in  hard  rock.  The  hardness  of  the  rock 
affects  the  rate  of  drilling  much  less  than  does  its  character.  A conglomer- 
ate rock  containing  loose  pebbles  that  come  out  during  the  drilling,  or  a 
crystalline  rock  containing  angular  pieces  that  come  out  during  drilling, 
will  cause  far  greater  trouble  than  the  hardest  material  ever  encountered  in 
diamond  drilling.  The  following  tables  will  give  some  idea  as  to  the  cost 
of  diamond  drilling  under  various  conditions. 

The  cost  of  drilling  2,084  ft.  of  hole  in  prospecting  the  ground  through 
which  the  Croton  aqueduct  tunnel  was  to  pass  is  given  as  follows: 

814  ft.  of  soft  rock  (decomposed  gneiss),  in  which  an  average  of  23.1  ft.  per 
day  was  drilled,  at  a cost  of  $1.15  per  ft. 

347  ft.  of  hard  rock  (gneiss),  in  which  an  average  of  11.1  ft.  per  day  was 
drilled,  at  a cost  of  $3.97  per  ft. 

923  ft.  of  clay,  gravel,  and  boulders,  in  which  from  6^  to  9 ft.  per  day  were 
drilled,  at  a cost  of  $4.07  per  ft. 

The  average  progress  per  day  in  drilling  the  entire  2,084  ft.  was  10.2  ft 
per  day. 


DRILLING  OR  BORE  HOLES. 


245 


In  the  Minnesota  Iron  Co.’s  mines,  at  Soudan,  Minn.,  the  diamond  drill  is 
used  for  drilling  holes  from  10  to  40  ft.  in  depth  in  the  back  of  the  stopes, 
practically  all  the  work  being  done  in  iron  ore.  The  average  cost  per  foot 
of  drilling  13,512  ft.  of  hole  was  $0.7703,  which  was  divided  as  follows: 


Carbons $0.34 

Supplies,  oil,  etc 0.07 

Fuel 0.04 

Repairs 0.05 

Labor 0.2703 


Total  $0.7703 


The  following  tables  give  the  cost  of  boring  at  two  Ishpeming,  Mich., 
mines; 


TABLE  I. 

Total  Cost 

r 400i  days  setter  at  $3.00 $1,200.75  1 Cost.  per  Ft. 

ToU.^r.J  372  days  runner  at  2.25 837.00  ! m aaq 

Labor  j 230i  days  runner  at  2.00 460.50  f ^^,506.10  $0,669 

[ 4i  days  laborer  at  1.75 7.85  J 

Carbon  68f  carats  at  $15,144  1,035.47  0.276 

Bits,  lifters,  shells,  barrels,  and  repairs 433.81  0.115 

Oil,  candles,  waste,  and  supplies 128.09  0.035 

Estimated  cost  compressed  air  374.60  0.100 


Total  $4,478.07  $1,195 

Number  holes  drilled  28 

Drilled  in  hematite  193  ft. 

Drilled  in  jasper 646  ft. 

Drilled  in  mixed  ore  986  ft. 

Drilled  in  dioritic  schist 1,921  ft. 

Total  drilling  3,746  ft. 

Number  of  10-hour  shifts  drill  was  running,  including 

moving  and  setting  up  603 

Amount  drilling  per  10-hour  shift 6.2  ft. 


TABLE  II. 

Underground  drilling 6,075  ft. 

Surface  drilling  1,414  ft. 

Stand  pipe  sunk 470  ft. 

Total  distance  run 7,959  ft. 

Actual  drilling  time  underground 672  shifts 

Actual  drilling  time  on  surface  165  shifts 

Time  of  foreman,  setter,  moving,  and  stand-piping 1,314  shifts 

Total  time  worked 2,151  shifts 

Average  progress  per  man  per  shift  3.70  ft. 

Average  progress  per  drill  per  shift  actually  run- 
ning   8.95  ft. 

Weight  of  carbon  consumed 111.00  carats 

Distance  drilled  per  carat  of  carbon  consumed 67.38  ft. 

Amount.  Per  Ft. 

Cost  of  carbon $1,887.00  $0,237 

Cost  of  supplies  and  oils 134.13  0.017 

Cost  of  fuel  360.73  0.045 

Cost  of  shop  material,  etc. 663.36  0.083 

Payroll 4,000.03  0.502 


Total  cost  f7,045,25  $0,834 


246 


PROSPECTING. 


Records  of  Cost  per  Foot  in  Diamond  Drilling. 


A 

B 

C 

D 

E 

F 

G 

H 

I 

J 

K 

L 

M 

N 

0 

Labor 

.707 

1.040 

2.483 

1.150 

.581 

1.615 

1.030 

1.720 

1.189 

1.284 

.721 

1.200 

.939 

.812 

.984 

Fuel 

.094 

.270 

.256 

.019 

.000 

.216 

.090 

.214 

.157 

.339 

.419 

.329 

.126 

.182 

.251 

Camp  account 

.373 

.559 

.789 

.5:18: 

.295 

.621 

.384 

; .549 

.516 

.495 

.519 

.595 

.644 

.722 

.636 

Repairs  .... 

.1:^9 

.110 

.294 

.171 1 

.135 

.144 

.103 

.185 

.154 

.165 

.040 

.087 

.138 

.126 

.116 

Supplies  . . . 

.034 

.065 

.039 

.074 

.023 

.032 

.011 

.039 

.048 

.097 

.020 

.092 

.076 

.097 

.088 

Carbon  .... 

.263 

.658 

.859 

.860 

.843 

1.587 

.934 

1 .684 

.684 

.733 

.227 

• .209 

.553 

.239 

1 .330 

Supt 

.239 

.322 

.628 

.040 

.063 

.192 

.140 

.305 

1 

.259 

.172 

.347 

.220 

.106 

.196 

.199 

Total . . . 

1.849 

3.024 

5.348 

2.852 

1 

1.940 

4.407  2.692 

1 

1 

3.696 

3.007 

3.285 

2.293 

2.732 

2.582 

2.374 

^2.604 

1 

A 5 holes,  1,066  ft.  T 

Sandstone  and  marble. 

B 1 hole,  1,293  ft. 

Black  slate  and  jasper.  J 

C 3 holes,  478  ft. 

Jasper,  very  hard.  K 

D 5 holes,  780  ft. 

Jasper,  hard.  L 

E 1 hole,  216  ft. 

Iron  slates.  M 

F 1 hole,  174  ft. 

Jasper  and  slate.  N 

G 2 holes,  267  ft. 

Jasper  and  slate.  0 

H 3 holes,  410  ft. 

Jasper. 


Average  cost  of  total  work  of 
drilling  21  holes.  Total  of 
4,684  ft. 

2 holes,  634  ft. 

Iron  slates. 

2 holes,  360  ft. 

Schist  and  jasper. 

6 holes,  1,350  ft. 

Iron  slates. 

2 holes,  611  ft. 

Schist,  jasper,  and  quartzite. 

6 holes,  2,091  ft. 

^Quartzite. 

Average  cost  of  drilling  18  holes, 
5,046  ft. 


The  following  figures,  taken  from  a letter  written  by  T.  F.  Richardson, 
Departmental  Engineer  of  Dam  and  Aqueduct  Department,  Metropolitan 
Water  Board  of  Boston,  and  published  by  the  U.  S.  Geological  Survey,  are  of 
interest,  as  they  show  the  rate  and  cost  of  diamond  drilling  under  certain 
conditions.  The  costs  do  not  take  into  account  depreciation  of  machinery 
nor  losses  of  time  in  moving  machines,  etc.  The  machines  employed  in 
this  work  were  a Badger  drill,  manufactured  by  the  M.  C.  Bullock  Manu- 
facturing Co.,  of  Chicago,  111.,  and  an  S-510  drill,  manufactured  by  the 
Sullivan- Machinery  Co.,  Claremont,  N.  H. 

The  total  amount  drilled  was  2,814  ft.,  the  deepest  hole  being  286  ft.  deep, 
and  the  average  depths  of  holes  about  60  ft.  The  amount  accomplished  per 
day  was  from  0 to  32  ft.,  the  average  amount  being  probably  about  10  or  12 
ft.  per  day.  The  cost  of  drilling  varied  very  largely,  both  with  the  hard- 
ness of  the  rock  and  the  condition  of  the  rock  as  to  being  seamy. 


The  following  was  the  cost  of  drilling  324.2  ft.  of  rather  hard,  tough 
diorite  rock: 


Labor $341.25 

Diamonds 74.30 

Coal 17.50 


Total $433.05 

Cost  per  foot 1.34 


(86.6  ft.  of  this  was  drilled  with  a If"  bit,  and  237.6  ft.  was  drilled  with  a 
li"  bit.) 


Drilling  150.7  ft.  of  very  hard  syenite  rock: 


Labor $158.00 

Diamonds 298.60 

Coal 10.50 


Total $467.19 

Cost  per  foot 3.10 

(Size  of  drill  U in.) 


DRILLING  OR  BORE  HOLES. 


247 


The  following  was  the  cost  of  drilling  286.1  ft.  of  soft  schist  rock: 


Labor S190.00 

Diamonds 87.75 

Coal 11.50 


Total $289.25 

Cost  per  foot 1.01 


(Size  of  drill,  If  in.) 

The  following  figures  will  be  of  considerable  interest,  owing  to  the  fact 
that  the  work  is  practically  all  of  the  nature  of  sinking  stand  pipes,  the 
object  of  the  exploration  being  to  ascertain  the  depth  of  wash  material  and 
the  character  of  the  bed  rock  over  the  area  of  certain  proposed  dam  sites  in 
the  southwestern  portion  of  the  United  States,  the  work  being  carried  on 
by  the  government.  The  machines  used  were  made  by  the  American 
Diamond  Rock  Drill  Co.,  of  New  York,  and  had  previously  been  employed 
in  similar  exploration  along  the  line  of  the  Nicaragua  Canal. 

Cost  of  operation  per  month  of  bed-rock  exploration: 


Foreman $150.00 

6 laborers,  at  $1.50  per  day,  28  days 234.00 

1 cook 45.00 

$429.00 

240  rations,  at  60  cents 144.00 

Total  repairs,  pipe  and  lumber  for  one 

party  for  10  months 500.00 

Total  commissary  charges  for  team,  feed, 

etc 350.00 

Total  moving 670.00 

Total  sundry  incidentals 200.00 

Total  supervision 350.00 

Total,  10  months $2,070.00 

Sundry  expenses  per  month 230.00 


Total  cost  per  month 803.00 

10  months,  at  $803 8,030.00 


Total  number  of  feet  sunk 3,254.20 

Total  cost $8,030.00 

Cost  per  foot 2.46 

Cost  per  hole,  7,227  -^52 154.42 

The  drills  were  purchased  second-hand  from  the  Nicaragua  Canal  Co., 
and  the  other  apparatus  was  new.  If  the  original  cost  of  all  this  machinery 
were  distributed  over  the  work,  the  results  would  be  as  follows: 

Operation $8,030.00 

Machinery 1,600.00 


Total  cost $9,630.00 

Or  average  cost  per  foot 2.86 


Both  machines  are  still  in  good  repair,  after  having  been  used  in  Nicara- 
gua and  in  various  localities  in  Arizona  and  California. 

The  total  depths  penetrated  in  all  materials  at  the  various  dam  sites  are 
as  follows : 


Covering. 

Rock. 

Total. 

The  Buttes 

1,621.2 

196.0 

1,817.2 

Queen  Creek 

857.8 

55.6 

413.4 

Riverside 

729.8 

40.2 

770.0 

Dikes 

80.0 

0.0 

80.0 

San  Carlos 

143.2 

30.4 

173.6 

Total  

2,932.0 

322.2 

3,254.2 

248 


PROSPECTING. 


Magnetic  Prospecting.—Bodiesof  magnetic  iron  ore  are  frequently  discov- 
ered or  located  on  account  of  their  magnetic  properties.  Two  forms  of 
compasses  are  employed  in  this  work;  the  dipping  needle,  or  miners’ 
compass,  and  the  ordinary  compass.  The  ordinary  compass  is  used  to  find 
the  center  of  magnetic  attraction  in  the  horizontal  plane,  and  after  this  has 
been  found  the  ground  may  be  run  over  with  the 
dipping  needle,  to  locate  the  center  of  attraction 
by  this  means.  The  ordinary  compass  does  not 
give  good  results  when  operating  over  a mag- 
netic deposit,  but  is  only  useful  in  determining 
its  outside  edge,  and  thus  locating  its  general 
position.  The  dipping  needle  differs  from  the 
ordinary  compass  in  that  the  needle  is  hung  in  a 
vertical  plane  in  place  of  horizontally,  so  that 
the  needle  is  free  to  assume  any  position  varying 
from  the  horizontal,  depending  on  the  downward  component  of  magnetic 
attraction  at  that  point.  The  vertical  magnetic  component  at  the  point 
should  be  compensated  for  by  balancing  the  dipping  needle  so  that  it  will 
ordinarily  stand  horizontally  when  not  affected  by  local  disturbances. 

The  actual  work  of  prospecting  may  be  carried  on  as  follows:  If  there 
were  an  outcrop  of  a vein  of  magnetic  material,  as  shown  in  Fig.  2,  covered 
with  a capping  of  wash  material,  the  preliminary  prospecting  would  be 
carried  on  as  shown  in  Fig.  3,  the  dipping  needle  being  carried  backwards 
and  forwards  zigzag  across  the  deposit,  noting  the  point  of  maximum  dip  in 
each  case  and  establishing  a stake  there  as  indi- 
cated by  the  crosses.  After  these  stakes  had  all 
been  established,  an  average  straight  line  would 
be  struck  through  them  that  would  follow  the 
course  of  the  deposit  as  nearly  as  possible.  Stakes 
would  be  placed  at  the  ends  of  this  line,  as  at  X and 
F,  and  the  line  X Y divided  off  into  100'  dis- 
tances by  means  of  stakes  marked  A,  B,  etc.  Lines 
at  right  angles  to  the  original  line  would  then  be 
turned  off  at  these  100'  points,  and  stakes  placed 
every  10  ft.  upon  the  branch  lines.  These  points 
on  the  branch  lines  would  be  lettered  with  small 
letters,  corresponding  to  the  large  letter  on  the  line 
X F,  as  shown  in  Fig.  4,  which  represents  the  obser- 
vations taken  at  the  first  station.  The  dip  would 
be  noted  at  each  one  of  the  10'  stations,  and 
recorded  in  the  note  book.  A convenient  method 
of  keeping  the  notes  is  to  have  a vertical  line  down 
the  center  of  the  page  for  the  line  X F,  and  other 
vertical  lines  to  the  right  and  left  of  it  for  the  indi- 
vidual stations  10  ft.  apart,  each  side  of  the  main 
line,  the  horizontal  lines  across  the  page  being  lettered  A,  B,  etc.,  the  sta- 
tions to  the  right  and  left  being  marked  with  primes  and  subscripts  of  the 
small  letters  corresponding  to  the  line.  After  the  observations  have  been 
taken,  lines  may  be  drawn  through  points  of  equal  dip  and  equal  deflection 

(isogonic  lines).  Bythis 
means  the  general  form  of 
the  bed  is  determined. 

The  maximum  dip,  in  the 
case  of  an  inclined  deposit 
like  that  shown  in  Fig.  2, 
would  occur  at  c,  over  the 
hanging  wall  of  the  outcrop, 
the  dip  at  6 being  consider- 
ably less,  and  the  dip  at  a 
being  less  than  that  at  h. 
After  the  center  of  magnetic 
attraction  has  been  discov- 
ered, prospecting  may  be  continued  by  means  of  the  diamond  drill,  or  by 
sinking  shafts  or  test  pits.  Sometimes,  where  deposits  of  magnetic  iron  ore 
have  been  eroded,  the  sands  near  the  surface  may  contain  such  a considerable 
amount  of  magnetic  disturbance  as  to  indicate  the  presence  of  a body  of  iron 
ore.  while  in  reality  there  may  be  such  a small  quantity  disseminated 
through  the  sand  that  it  could  not  be  made  to  pay  for  its  removal. 


Fig.  3. 


Fig.  4. 


GEOLOGICAL  MAPS  AND  CROSS-SECTIONS. 


249 


Any  body  of  magnetic  iron  ore  is  affected  by  polarity,  and  one  end  of  it 
will  attract  one  end  of  the  dipping  needle,  while  the  other  end  will  attract 
the  opposite  end.  Where  the  body  is  badly  broken  up,  this  dip  of  the 
needle  may  be  reversed  several  times  in  a comparatively  short  distance. 

Prospecting  for  Petroleum,  Natural  Gas,  and  Bitumen. — Among  the  surface 
indications  of  petroleum  and  bitumen  may  be  mentioned  white  leached 
shales  or  sandstones,  shales  burned  to  redness,  fumaroles,  mineral  springs, 
and  deposits  from  mineral  springs.  Also  natural  gas,  springs  of  petroleum 
oil  and  naphtha,  porous  rocks  saturated  with  bitumen,  cracks  in  shale,  and 
other  rock  partly  filled  with  bitumen.  Petroleum  is  never  found  in  any 
quantity  in  metamorphic  rocks,  but  always  in  sedimentary  deposits. 
Bitumen  can  be  told  from  coal,  vegetable  matter,  iron,  manganese,  and 
Other  minerals,  which  it  sometimes  closely  resembles,  by  its  odor  and  taste, 
also  by  the  fact  that  it  melts  in  the  flame  of  a match  or  candle,  giving  a 
bituminous  odor.  (Iron  and  manganese  do  not  fuse,  and  coal  and  vegetable 
matter  burn  without  fusion.)  Bitumen  is  also  soluble  in  bisulphide  of 
carbon,  chloroform,  and  turpentine,  usually  giving  a dark,  black,  or  brown 
solution.  Frequently,  springs  or  ponds  have  an  iridescent  coating  of  oil 
upon  the  surface.  Sometimes  iron  compounds  give  practically  the  same 
appearance,  but  the  iron  coating  can  always  be  distinguished  from  the  oil  by 
agitating  the  surface  of  the  water,  when  the  iron  coating  will  break  up  like 
a crust  of  solid  material,  while  the  oil  will  behave  as  a fluid,  and  tend  to 
remain  over  the  entire  surface  even  when  it  is  agitated. 

Frequently,  bubbles  of  gas  are  seen  ascending  from  the  bottoms  of  pools 
or  creeks.  These  may  be  composed  of  carbureted  hydrogen  or  natural  gas, 
which  is  a good  indication  of  the  presence  of  petroleum  or  bitumen;  they 
may  be  composed  of  sulphureted  hydrogen  or  carbonic-acid  gas.  Carbu- 
reted hydrogen  can  be  distinguished  by  the  fact  that  it  burns  with  a yellow 
luminous  flame,  whereas  sulphureted  hydrogen  burns  with  a bluish  flame, 
and  carbon  dioxide  will  not  support  combustion,  but,  on  the  contrary,  is  a 
product  of  combustion. 

When  carbureted  hydrogen  gas  is  discovered  ascending  from  water,  the 
bottom  of  which  is  not  covered  with  decaying  vegetation,  it  is  almost  a 
certain  sign  that  there  is  petroleum  or  bitumen  somewhere  in  the  underlying 
or  adjacent  formations. 

If  natural  gas  or  bitumen  is  found  upon  the  surface  of  shale,  it  is  probable 
that  the  material  ascended  vertically  through  cracks  in  these  rocks  from 
porous  strata  below;  while  if  it  is  found  in  connection  with  sandstones,  it  is 
probable  that  the  material  was  derived  from  the  porous  sandstone  itself. 
This  is  especially  liable  to  be  true  if  the  sandstone  has  a steep  pitch. 

As  a rule,  deposits  of  bitumen  or  petroleum  occur  in  porous  formations 
overlaid  by  impervious  strata,  such  as  shales,  slates,  etc.  Anticlines  are 
more  liable  to  contain  such  deposits,  though  they  are  not  absolutely  neces- 
sary to  retain  them,  as  at  times  portions  of  the  underlying  porous  strata 
have  been  rendered  impervious  by  deposits  of  calcium  salts,  silica,  etc.,  and 
hence  the  petroleum  or  bitumen  will  be  confined  to  the  porous  portions. 
Natural  gas  also  occurs  under  similar  conditions,  but  usually  in  anticlines 
only. 

Construction  of  Geological  Maps  and  Cross-Sections. — After  the  surface  exam- 
ination of  a property  is  complete,  the  data  should  be  entered  on  the  best 
map  procurable,  or  a map  constructed.  The  scale  depends  on  the  size  of 
the  property,  the  complexity  of  the  geological  formation,  the  value  of  the 
property,  and  the  material  to  be  mined  from  it.  The  amount  of  work  that 
it  will  pay  to  put  on  the  survey  will  depend  largely  on  the  value  of  the 
property,  more  detail  being  justified  in  the  case  of  high-grade  properties. 
If  a property  1,200  ft.  X 3,000  ft.  (the  size  of  four  U.  S.  mining  claims)  were  to  be 
surveyed  and  mapped  with  a scale  of  1 in.  equal  to  100  ft.,  the  map  would 
be  12  in.  X 30  in.  A vein  of  strata  10  ft.  wide  on  this  map  would  appear  as  yV  of 
an  inch  wide,  which  is  about  the  smallest  division  that  could  be  shown 
with  its  characteristic  symbol;  for  greater  detail,  a larger  scale,  or  larger 
scaled  sheets  of  the  most  important  portions  of  the  deposit,  will  be 
necessary.  If  the  geologist  constructs  the  topographical  contour  map,  he 
can  take  note^  on  the  geology  at  the  same  time.  When  the  boundaries  of 
the  property  are  being  surveyed,  certain  points  should  be  established,  both 
vertically  and  horizontally,  as  stations  in  future  topographical  work.  If  the 
map  is  on  government  surveyed  land,  the  government  lines  may  be  used 
for  horizontal  locations,  but  it  will  be  necessary  to  determine  the  elevation 
of  the  different  points.  If  the  property  is  much  broken,  it  is  well  to  run  a 


250 


PROSPECTING. 


few  lines  of  levels  across  it,  to  establish  points  from  which  to  continue  the 
work.  This  work  is  usually  done  with  a Y level  and  chain,  the  other  details 
being  subsequently  filled  in  with  a transit  and  stadia,  the  levels  of  the  other 

points  being  taken 
either  by  using  the 
transit  as  a level,  by 
vertical  angles,  by  bar- 
ometric observations, 
or  by  means  of  a hand 
level.  Where  lines  of 
levels  are  run  across 
the  property  in  various 
directions,  it  is  best  to 
run  them  in  such  a 
direction  that  they  will 
cross  the  strike  of  the 
strata  as  nearly  at  right 
angles  as  possible,  so 
that  the  profile  thus  de- 
termined may  be  used 
in  constructing  a cross- 
section.  Sometimes, 
for  preliminary  work, 
simply  a sketch  map  is 
all  that  may  be  neces- 
sary. All  of  the  outcrops  and  exposures,  together  with  their  proper  dip, 
should  be  entered  on  the  map. 

To  Obtain  Dip  and  Strike  From  Bore-Hole  Records. — Before  the  results 
obtained  from  bore  holes  are  available  for  use  in  map  construction,  the  dip 
and  strike  of  the  various  strata  must  be  ascertained.  The  process,  in  the 
case  of  stratified  rock,  is  as  follows:  If  three  holes  were  drilled,  as  at  A,  J5, 
and  (7,  Fig.  6,  each  intersecting  a given  bed,  the  strike  and  angle  of  dip  of  the 
bed  may  be  obtained  by  reducing  the  results  from  the  three  holes  to  a plane 
passing  through  the  highest  point  of  intersection,  which  is  at  A.  The  hole  B 
intersected  the  bed  at  the  distance  Be,  and  C at  the  distance  Cd  below  the 
point  A.  By  continuing  the  line  CB  indefinitely,  and  erecting  two  lines  Be 
and  Cd  perpendicular  to  it,  each  representing  the  distance  from  the  hori- 
zontal plane  through  A to  the  intersection  of  the  strata,  two  points  in  the 
line  de  are  obtained,  which  line  intersects  CB  produced  at/;  / is  one  point 
in  the  line  of  strike  through  A.  In  order  to  find  the  angle  of  dip,  the 
perpendicular  Cg  is  dropped  from  the  deepest  hole  C upon  the  line  of 


Fig.  7. 


strike  A f.  The  distance  Ch,  equal  to  Cd,  is  laid  off  at  right  angles  to  Cg, 
when  the  angle  Cgh  gives  the  maximum  dip.  The  results  obtained  from 
bore  holes  may  thus  be  reduced  to  such  form  that  the  dips  can  be  projected 
on  the  surface  to  obtain  the  line  of  outcrop  for  each  stratum.  Bore  holes  also 
furnish  data  for  constructing  underground  curves  in  cross-sections  of 
stratified  rocks,  and  in  locating  the  probable  outline  of  ore  bodies  in  other 
formations. 


SAMPLING  AND  ESTIMATING  AVAILABLE  MINERAL.  251 


Having  recorded  on  the  map  all  exposures,  whether  surface  or  those 
obtained  from  underground  work,  draw  the  line  of  strike  and  the  outcrops. 
Also  construct  a cross-section.  If  the  vein  is  perpendicular,  the  outcrop  will 
be  a straight  course  across  the  map.  If  the  bed  or  seam  is  horizontal,  the 
outcrop  will  correspond  with  the  contour  line.  For  beds  or  veins  dipping 
at  any  other  angle,  results  between  these  limits  will  be  obtained. 

If  the  property  being  examined  is  cut  by  synclines  or  anticlines,  the  dips 
will  not  all  be  in  the  same  direction,  and  if  there  is  a dip  along  the  axis  of 
the  synclines  or  anticlines,  the  construction  of  the  map  will  be  considerably 
complicated.  Fig.  5 represents  a plan  or  map  on  which  there  is  an  axis  x y 
toward  which  the  strata  dip  from  both  sides.  Outcrops  are  indicated  at 
A,  B,  C,  A',  and  B',  each  having  a dip  in  the  direction  of  the  arrow.  The 
lines  mn,  op,  qr  are  contours.  If  the  cross-section  were  constructed  on  the 
line  EG,  perpendicular  to  the  axis  x y,  the  various  beds  or  deposits  would  be 
cut  at  such  an  angle  as  to  show  a thickness  in  the  cross-section  greater  than 
that  which  actually  exists.  In  order  to  show  the  actual  thickness  for  each 
seam,  the  cross-section  must  be  taken  along  the  line  perpendicular  to  the 
strike  of  the  strata,  which,  in  the  present  case,  is  along  the  line  IHK.  In 
other  words,  the  cross-section  must  be  constructed  in  two  parts.  Where  a 
general  sketch  is  all  that  is  necessary,  a single  cross-section  with  notes 
correcting  the  thickness  of  the  seams  may  answer. 

In  order  to  construct  the  cross-section  IHK,  the  outcrops  A,  B,  C,  A',  and 
B'  must  be  projected  to  the  points  a,  h,  c,  a',  and  b',  this  projection  being 
along  their  contours.  If  the  points  on  the  line  of  the  intended  cross-section 
were  not  upon  the  contour,  it  would  be  necessary  to  project  them  on  the 
plane  of  the  cross-section,  as  shown  in  the  figure,  and  then  from  the  dip  of 
the  strata  and  the  difference  in  elevation  to  obtain  a corrected  point  along 
the  line  IHK.  The  cross-section  is  constructed  as  shown  in  Fig.  7,  each 
seam  having  its  actual  thickness  as  shown  at  the  outcrop.  If  the  upper 
surface  of  the  cross-section  is  not  a true  profile  of  the  surface,  and  the  points 
are  not  projected  in  the  plane  on  the  cross-section,  on  this  cross-section, 
according  to  their  dips,  there  is  considerable  danger  of  exaggerating  their 
thickness  one  way  or  the  other. 

On  mine  maps,  the  supposed  course  of  the  beds  should  be  sketched  in, 
subject  to  revision,  as  more  data  are  brought  out  by  later  development  work. 
Even  in  the  case  of  stratified  rocks,  it  is  difficult  to  form  a definite  idea  as 
to  the  underground  conditions  from  surface  indications,  and,  in  the  case  of 
metamorphic  or  crystalline  rocks,  it  is  absolutely  necessary  to  determine 
the  underground  conditions  by  drilling,  or  actual  development  work.  If 
the  property  being  examined  is  liable  to  become  a large  and  valuable 
mining  property,  the  original  survey  should  be  tied  to  monuments  or  natural 
landmarks,  so  that  it  can  be  checked  by  future  observations,  and  these 
monuments  or  landmarks  should  become  the  basis  of  future  and  more 
careful  mining  surveys. 

Some  of  the  advantages  of  a careful  geological  examination  of  a property 
are  that  other  materials  of  economic  value  would  probably  be  discovered, 
if  any  should  exist  on  the  property;  also,  such  an  examination  of  the 
property  gives  information  as  to  the  drainage  system  of  the  country  that  may 
be  of  great  advantage  in  laying  out  the  mine,  and  future  exploration  by 
drilling  or  sinking  can  be  done  to  better  advantage  after  a careful  surface 
examination. 

Sampling  and  Estimating  the  Amount  of  Mineral  Available.— In  many  cases,  it  is 
necessary  to  do  some  development  or  exploration  work  before  fair  average 
samples  can  be  obtained.  The  samples  as  taken  should  fairly  represent  the 
material  as  it  will  be  extracted.  Such  gangue  as  cannot  be  separated 
from  the  ore  in  mining,  or  slate  that  would  be  sold  with  the  coal,  should  be 
included  in  the  sample.  When  sampling  any  property  it  is  well  to  divide 
the  deposit  up  into  blocks,  and  sample  each  one  separately.  The  samples 
may  then  be  assayed  and  an  average  obtained  later,  or  the  different  samples 
may  be  mixed  and  an  average  assay  obtained.  The  amount  of  material 
broken  for  sample  may  vary  from  a few  pounds  to  many  tons,  depending  on 
the  nature  of  the  material  under  consideration.  Large  samples  may  be 
reduced  by  shoveling  (that  is,  taking  i proportionate  number  of  shovelfuls 
for  the  sample,  as  every  third  or  fourtn  shovelful).  After  the  sample  has 
been  partially  reduced,  the  operation  may  be  carried  on  by  quartering, 
which  may  be  described  as  follows: 

The  material  is  shoveled  into  a conical  pile  by  throwing  each  shovel- 
ful on  to  the  apex  of  the  cone.  After  this,  the  cone  may  be  reduced  by 


252 


phospecting. 


scraping  it  down  with  a shovel,  passing  slowly  around  it.  If  the  amount 
of  material  is  small,  a flat  plate  may  be  introduced  into  the  cone,  and  the 
pile  flattened  by  revolving  the  plate.  The  pile  is  then  divided  into  quarters 
by  drawing  lines  across  it.  After  this,  two  alternate  quarters  are  scraped 
out  and  shoveled  away,  and  the  other  two  quarters  are  left  as  the  sample. 
The  process  may  be  repeated  until  the  block  has  been  sufficiently  reduced. 
In  shoveling,  away  the  discarded  portions,  care  should  be  taken  to  see  that 
the  fine  dust  under  them  is  brushed  away  also,  as  they  often  contain  fine 
and  valuable  mineral  that  would  unduly  increase  the  value  of  the  resulting 
sample.  When  the  sample  consists  of  only  a few  pounds,  it  may  be  reduced 
by  means  of  a riffle.  Large  samples  consisting  of  several  tons  are  sometimes 
sent  to  sampling  works  to  be  reduced  by  automatic  sampling  machines.  If 
the  property  being  examined  is  a mine  in  active  operation,  samples  may 
be  taken  from  the  working  faces,  and  also  from  cars,  loading  chutes,  etc. 
Usually  the  samples  from  the  face  are  kept  separate  from  those  from  the  cars 
and  loading  chutes,  the  latter  being  intended  as  a check  on  the  former. 
In  the  case  of  ores  of  the  precious  metals,  large  samples  are  sometimes  taken 
and  used  for  mill  runs. 

Stock  piles,  or  dumps,  may  be  roughly  sampled  by  taking  pieces  from 
intervals  over  the  surface,  being  careful  to  obtain  a fair  average  of  coarse 
and  fine  material,  and  of  rock  and  ore.  These  samples  are  quartered  down 
and  assayed,  but  if  a close  valuation  is  d esired,  it  will  be  necessary  to  drive 
cuts  or  tunnels  through  the  mass,  and  to  take  a certain  amount,  as  every 
fifth  or  tenth  shovelful,  for  the  sample.  When  sampling  dumps  of  fine 
material  (as,  for  instance,  tailings)  it  is  possible  to  take  samples  from  the 
pile  by  means  of  a drill,  an  auger  1 in.  or  2 in.  in  diameter  usually  being 
employed  for  this  purpose. 

The  human  factor  always  plays  a large  part  in  the  value  of  a sample  as 
finally  selected,  and  hence  it  should  be  taken  by  a man  who  has  had  con- 
siderable experience  in  this  class  of  work.  For  this  reason,  it  is  best  to 
employ  a mining  engineer.  One  not  accustomed  to  sampling  very  rarely 
undervalues  a property,  owing  to  the  fact  that  it  seems  to  be  human  nature 
to  pick  up  a rich  piece  of  ore  or  coal,  rather  than  the  barren  gangue  material 
or  slate. 

When  only  surface  exposures  or  shallow  prospect  openings  are  available, 
it  is  impossible  to  determine  the  amount  of  ore  in  sight,  or  to  form  more 
than  a guess  as  to  the  size  of  the  deposit.  It  is  not  safe  to  count  any  ore  in 
sight  unless  it  is  exposed  on  at  least  three  faces.  Ore  that  is  exposed  on  one  or 
two  faces  can  be  counted  as  probable  ore,  while  slight  exposures  can  be 
counted  only  as  chances  indicated. 

The  amount  of  material  available  in  coal  deposits  can  be  estimated  much 
closer  than  in  the  case  of  ores.  If  a seam  is  penetrated  by  a number  of  bore 
holes,  or  by  workings  extended  over  a considerable  area,  it  is  fair  to  esti- 
mate that  the  material  will  run  practically  as  exposed  for  a considerable 
area;  but  especially  in  the  case  of  bituminous  coal,  it  is  a comparatively 
easy  matter  to  form  some  estimate  as  to  the  amount  of  material  available. 

When  dealing  with  ores,  it  is  impossible  to  form  reliable  estimates,  owing 
to  the  fact  that  horses  or  other  masses  of  rock  may  be  exposed  at  any  i)oint, 
and  the  ore  bodies  themselves  are  usually  very  irregular,  hence  it  will  be 
necessary  to  do  careful  blocking  out  before  making  any  estimates. 

When  estimating  the  amount  of  mineral  available,  only  that  portion 
which  can  actually  be  removed  in  sloping  should  be  counted,  and  if  the 
seam  is  so  narrow  that  it  is  necessary  to  break  material  from  the  walls,  or  if 
there  are  masses  of  country  rock  that  have  to  be  removed  with  the  ore,  the 
expense  of  removing  them  should  be  estimated  and  deducted  from  the  value 
of  the  ore. 


DIAGRAM  FOR  REPORTING  ON  MINERAL  LANDS. 

The  following  diagram  will  be  useful  as  a guide  in  making  out  a report 
on  a mining  property: 


1.  Situation 
AND  Sur- 
roundings. 


{ 


1.  Name.  | 

2.  Distance 


■ 1.  Location,  if  on  surveyed  land. 

2.  Nearest  town  or  village. 

3.  Mineral  district. 

. 4.  County,  state,  or  territory. 

and  direction  from  one  or  more  points. 


REPORTS  ON  MINERAL  LANDS. 


253 


DIAGRAM  FOR  REPORTING  ON  MINERAL  LAN DS— (C'onfowwed). 

{1.  Hills  or  mountains. 

2.  Character  of  surface,  vegetation,  and  timber, 

3.  Streams  and  water  supply. 

4.  Elevations. 


3.  Geology. 


' 1.  Rocks. 

2.  Axes. 

3.  Faults. 

1.  Struc- 
ture. 

4.  Dikes. 


^ 5.  Horses. 

2.  Geological  period. 

3.  (a) Coal  / 1.  Number, 
beds.  ( 2.  Thickness. 


or 


1.  Veins. 


(6)  Ore 
bodies. 


2.  B e d s or 
lenses. 


( 1.  Stratified. 

< 2.  Crystalline, 
f 3.  Igneous. 

Anticlines  or  synclines. 
' 1.  Number. 

2.  Strike. 

3.  Dip. 

, 4.  Throw. 

' 1.  Number. 

2.  Strike. 

- 3.  Dip. 

4.  Filling. 

_ 5.  Throw. 

' 1.  Number  and  size. 

^ 2.  Location. 

3.  Material. 


Uniformity.  ^ u?emenr’ 
Number.  urement. 

Character. 

Strike. 

Dip. 

Width. 

Vein  filling. 

Ore  chutes. 

Walls. 

Throw  of  walls. 

Number. 

Walls. 

Strike. 

Dip. 

Length. 

Height. 

Maximum  width. 

Average  width. 


4.  (a)  Quality  of 
coal,  specimens, 
appearance 
in  mine,  in  cars, 
benches. 


or 


(5)  Ore. 


1.  Color,  external,  powder. 

2.  Luster. 

3.  Clearness  from  clay  or  sand,  shale. 

4.  Sulphur. 

5.  Resin. 

6.  Firmness,  size  of  lumps,  air  slaking. 

7.  Cleavage  or  fiber. 

8.  Coking. 

9.  Color  of  ashes. 

10.  Use:  Gas,  steam,  domestic,  forge, 
metallurgy. 

11.  Analyses  or  assays. 

1.  Shipping. 

2.  Concentrating. 

3.  Metals  or  minerals. 

4.  Gangue. 

5.  Impurities. 

6.  Assays  or  analyses. 


254 


PROSPECTING. 


4.  Mining. 


1.  History. 


DIAGRAM  FOR  REPORTING  ON  MINERAL  LAN  DS— ( 

1.  Dates  of  opening,  abandoning,  reopening, 
number  of  mines  and  names, 

2.  Ownership. 

3.  Superintendence. 

1.  Shaft,  slope,  or  tunnel, 
r 1.  Total  depth. 

2.  Extent  of  J 2.  Depth  below  water  level, 
workings,  j 3.  Number  of  levels. 

t 4.  Extent  of  levels. 

3.  Water  pumps,  size,  and  kind,  water  cars, 
number  and  size,  natural  drainage. 

4.  Ventilation,  natural,  furnace,  fan  (for- 
cing or  drawing  out),  sufficient  or  insuf- 
ficient. 

5.  Lighting,  system  used. 

6.  Powder,  kind  and  grade  used. 

7.  Explosive  or  noxious  gases. 

8.  Coal-cutting  machines  and  power  drills. 

9.  (a)  Mode  of  working,  holding  under, 
shearing,  blasting,  or  wedging. 

tid  sloping. 


2.  Mine. 


(6)  Mode  of 
working. 


1.  Underhand 

2.  Overhead  sloping.' 

3.  Filling. 

4.  Caving. 

5.  Rooming  with  or  with- 
out timber. 

6.  Square  sets. 

10.  Rooms,  or  slopes,  pillars,  dimensions,  and 
general  plan. 

11.  Timbering,  timber  trees. 

12.  Roof,  or  hanging  wall,  strong  or  weak, 
air  slakes  or  not. 

13.  Floor,  or  foot- wall,  hard  or  soft,  creeps 
or  not. 

14.  Roads,  rails,  and  cars. 

' 1.  Men. 


15. 


System  of  under- 
ground tram- 
ming. 


16.  System  of  hoisting. 


2.  Mules. 

3.  Electricity. 

4.  Compressed  air. 

5.  Wire  rope. 

6.  Chain. 

7.  Locomotive. 
Cage. 

Skip. 

Cars. 


L '•  -L 


5.  Maps  and 

Drawings. 


1.  Of  the  whole  region. 

2.  Of  the  underground  workings. 

II.  Cross. 

2.  Longitudinal. 

(1.  General. 

3.  Columnar.  < 2.  Coal  bed  or  other  de- 
[ posit. 

4.  Buildings,  works,  or  machinery. 

' 1.  Scale. 

2.  North  line,  magnetic  variations. 
3.  Date. 

4.  Maker. 

5.  Can  buy,  take,  borrow,  or  have 
copied. 


5.  Explanation. 


6.  Concentra- 
tion. 


1 1 


Hand  picking. 
Cobbing  and  picking. 
Magnetic. 

4.  Mechanical,  jg  Diy 


REPORTS  ON  MINERAL  LANDS. 


255 


Coke 

Ovens. 


6.  Operations. 


DIAGRAM  FOR  REPORTING  ON  MINERAL  LfKHDS-^{Vontinued). 

1.  History,  ownership,  etc. 

2.  Number. 

3.  Character  of  ovens. 

4.  Dimensions. 

5.  Construction,  materials,  etc. 

' 1.  Charge,  quantity,  etc. 

2.  Working. 

, 3.  Discharging,  quenching. 

7.  Repairs. 

8.  Quality  of  product.  (Assays,  if  any.) 

^ 9.  Disposition  of  by  products. 

" ^ In  heaps. 

In  stalls. 

In  kilns. 

4.  By  mechanical  calciners. 

5.  Number  and  dimensions  of  roasters. 

1.  Base  bullion. 


I.  Metallur- 
gical Works 
AND  Treat- 
ment OF  Ore. 


1.  Roasted. 


jn  oi 
\ 3. 


2.  Smelted. 


9.  Disposition 
OF  Product. 


1.  Shipped. 


, 2.  Shipment. 


10.  Statistics. 


' 1.  In  shaft  fur- 
nace  to 


2.  In  reverber- 
atory furnace 
to 


3.  In  retorts  to 


1.  As  mined  to 


2.  As  concen- 
trates or  coke. 

3.  Metal  or 

matte  to 

1.  Distance. 

2.  Roads. 

3.  Railroads. 

4.  Navigation, 
f 1.  Capacity. 


2.  Matte. 

3.  Metal. 

4.  Number  and  dimen- 
sions of  furnaces. 

1.  Metal. 

2.  Matte. 

3.  Number  and  dimen- 
sions of  furnaces. 

1.  Metallic  zinc. 

2.  Mercury. 

3.  Number  and  size  of 
retorts. 

1.  Smelter. 

2.  Concentrator. 

3.  Sampling  works. 

4.  Jobber  at 

1.  Smelter  or  furnace. 

2.  Sampling  works. 

3.  Jobber  at 

1.  Refinery. 

2.  Smelter. 

t 3.  Jobber  at 


1.  Production. 


2.  Labor. 


I 2.  Actual 


Daily,  weekly,  or  month- 
ly, in  tons. 

2.  Yearly  in  tons. 

[S.  Average. 

1.  Whole  number  of  workers. 

2.  Number  of  workers  in  each  class. 

3.  Number  of  horses  or  mules. 


3.  Prices. 


1.  Timber. 

2.  Tools. 

3.  Fuel. 

4.  Oil. 

5.  Powder. 

C 1.  Day,  different  classes. 

6.  Labor.  ^ 2.  Contract  or  piece,  yard  or 

( ton. 

7.  Carriage. 

8.  Local  sales  of  product. 

f 1.  Machinery. 

2.  Buildings. 

9.  Value  of  plant.  ^ 3.  Roads, tracks, etc. 

4.  Rolling  stock. 

. 1,5.  Supplies. 


256 


PROSPECTING. 


DIAGRAM  FOR  REPORTING  ON  MINERAL  LAN DS— ( 


11.  Surface 


Plant. 


1.  Power  plant. 


2.  Shops. 


Powder 

houses. 


14.  Water. 


1.  Boilers. 

2.  Waterwheels. 

3.  Air  compressors. 

4.  Steam  and  gas  engines. 

5.  Electric  plants. 

1.  Power  for. 

2.  No.  of  forges. 

3.  Steam  hammers. 

4.  Other  tools. 

1.  Power  for. 

2.  Saws. 

3.  Lathes. 

4.  Other  machines. 

5.  Benches  and  vises. 

1.  Power. 

2.  Lathes. 

3.  Planers. 

4.  Shapers. 

5.  Drill  presses. 

6.  Other  tools. 

7.  Benches  and  vises. 


1.  Smith’s 
shop. 


2.  Carpenter 
shop. 


3.  Machine 
OflSces.  t shop. 

Dry  or  change  houses. 

Storehouses. 

Boarding  and  dwelling  houses. 

Stables. 

Shaft  houses. 

Tipples. 

Pockets  or  ore  bins. 

Company  store. 

Timber  yard  and  plant  for  preparing  timber. 

" 1 Citv  or  eoTo-  f 1'  Quality  of  water. 
me??ial  J 2-  Sufficient  or  in- 
merciai  sufficient. 

3.  Pressure. 

1.  Quality  of  water. 

2.  Suflacient  or  in- 
sufficient. 

2.  Company  3.  Gravity  system, 
service.  f 1.  Direct, 

4.  Pump- 
ing sys- 
tem. 


2.  Reser- 
voir or 
stand 
pipe. 


15.  Lighting. 


1.  Character. 

2.  Origin. 


16. 


Hoisting  or  wind- 
ing plant. 


17. 


Surface  trans- 
portation. 


1.  Gas. 

2.  Electric. 

1.  Commercial  plant. 

^ 2.  Company  plant. 

3.  Sufficient  or  insufficient. 

1.  Steam  engines. 

2.  Compressed-air  engines. 

3.  Oil  or  gasoline  engines. 

I 4.  Electric  motors, 
t 5.  Water  motors. 

' 1.  Gauge. 

2p  Total  length. 

3.  Size  of  cars. 

4.  No.  of  cars. 

5.  Power  used. 

6.  No.  of  motors. 

1.  Character  and 
surface  of. 

2.  Length. 

3.  No.  of  wagons 
and  teams. 

1.  Size  and  capac- 
ity of. 

2.  No.  of  w agons 
for, 


1.  Railroad. 


2.  Wagon 
roads. 


3.  Traction 
engines. 


OPENING  A MINE. 


257 


Diagram  for  reporting  on  mineral  lands— (Cbwfo’nwed) 
12.  Miscellaneous. 

. Gross. 


13.  Conclu- 
sions. 


1.  Yearly  income,  last  year,  or  for  any  year.  | ^ 

2.  Average  cost  per  lb.,  or  ton  of  material. 

" 1.  Quality  of  ore  or  product. 

2.  Amount  of  ore  or  ( 1.  Gross, 
material  in  sight.  ( 2.  Net. 

, 3.  Value  of  material  in  sight. 
2.  Value  of  plant  and  works. 

' 1.  Continue  present  system. 


3.  Merits  of 
property. 


1.  Deposits 
of  value. 


4.  Advice. 


1.  Mining. 

2.  Disposition 
of  product. 


5.  Local  considerations. 


1 2.  Change  system  to  - 
I 1.  Ship  as  mined. 

I 2.  Concentrate,  or  coke  and 
j ship. 

[ 3.  Smelt  and  ship. 

1.  Troubles. 

2.  Labor. 

3.  Supplies. 

4.  Climate. 

5.  Shipment  facilities. 

^ 6.  Markets. 


OPENING  A MINE. 


The  location  of  the  surface  plant  and  the  mine  opening  depend  on  the 
formation  of  the  deposit  primarily,  and  secondarily  on  the  facilities  for 
transporting  the  product  to  market.  It  is  impossible  for  one  not  on  the 
ground,  and  unfamiliar  with  natural  or  railroad  transportation  facilities  in 
the  neighborhood,  to  give  an  idea  as  regards  the  second  consideration.  In 
regard  to  the  first  consideration,  the  following  observations  will  be  found 
of  value: 

When  the  seam  or  vein  outcrops  within  the  limits  of  the  property  and  is 
flat,  a water-level  drift  is  the  best  method  of  opening  it.  If  it  has  any  con- 
siderable inclination,  it  should  be  opened  by  a slope,  or  by  a tunnel  driven 
across  the  intervening  measures.  Where  the  deposit  has  an  inclination  of 
but  from  of  1°  to  li°,  the  water-level  drift  is  generally  used,  and  the  main- 
haulage  entry  is  opened  at  the  lowest  accessible  point  on  the  outcrop,  which 
insures  free  drainage  and  a favorable  grade  for  haulage.  When  the  outcrop 
dips  into  the  hill,  the  drift  is  usually  commenced  a few  feet  below  the  out- 
crop terrace,  and  driven  on  a slight  upgrade  until  the  normal  dip  is  reached. 

When  the  inward  dip  is  too  strong,  the  better  plan  is  to  sink  a shaft  in  the 
center  of  the  basin,  provided  the  depth  is  not  too  great  and  the  amount  of 
water  to  be  pumped  is  comparatively  small.  If  the  inward  dip  to  the  center 
of  the  basin  does  not  exceed  a total  of  25  ft.  difference  in  level,  a drift  may 
be  used  and  drainage  be  effected  by  a siphon. 

Water-level  drifts  are  only  profitable  where  the  inclined  seam  is  exposed 
in  ravines  or  gorges  eroded  across  the  strike  of  the  measure,  or  where  the 
vein  can  be  reached  by  a short  tunnel  from  the  surface  to  the  seam  across 
the  measures.  This  is  often  the  case  when  the  seam  dips  with  the  hill,  but 
when  the  dip  is  against  the  hill,  the  tunnel  is  generally  a long  one.  While 
the  expense  of  operating  a mine  opened  by  a long  tunnel  is  less  than  one 
opened  by  a slope  or  shaft,  owing  to  cheaper  drainage  and  haulage,  when 
the  coal  above  water  level  is  exhausted  the  tunnel  is  almost  worthless. 
When  the  seam  is  inclined  and  is  accessible  at  no  point  along  its  outcrop 
low  enough  to  furnish  sufficient  lift  or  breast  length,  it  should  be  opened 
by  a slope  or  shaft.  Or,  if  the  seam  is  flat  and  does  not  crop  on  the  tract, 
a shaft  is  the  only  method  of  working  it,  unless  it  lies  so  near  the  surface 
that  it  can  be  stripped. 

Where  a seam  has  a dip  of  20°  or  more,  and  is  brought  close  to  the  surface 
by  an  anticlinal  axis  or  “saddle,”  a “rock  slope,”  or,  in  other  words,  a 
tunnel  dipping  the  same  as  the  seam  may  be  started  from  the  surface,  and, 
when  the  seam  is  reached,  may  be  continued  to  the  desired  depth  in  the 


258 


OPENING  A MINE. 


seam.  In  sinking  slopes  for  coal  mines,  it  is  customary  to  sink  an  airway 
alongside  of  and  parallel  with  the  slope,  with  a pillar  of  about  10  yd.  between. 
The  slope  for  coal  mines  is  usually  sunk  so  that  there  is  a “lift”  of  from 
100  to  lie  yd.,  and  then  gangways  are  turned  off  on  each  side.  The  term 
“ lift  ” in  siiis  connection  means  the  length  on  pitch  that  breasts  or  rooms, 
driven  at  right  angles  to  the  gangway,  can  be  driven  in  good  coal.  Subse- 
quent hfts  are  usually  from  80  to  100  yd.  long. 

. Op  3ning  Up  a Gold  Mine.— The  following  description  of  the  method  of  open- 
ing up  a gold  mine,  by  Mr.  S.  A.  Joseph!  (“  Mines  and  Minerals,”  February, 
1900),  will  also  apply  in  general  for  the  opening  of  any  inclined  narrow  ore 
deposit:  The  equipment  for  the  top  of  shaft  for  the  preliminary  work  con- 
sists of  three  pieces  of  timber,  either  sawed  or  rough  hewn,  12  to  16  ft.  long, 
8 to  10  in.  in  diameter,  arranged  as  a tripod;  they  should  be  strongly  bolted 
together,  a pulley  hung  from  the  center,  through  this  a rope  passed  with  a 
bucket  fastened  to  the  end  entering  the  shaft,  and  a horse  hitched  to  the 
other  end.  This  equipment  is  called  a whip,  and  is  sufficient  for  the  first 
100  ft.  in  depth.  In  locating  the  shaft,  care  should  be  exercised  in  placing 
it  where  there  is  ample  dump,  or  ground  for  waste  or  valueless  vein  matter. 
Should  the  character  of  the  surface  not  admit  of  sufficient  ground  for  this 
purpose,  have  collar  (or  top)  of  shaft  elevated  10  or  12  ft.,  and  throw  waste 
around  the  outside  of  same  until  filled  up  solid. 

The  timbers  should  be  square  sets,  made  of  rough  or  square  timbers, 
preferably  the  latter,  8 in.  X 8 in.;  divide  the  shaft  into  two  compartments 
4 ft.  X 4 ft.  each,  one  for  the  bucketway,  the  other  for  the  ladderway.  Where 
air  is  bad,  board  up  the  ladderway  to*  aid  the  circulation.  The  sets  should 
be  not  less  than  4 ft.  and  not  over  6 ft.  apart,  in  the  clear. 

Sink  on  the  dip  of  the  vein,  and  keep  a careful  record  of  the  location, 
width,  and  value  of  ore  body,  until  the  depth  of  100  ft.  is  attained;  here 
place  station  sets  8 ft.  high,  start  levels  each  side  of  shaft,  and,  if  there  is 
water  in  the  shaft,  a sump  16  ft.  to  30  ft.  deep  should  be  sunk.  The  sump 
should  be  built  in  the  same  manner  as  the  shaft,  so  that  it  will  serve  as  a 
continuation  of  same  when  greater  depth  is  wanted. 

Levels  should  be  run  on  both  sides  of  the  shaft  sufficiently  long  to  deter- 
mine length  of  the  ore  chute,  and  also  to  determine  the  existence  of  other 
ore  chutes  in  the  vein.  This  development  work  should  be  an  indicator  of 
the  strength,  value,  and  permanence  of  the  property;  it  is  now  ready  for 
another  examination  by  competent  authorities,  to  determine  the  above 
conditions.  Should  their  verdict  be  favorable,  continue  the  shaft  to  the 
depth  of  an  additional  100  ft.;  if  water  is  found  in  but  small  quantities,  this 
can  best  be  done  by  replacing  the  whip  with  a whim;  this  runs  by  the  same 
horsepower,  costing  in  the  neighborhood  of  8100.  It  is  well  adapted  to  put 
the  shaft  down  250  ft. 

When  the  shaft  is  down  200  ft.,  start  levels  as  at  the  100-ft.  depth,  provide 
sump,  and  drift  both  ways  upon  the  vein,  proving  up  ore  bodies  as  before. 

Thus  far  the  cost  has  been  slight.  The  shaft,  including  timbers,  supplies, 
and  contingent  expenses,  should  not  cost  over  820  a foot,  a total  of  84.000;  the 
drifts  86  a foot,  say  200  ft.  each  way  from  shaft  on  both  levels,  a total  of 
800  ft.  or  84,800;  total,  88,800,  less  amount  received  from  mineral  extracted  in 
sinking  and  drifting,  which  is  usually  small. 

Now  it  is  to  be  decided  what  further  amount  the  owners  are  willing  to 
expend,  and  how  extensively  they  desire  the  mine  opened  up  before  the 
actual  extraction  of  ore  is  to  commence.  We  will  put  the  depth  of  shaft  at 
500  ft.,  the  drifts  the  full  length  of  the  claim,  usually  1,500  ft. 

For  this  purpose,  a shaft  house  should  be  built,  say  40  ft.  X 60  ft.,  with  ore 
house,  say,  40  ft.  X 40  ft.  The  equipment  should  be  a 40  H.  P.  engine  and  a 60 
H.  P.  boiler  (if  a large  flow  of  water  is  encountered,  an  additional  boiler  and 
pump  must  be  provided),  the  shaft  continued  to  the  above  stated  depth,  and 
levels  extended  at  each  100  ft.  It  will  also  be  advisable  to  make  upraises  at 
the  farthest  point  practical  from  the.  shaft,  on  each  side,  connecting  each 
level  with  the  other,  and  extending  to  the  surface.  These  upraises  should 
be  made  in  ore.  and  are  valuable  both  for  ventilation  and  escape  for  men, 
in  case  of  accident  to  or  near  the  shaft.  They  should  be  furnished  with 
ladders.  The  machinery,  shaft  house,  and  skip,  with  which  all  incline  shafts 
should  be  equipped,  will  cost  about  84,500.  The  additional  300  ft.  of  shaft, 
including  contingent  expenses  of  engineers,  fuel,  etc.  will  cost  840  a foot,  or 
812,000;  the  drifts,  86  a foot.  The  upraises,  being  on  ore,  should  pay  for  the 
labor. 

It  is  prudent  to  estimate  the  cost  of  thoroughly  opening  up  a gold  mine  to 


SHAFTS, 


259 


be  between  S40,000  and  850,000,  which  fact  probably  originated  the  remark 
that  “it  takes  a gold  mine  to  make  a gold  mine.”  This  is  practically  true, 
and  no  one  should  attempt  to  engage  in  the  mining  business,  as  a business, 
without  both  money  and  a willingness  to  use  it.  More  failures  can  be 
attributed  to  insufficient  capital  for  development  than  to  any  cause  save 
mismanagement.  


SHAFTS. 

Shafts  and  tunnels  may  be,  first,  temporary,  or  those  that  are  simply 
driven  for  exploration  purposes,  and  are  not  to  be  used  for  any  great  length 
of  time;  second,  permanent,  or  those  that  are  driven  for  a specific  purpose 
and  usually  have  a definite  predetermined  capacity. 

Form  of  Shaft.— In  the  United  States,  shafts  are  usually  square  or  rectangu- 
lar in  form.  This  is  largely  due  to  the  fact  that  timber  is  used  in  lining 
such  shafts.  In  Europe,  round  or  oval  shafts  are  frequently  employed  with 
a lining  of  brick,  iron,  or  masonry. 

Compartments.— The  number  of  compartments  in  a shaft  and  their  arrange- 
ment depends  largely  on  the  use  to  which  the  shaft  is  to  be  put;  also  on  the 
number  of  shafts  at  the  property,  and  the  depth  of  the  shaft.  Where  the 
material  to  be  removed  is  comparatively  near  the  surface,  it  is  usually 
cheaper  to  sink  a number  of  2-  or  3-compartment  shafts  than  it  is  to  tram  all 
the  ore  to  one  large  shaft;  while,  in  the  case  of  very  deep  mines,  large  4-  or 
6-compartment  shafts  are  sunk,  and  the  underground  haulage  extends  over 
a greater  area.  When  the  shafts  are  lined  with  timber,  a stronger  con- 
struction can  be  obtained  by  placing  the  compartments  side  by  side,  as 
shown  in  Fig.  1,  than  by  placing  them  in  the  solid  block,  as  shown  in  Fig.  2. 
When  a body  of  material  compara- 
tively near  the  surface  is  being  re- 
moved through  a number  of  shafts, 

2-compartment  shafts  are  frequently 
employed,  both  compartments  being 
used  for  hoisting,  and  separate 
shafts  being  provided  for  the  pump 
column  and  ladderways.  This  re- 
duces both  the  size  of  the  shaft  and 
the  timbering  necessary,  and  also 


Fig.  1. 


Fig.  2. 


does  away  with  the  special  danger  from  fire  that  always  exists  when  there 
is  a ladderway  in  the  shaft,  for  it  is  always  difficult  to  fight  fire  in  these 
special  compartments. 

Shaft  Sinking. — As  a general  thing,  the  loose  material  or  wash  above  bed 
rock  is  not  thick  enough  to  cause  any  serious  trouble,  and  ordinary  cribbing 
of  heavy  timber  or  a masonry  curbing  is  sufficient.  But  when  the  surface  is 
very  thick  or  loose,  and  runs  like  quicksand,  considerable  difficulty  is 
experienced.  The  general  method  of  overcoming  this  difficulty  in  the  past 
was  to  at  once  divide  the  shaft  into  the  required  number  of  compartments 
by  heavy  timbers  alternating  or  placed  “skin  to  skin,”  which  had  the  effect 
of-bracing  the  cribbing  against  the  lateral  pressure  of  the  loose  material. 
This  method  is  effectual  where  the  wash  will  remain  solid  or  stand  long 
enough  to  allow  the  timbering  and  cribbing  to  be  put  in.  But  when  the 
surface  is  thick,  loose,  or  watery,  or  of  quicksand,  some  one  of  the  following 
special  methods  of  sinking  must  be  adopted: 

“ Forepoling.” 

“Metal  linings.”  (Forced 
down  without  the  use  of 
compressed  air.) 
“Pneumatic”method.  (Limited 
to  about  100  ft.  in  depth. ) 

^ “ Poetsch  ” process.  (Freezing 
j method. ) 

Rock  (hard  or  soft,  but  very  wet)  | “ Kind-Chaudron  ” method. 

Rock  (hard  or  soft,  but  not  very  wet)  — I * Continuous, ”or “Long-Hole,” 

’ ( method. 

Size  of  Shafts. — Shafts  vary  greatly  in  size,  depending  on  the  number 
of^  compartments  desired  and  the  size  of  the  compartments.  For  coal 
mines,  they  are  generally  from  10  to  12  ft.  wide  inside  of  timbers,  and  each 


Quicksand  . 


260 


OPENING  A MINE. 


compartment  is  from  6 to  7 ft.  wide  inside  the  guides.  This  would  make  the 
outside  dimensions  of  a double-compartment  shaft  about  13  to  15  ft.  wide,  17 
to  18  ft.  long,  and  a triple-compartment  shaft  from  24  to  25  ft.  long.  Shafts  at 
metal  mines  are  generally  smaller  than  those  at  coal  mines,  but  the  prac- 
tice in  different  localities  varies  so  that  it  is  impossible  to  give  general 
dimensions  that  would  be  of  value. 

The  table  on  opposite  page  gives  the  dimensions  of  a few  well-known 
shafts  in  different  localities. 

Fore  poling.— When  the  ground  is  so  bad  that  it  will  not  stand  for  several 
days  between  excavation  and  the  completion  of  the  lining,  it  becomes 
necessary  to  carry  the  timber  to  the  bottom  of  the  work.  This  may  be 
accomplished  by  using  square-set  shaft  timbering  and  driving  laths,  or 
forepoling  behind  the  timber  so  as  to  keep  the  soft  material  from  running 
into  the  opening.  The  advantages  of  forepoling  are  that,  if  the  shaft  is 
being  lined  with  square  sets,  it  can  be  commenced  at  any  point,  and,  if  the 
ground  is  not  too  bad,  the  work  can  be  continued  by  this  means  until  solid 
material  is  encountered.  When  the  ground  is  particularly  bad,  it  may 
become  necessary  to  use  breast  boards,  which  are  simply  boards  braced 
against  the  bottom  of  the  shaft  so  as  to  keep  the  material  from  rising  into 
the  opening,  only  one  board  at  a time  being  removed  while  the  material 
behind  it  is  excavated. 

In  particularly  bad  ground,  where  breast  boards  have  to  be  used,  the 
progress  made  is  very  slow.  After  the  shaft  has  been  put  down  by  fore- 
poling, it  is  sometimes  very  difficult  to  repair  or  replace  the  lining.  When 
the  forepoling  method  is  employed  in  quicksand,  there  is  considerable  risk 
of  losing  the  shaft  altogether,  owing  to  sudden  rushes  or  “boils”  of  the 
material  that  throw  the  timbering  out  of  line  and  fill  up  the  shaft. 

Metal  Linings  Forced  Down.— Metal  linings  forced  down  without  the  use  of 
compressed  air  are  rarely  resorted  to,  though  in  some  cases  they  have  been 
quite  successful.  If  the  formation  contains  but  few  boulders,  it  is  some- 
times possible  to  force  the  lining  down 
by  flushing  out  the  material  from  the  in- 
side with  jets  of  water.  At  other  times, 
men  enter  the  shaft  and  excavate  the  ma- 
terial as  the  work  progresses. 

The  pneumatic  method  of  shaft  sinking  was 
developed  from  the  system  in  use  for  put- 
ting down  foundations  for  bridge  piers. 
At  the  bottom  of  the  shaft  there  is  a small 
chamber  called  a caisson,  in  which  a suffi- 
cient air  pressure  is  maintained  to  exclude 
the  water  at  all  times.  The  shaft  lining 
is  built  on  above  this  chamber,  and  grad- 
ually forced  down  into  the  soil.  Men 
enter  the  chamber  and  excavate  the  mate- 
rial from  under  the  caisson  as  it  descends. 

By  this  method  the  sinking  commences 
at  once  and  is  continued  without  interrup- 
tion until  the  lining  is  completed  to  bed 
rock,  to  which  the  lining  is  joined,  as 
shown  in  Fig.  3.  An  air  compressor,  which 
is  subsequently  used,  is  the  only  auxiliary 
machine  necessary,  while  in  the  freezing 
process  an  ice  machine  is  required. 

It  is  best  to  use  electric  lights  in  the 
caisson;  hence,  it  may  be  necessary  to 
install  a small  dynamo  if  the  company 
does  not  have  an  electric-light  system 
in  operation.  In  the  pneumatic  system,  the  bottom  of  the  shaft  is  always 
exposed  to  view,  and  the  workmen*  know  when  they  reach  a solid  founda- 
tion; while,  in  the  freezing  process,  it  is  sometimes  difficult  to  tell  to  what 
depths  the  pipes  should  be  sunk  so  as  to  reach  below  any  fissures  or  seams  in 
the  bed  rock.  In  the  pneumatic  process,  the  fine  material  is  aspirated  out 
of  the  caisson  by  the  air  pressure.  The  pneumatic  process  is  limited  to  a 
depth  of  about  100  ft.,  as  it  is  impossible  for  men  to  work  under  a greater  air 
pressure  than  that  which  corresponds  to  about  100  ft.  of  hydrostatic  pressure. 

By  the  freezing  process,  pipes  are  sunk  in  the  ground  about  the  area  to  be 
frozen,  as  a rule,  not  more  than  3 or  4 ft.  apart.  The  lower  ends  of  the  pipes 


Fig.  3. 


OP  Well-Known  Shafts. 


SHAFT  SINKING, 


261 


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Si 


Depth. 

Feet. 

1,039 

326* 

578 

282 

50  to  550 

1,610 

1..500 

4,900 

4,615 

1,460 

1,400 

2,500 

1,400 

940 

980 

Size  of  Shaft 
Over  All. 

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Size  of 
Hoisting 
Compart- 
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Material 

Mined. 

Anthracite 

Anthracite 

Anthracite 

Bituminous 
Bituminous 
Gold,  Silver, 
Copper,  Lead 
Silver 
Copper 
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Iron 

Iron 

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# Depth  completed,  1,150  ft.  tin  the  clear. 


262 


OPENING  A MINE. 


are  sealed  or  closed,  and  an  inner  tube  introduced  so  that  a freezing  mixture 
may  be  caused  to  circulate  down  through  the  inner  tube,  and  up  through 
the  outer  tube.  This  freezing  mixture  may  be  either  liquid  ammonia  gas, 
which  is  allowed  to  expand  in  the  outer  tube,  or  it  may  be  a solution  of 
calcium  chloride  that  has  previously  been  reduced  to  a very  low  tempera- 
ture by  means  of  an  ordinary  refrigerating  machine.  The  circulation  is 
maintained  in  the  pipes  until  the  ground  between  them  is  frozen  solid,  after 
which  the  work  may  be  continued  as  though  the  formation  were  solid  rock, 
the  material  being  blasted  and  hoisted  in  buckets.  The  freezing  process 
may  be  applied  to  any  wet  formation,  whether  hard  or  soft,  while  the 
pneumatic  process  is  applicable  only  to  soft  formations.  The  freezing 
process  may  be  carried  to  practically  any  depth.  As  a rule,  the  freezing  pipes 
are  never  sunk  inside  of  the  shaft  area. 

The  Kind-Chaudron  method  is  applicable  only  to  round  shafts,  and  is 
suitable  for  shafts  passing  through  very  wet  and  at  the  same  time  com- 
paratively soft  formations.  The  excavation  is  carried  on  by  means  of  a 
large  set  of  boring  tools  armed  with  steel  teeth,  and  operated  in  a manner 
similar  to  that  employed  in  drilling  wells  by  the  percussive  system.  First, 
a pit  or  shaft  4 or  5 ft.  in  diameter  is  drilled;  this  is  followed  by  a reaming  bit 
that  enlarges  the  hole  to  the  desired  diameter,  or  the  work  may  be  accom- 
plished in  three  stages  by  using  two  reaming  bits.  The  material  removed  by 
the  first  bit  is  hoisted  out  by  means  of  a sand  bucket,  or  sludger,  while  that 
removed  by  the  succeeding  tools  is  hoisted  out  by  buckets  that  are  placed 
in  the  bottom  of  the  first  pit  and  kept  there  while  the  tools  are  in  operation. 
No  water  is  pumped  from  the  shaft  while  it  is  being  excavated  or  lined, 
and  hence  practically  all  the  tendency  that  the  sides  would  have  to  cave 
is  removed.  After  the  shaft  has  been  excavated  down  to  and  into  a solid 
formation,  it  is  lined  by  lowering  cast-iron  tubbing  into  the  hole  and  making 
a tight  joint  against  the  bottom  by  means  of  an  expansive  packing  that  is 
forced  out  by  the  weight  of  the  tubbing,  or  lining.  After  the  lining  is  in 
place,  the  space  between  it  and  the  sides  of  the  excavation  is  filled  with 
cement.  When  the  cement  is  thoroughly  hardened,  the  water  is  pumped 
from  the  inside  of  the  lining,  and  men  descend  and  examine  the  joint  at 
bed  rock.  In  this  method,  no  workmen  enter  the  shaft  until  it  is  lined 
through  the  troublesome  formation. 

Long-Hile  Process. — The  long-hole  process  consists  in  the  drilling  of  a 
series  of  diamond-drill  holes  over  the  area  of  the  proposed  shaft,  then  filling 
the  holes  with  sand,  after  which  the  work  progresses  by  removing  the  first 
5 or  6 ft.  of  sand  from  the  holes  in  the  interior  of  the  shaft,  charging  these 
holes  with  explosives,  and  firing  them  by  electricity.  Next,  the  holes 
around  the  boundary  of  the  shaft  are  charged  and  fired  in  the  same  manner, 
and  the  process  is  continued  until  the  bottoms  of  the  diamond-drill  holes  are 
reached.  This  method  is  especially  applicable  to  work  in  hard  rock,  where 
great  speed  in  sinking  is  desired,  for  all  the  drilling  is  accomplished  at  one 
operation,  after  which  the  sinking  progresses  by  simply  cleaning  out  the 
drill  hole  and  blasting  the  material. 

General  Comparison  of  Methods  of  Shaft  Sinking.— Where  a shaft  is  sunk  by 
forepoling,  it  is  usually  made  rectangular  in  form.  The  pneumatic  method 
may  be  used  for  either  round  or  rectangular  shafts,  and  the  lining  may  be 
either  of  metal  or  wood.  The  freezing  process  may  be  used  for  either  round 
or  rectangular  shafts,  and  the  lining  may  be  either  timber,  metal,  or  masonry, 
as  the  entire  opening  can  be  left  open  until  the  solid  rock  is  reached,  when 
the  lining  can  be  built  upon  it.  The  Kind-Chaudron  method  is  applicable 
only  to  round  shafts,  on  account  of  the  fact  that  the  hole  is  bored.  The 
long-hole  process  is  applicable  to  either  round  or  rectangular  shafts,  but  was 
originally  introduced  for  sinking  rectangular  shafts. 

Sinking  Head-Frames.— Head-frames  of  very  simple  form  are  used  for  sink- 
ing, The  skeleton  of  the  frame  is  formed  of  heavy  squared  timber  (10"  X 10" 
or  12"  X 12")  mortised  and  pinned  together,  and  braced  by  diagonal  braces. 
A good  height  from  the  surface  to  the  center  of  the  sheave  is  from  20  to  25  ft. 
The  sheave  should  be  from  6 to  8 ft.  in  diameter.  The  sinking  bucket  should 
be  of  boiler  iron,  or  of  heavy  hard  wood  strengthened  by  iron  bands,  about 
3 ft.  in  diameter  at  the  top  by  from  to  3 ft.  deep.  It  should  be  suspended 
by  a handle  pivoted  a trifle  below  the  center,  and  it  should  have  a pin  on 
the  rim  of  the  bucket  that  will  hold  it  in  an  upright  position  when  a loose 
ring  on  the  handle  is  slipped  over  it.  A chain  fastened  to  the  top  of  the 
head-frame,  with  a hook  on  its  loose  end,  is  suspended  so  that,  when  hang- 
ing plumb,  it  is  over  a chute  leading  to  the  dump  car.  As  the  bucket  la 


SHAFT  SINKING, 


263 


hoisted  out  of  the  shaft,  this  chain  is  attached,  and  the  engine  reversed. 
The  bucket  swings  over  the  chute,  the  ring  holding  it  upright  is  knocked  off 
the  pin,  and  the  rock  is  dropped  into  the  chute.  Rocks  too  large  for  the 
bucket  are  suspended  in  chains  and  are  hoisted  in  that  way,  and  removed 
on  a truck  that  runs  on  a track  inside  of  the  head-frame,  the  gauge  of 
which  is  sufficiently  wide  to  give  plenty  of  clearance  for  the  bucket. 

Sinking  Engines.— Most  shafts  and  slopes  are  sunk  with  old  engines,  or 
else  by  engines  especially  designed  for  such  work,  and  so  constructed  that 
they  can  easily  be  moved  from  place  to  place.  In  some  cases  where  an  old 
engine  can  be  readily  had,  it  is  set  up  on  temporary  timber  foundations  and 
used  until  the  shaft  or  slope  is  finished,  when  it  is  replaced  by  the  perma- 
nent engines,  and  the  old  one  is  dismantled  and  disposed  of  to  the  best 
advantage. 

Tools. — The  old  method  of  hand  drilling  is  still  adhered  to  in  many 
instances,  but  it  is  gradually  giving  way  to  machine  drilling,  especially  in 
deep  shafts.  When  properly  managed,  the  work  is  done  much  more  rapidly 
and  economically  by  the  several  excellent  types  of  rock  drills  now  on  the 
market.  They  are  constructed  in  a variety  of  shapes  by  the  makers,  and 
there  are  so  many  convenient  accessories  in  the  shape  of  fittings,  etc.  that 
all  contractors  prominent  in  the  various  coal  fields  possess  one  or  more  of 
their  favorite  type  of  drills.  These  drills  are  run  either  by  compressed  air, 
steam,  or  electric  power,  and  in  large  shafts  two  are  usually  employed,  so 
that  work  may  not  be  delayed  by  a breakdown  of  one  drill.  The  center  or 
one  side  of  the  shaft  is  usually  kept  in  advance  of  the  rest,  so  as  to  furnish 
a sump  for  the  collection  of  the  water.  The  holes  are  drilled  from  3 to  6 ft. 
apart,  and  the  depth  varies  with  the  character  of  the  rock.  When  a suf- 
ficient number  of  holes  are  drilled,  the  drill  is  removed,  and  a cartridge 
made  of  dynamite,  dualine,  or  some  other  form  of  high  explosive  is  tamped 
in  each  hole.  These  are  all  fired  simultaneously  by  an  electric  battery, 
detonating  caps  being  placed  in  each  charge. 

To  keep  the  shaft  the  required  shape,  if  rectangular,  a plumb-bob  is  sus- 
pended in  each  corner,  either  from  the  fiooring  on  top,  or  from  a beam  laid 
across  the  cribbing,  and  these  guide  the  miner  in  squaring  the  corners  and 
sides.  If  the  shaft  is  a circular  one,  a plumb-line  is  let  down  in  the  center, 
from  time  to  time,  and  a rod  cut  the  exact  radius  is  revolved  around  it.  If 
it  strikes  the  rib,  the  miner  knows  that  at  that  point  the  shaft  is  not  true. 

Drainage  and  Ventilation. — When  only  a small  amount  of  water  is  encoun- 
tered while  sinking,  the  best  plan  is  to  allow  it  to  collect  in  a depression  and 
bail  it  from  there  into  the  bucket,  hoisting  it  the  same  as  the  rock.  Where 
the  water  is  excessive  in  quantity,  a steam  pump  is  necessary.  All  the 
leading  pump  works  make  pumps  especially  designed  for  sinking  purposes, 
and  it  is  not  in  the  province  of  this  work  to  mention  the  advantages  pos- 
sessed by  one  over  the  other. 

When  the  shaft  is  of  moderate  depth,  a fire  burning  in  one  corner  will 
supply  ample  ventilation.  To  rapidly  clear  away  smoke,  a good  plan  is  to 
burn  a bundle  of  straw  or  shavings  in  one  end  of  the  shaft,  and  throw  a 
couple  of  buckets  of  water  down  the  other  end.  When  the  shaft  is  very 
deep,  or  when  the  sectional  area  is  small,  ventilation  is  produced  either  by  a 
steam  jet,  or  by  a small  fan  turned  either  by  steam  or  by  hand.  In  some 
cases,  a fire  is  used  that  draws  into  a board  pipe. 

Speed  and  Cost  of  Sinking.— Any  attempt  at  a general  estimate  regarding 
the  speed  and  cost  of  sinking  is  impossible,  for  many  reasons  appreciated  by 
the  practical  miner.  Shafts  vary  so  much  in  size,  and  in  the  character  of  the 
material  through  which  they  pass,  that  even  if  there  were  no  other  items  to 
be  considered,  a general  estimate  could  not  be  made.  But  if  the  ground  is 
pretty  well  known,  and  the  sectional  area  and  the  dei)th  given,  the  experi- 
enced contractor  knows  how  much  he  can  drive  in  a given  time,  and 
he  can  consequently  form  a good  estimate  for  each  separate  shaft.  The 
range  of  cost  is  so  great  that  it  may  be  anywhere  from  to  ^10  per  cubic 
yard  of  material  excavated. 

Slope  Sinking.— A slope  is  an  inclined  plane  driven  down  on  the  bed  of  the 
seam,  and  is  generally  through  coal  or  ore,  though  sometimes  they  are 
driven  through  rock  across  measures  to  cut  the  seam  that  cannot  be  conve- 
niently worked  by  a slope.  In  the  latter  case,  it  is  merely  an  “inclined 
tunnel.”  In  the  former  it  might  be  termed  an  “inclined  gangway.” 

A slope  and  an  inclined  plane,  when  mentioned  hereafter,  will  mean  an 
inclined  opening  in  coal  or  ore,  used  as  a passageway  for  mine  cars. 

When  the  location  of  the  slope  has  been  decided  on,  erect  a temporary 


264 


OPENING  A MINE. 


sinking  plant;  an  old  engine  is  generally  used.  For  a short  distance, varying 
with  the  nature  of  the  ground,  but  usually  ranging  from  10  to  20  ft.  on  the 
pitch,  an  open  cut  is  made,  and  the  earth,  rock,  or  crop  coal  is  thrown  out 
by  hand.  As  soon  as  sufficient  cover  is  reached,  the  work  of  undermining 
and  timbering  is  commenced,  and  at  the  same  time  a double  or  single  track 
is  laid,  so  that  the  material  can  be  taken  out  in  a car  or  self-dumping  skip. 
When  the  latter  is  used,  the  track  is  continued  up  a trestle  some  distance 
above  the  surface,  and  a head-sheave  so  placed  as  to  draw  the  skip  up  the 
required  distance  and  dump  the  material  in  a chute  beneath  the  trestling. 

The  width  of  the  slope  depends  on  the  size  of  the  cars  and  the  number  of 
compartments.  The  most  common  arrangement  is  to  divide  the  slope  into 
three  compartments;  two  large  ones  for  hoistways,  and  a smaller  one  for 
pump  rod,  column  pipe,  steam  pipe,  and  traveling  way.  This  last  is  also 
used  as  an  airway  while  sinking  is  going  on. 

In  some  instances,  slopes  have  but  one  hoistway,  laid  with  three  rails 
and  a turnout  at  the  middle  of  the  hoist,  and  some  have  single  track  with  a 
central  turnout.  This  may  be  economy  in  first  cost,  but  is  not  in  the  long 
run.  Collisions  are  apt  to  occur,  and  the  breaking  of  a rope  or  the  falling  of 
coal  from  an  ascending  car  is  apt  to  cause  more  damage  than  when  two 
compartments  are  used. 

When  several  lifts  are  simultaneously  worked,  a single-track  slope  is 
used;  but  unless  the  pitch  is  light  and  several  cars  can  be  hoisted  at  once, 
this  method  produces  a comparatively  small  output. 

When  the  dip  of  a slope  is  under  40°,  the  height  of  the  slope  should  be 
about  7 ft.  in  the  clear.  When  the  slope  dips  more  than  40°,  unless  self- 
dumping skips  or  gunboats  are  used,  a cage  is  necessary,  and  then  the 
height  must  be  made  greater. 

The  sinking  of  a slope  is  similar  to  gangway  driving,  and  the  tracks  and 
timbering  are  kept  well  up  to  the  face. 

The  timbering  is  very  similar  to  gangway  timbering,  except  that  squared 
timber  is  more  frequently  used  (but  it  is  not  necessary)  and  the  joints  are 
cut  with  more  care.  On  steep  pitches,  a heavy  “ mud  sill  ” is  let  into  the  rib 
on  each  side,  to  prevent  the  road  from  slipping  down  the  pitch. 

The  Sump. — When  the  shaft  or  slope  is  completed,  among  the  first  things 
necessary  is  a sump  in  which  to  collect  the  drainage  of  the  mine.  This  is  an 
opening  lower  in  the  vein,  when  it  is  a pitching  one,  or  in  the  rock  when  it 
is  a flat  seam  reached  by  a shaft.  It  should  be  large  enough  to  hold  any 
excess  of  water  that  the  pumps  cannot  handle;  and  the  pumping  machinery 
should  be  powerful  enough  to  handle  the  ordinary  drainage  by  running  not 
over  10  hours  per  day.  When  this  is  the  case,  in  an  emergency,  the  pumps 
can  be  run  continuously,  and  thus  handle  the  surplus  water. 

Driving  the  Gangway.— In  bituminous  coal  seams,  the  height  of  the  gangway 
is  governed  by  the  thickness  of  the  seam,  and  this  is  also  true,  in  a certain 
sense,  in  the  anthracite  regions.  But  -in  the  anthracite  regions  they  are  very 
seldom  less  than  6 ft.  in  height.  In  the  larger  seams  they  are  from  6 ft.  6 in. 
to  7 ft.  6 in.  high  in  the  clear,  and  from  10  to  15  ft.  wide.  The  gauge  of  track 
varies  from  24  to  48  in.  The  grade  should  rise  at  least  4 in.  in  100  ft.,  and 
a gutter  3 ft.  wide  by  18  in.  deep  should  be  cut  in  the  coal  on  the  low  side. 
This  gutter  should  be  a gutter,  and  not  a receptacle  for  refuse.  There  is  no 
economy  in  a shallow  gutter,  or  in  neglecting  it  because  it  costs  a few  cents 
a day  to  keep  it  open.  Some  authorities  advise  a rise  of  from  6 in.  to  1 ft.  in 
every  100  ft.,  but  they  evidently  do  not  take  into  consideration  that  so  great 
a rise  means  a loss  of  from  26  to  53  ft.  in  lift  at  the  end  of  a gangway  a mile 
long,  or,  in  other  words,  in  the  loss  of  from  68,000  to  137,000  sq.  ft.  of  the  area 
of  coal  to  be  reached  by  the  gangway.  This  applies  to  pitching  seams. 
Where  the  seam  is  flat,  or  nearly  so,  the  gangway  must,  of  course,  be  driven 
on  a grade  that  best  suits  the  formation.  Turnouts  constructed  on  each  side 
of  the  shaft  or  slope,  of  a suitable  length,  are  a necessity,  if  the  slope  or  shaft 
is  to  be  kept  constantly  supplied  with  coal.  These  turnouts  vary  in  length, 
depending  on  the  length  of  the  cars,  and  the  number  necessary  to  keep  the 
machinery  in  motion  between  trips.  They  should  be  wide  enough  to  allow 
at  least  3 ft.  in  the  clear  between  the  bodies  of  the  cars;  5 ft.  is  even  better. 
When  possible  to  avoid  it,  there  should  be  no  center  props  between  the 
tracks. 

Levels  in  Metal  Mines.— The  cross-section  of  the  level  depends  largely  on 
the  character  of  the  ore  mined,  and  the  desired  output  from  the  deposit.  In 
the  case  of  precious  metal  mines,  producing  high-^ade  mineral  from  narrow 
veins,  the  levels  are  driven  as  small  as  possible.  Immediately  adjoining  the 


MINE  TIMBER  AND  TIMBERING. 


265 


shaft  there  is  a plat  or  station  the  full  width  of  the  shaft.  This  is  heavily 
timbered  and  provided  with  a double  track,  but,  as  a rule,  the  levels  have 
but  a single  track,  and  in  some  cases  there  is  but  a single  track  at  the  shaft, 
there  being  a turnout  or  switch  in  the  level  a short  distance  from  the  shaft. 
In  this  class  of  mines,  5 ft.  X ft.  in  the  clear  would  probably  be  the  average 
size  of  a level,  it  being  driven  as  small  as  possible.  In  the  case  of  mines 
producing  lower  grade  material  and  handling  heavy  tonnages  from  large 
deposits,  as,  for  instance,  in  some  of  the  iron  and  copper  mines,  the  levels  are 
driven  larger,  and  in  some  instances  are  double-tracked,  being  from  7 ft.  to 
8 ft.  high  in  the  clear,  and  from  7 ft.  to  12  ft.  wide  inside  timbers;  but,  even  in 
this  class  of  mines,  in  most  cases  single-track  levels  7 ft.  X 7 ft.  to  8 ft.  x 8 ft. 
in  the  clear  are  employed  with  turnouts  or  passing  points  at  intervals,  and 
a double  or  triple  track  at  the  shaft.  The  levels  are  usually  driven  with  a 
slight  grade  away  from  the  shaft,  so  that  they  will  drain  to  the  shaft,  and 
the  grade  will  be  in  favor  of  the  loaded  car.  In  some  mines  where  electric 
tramming  is  employed,  the  levels  are  so  driven  that  the  motor  makes  a 
circuit  through  the  mine,  following  the  foot-wall  in  one  direction,  and 
returning  along  the  hanging  wall,  or  one  of  the  drifts  may  be  in  the 
country  rock.  Such  systems  as  this  are  employed  only  in  large  properties 
handling  a very  great  tonnage.  


TUNNELS. 

Mining  tunnels  are  usually  of  small  cross-section  compared  with  those  that 
occur  in  railroad  work,  it  being  rare  that  their  size  is  such  that  they  cannot 
be  driven  in  full  section,  and  if  the  ground  is  firm  the  operation  of  placing 
the  lining  may  follow  behind  the  work  of  driving.  They  are  generally 
lined  with  timber,  and  in  case  the  ground  is  of  a soft  or  treacherous  nature, 
bridged  square  sets  and  forepoling  are  employed,  with  or  without  breast 
boards,  as  the  necessity  of  the  case  demands.  When  the  material  is  firm 
rock,  the  tunnel  is  sometimes  not  lined,  the  roof  being  given  an  arched 
form.  The  various  forms  of  timbering  employed  as  tunnel  linings  are 
shown  in  the  sections  on  Timbering. 


MINE  TIMBER  AND  TIMBERING. 


Choice  of  Timber. — Timber  used  for  underground  supports  in  mines  should 
be  long-grained  and  elastic,  and,  at  the  same  time,  should  not  be  too  heavy. 
Oak,  beech,  and  similar  woods  are  very  strong,  but  are  heavy  to  handle,  and 
when  set  in  place  are  treacherous,  owing  to  the  fact  that  they  are  short- 
grained and  not  elastic,  so  that,  though  strong,  when  they  do  break,  they 
break  without  warning.  Mine  timber  is  placed,  not  with  the  intention  of 
ultimately  resisting  the  great  pressure  of  the  earth,  but  so  that  it  may  keep 
any  loose  pieces  in  place  and  also  to  give  warning  to  the  workmen,  thus 
enabling  them  to  escape  before  a fall  occurs.  For  this  reason,  pine  and  fir 
are,  as  a rule,  better  for  mine  timbering,  as  they  combine  a fair  amount 
of  strength  with  considerable  elasticity,  and  hence  give  warning  long  before 
they  break.  Very  elastic  timbers,  such  as  cypress,  willow,  etc.,  are,  as  a rule, 
to  be  avoided,  on  account  of  the  fact  that  they  will  simply  bend  like  a bow, 
without  offering  the  necessary  resistance  to  hold  the  material  in  place  for  a 
short  time. 

Preservation  of  Timbers.— The  character  of  the  ventilation  in  a mine  has 
considerable  effect  on  the  life  of  any  timber  supports.  Damp  stagnant  air 
will  cause  mold  and  fungus  growth,  which  will  be  followed  by  the  destruc- 
tion of  the  timber  through  decay  or  dry  rot.  All  timbered  openings  should 
be  well  ventilated,  and  provision  made  for  the  speedy  removal  of  damp  hot 
air,  such  as  commonly  occurs  around  pump  rooms  and  along  steam  lines. 

Water  is  a good  preservative,  as  it  washes  off  the  spores  of  the  fungi  as 
fast  as  they  are  formed,  and  sometimes  shaft  timbers  are  kept  wet  on 
account  of  the  preservative  action  of  the  water. 

Timber  may  be  also  preserved  (1)  by  a solution  of  common  salt  and 
water;  (2)  by  impregnating  the  wood  with  such  metallic  substances  as  sul- 
phates of  copper,  iron,  etc.;  (3)  by  impregnation  with  the  chloride  of  mag- 
nesium or  zinc;  (4)  by  creosoting;  (5)  by  coal  tar;  (6)  by  carbolineum. 

A solution  of  1 lb.  of  salt  in  4 or  5 gal.  of  water  mves  a cheap  and  easily 
applied  preservative  with  which  the  timber  should  be  thoroughly  soaked. 


266 


MINE  TIMBER  AND  TIMBERING. 


Sulphate  of  iron  is  economical  and  eifective.  In  the  zinc  process,  a solution 
of  1 gal.  of  liquid  chloride  of  zinc  (Sp  Gr.  1.5)  mixed  with  35  gal.  of  water 
is  forced  into  the  wood  by  pressure.  Impregnation  with  crude  creosote 
oil  is  eifective,  but  it  has  the  disadvantage  of  making  the  timber  very 
inflammable.  Creosote  acts  in  a threefold  manner:  (1)  It  fills  the  pores 
and  prevents  saturation  by  water;  (2)  it  destroys  organic  life;  (3)  the  car- 
bolic acid  that  it  contains  coagulates  the  albuminoids  and  prevents  decay. 
Painting  with  liquid  tar  is  eifective,  but  makes  the  wood  very  inflammable. 
Painting  with  ordinary  whitewash  is  also  said  to  give  good  results.  Car- 
bolineum  is  said  to  be  eifective,  but  is  quite  expensive.  It  is  applied  with 
a brush,  or  by  steeping  in  a tank;  1 gal.  will  cover  300  to  400  ft.  of  timber. 

Professor  Louis,  of  England,  has  shown  that  preservatives  decrease  the 
strength  of  timber  from  8^  to  20^,  depending  on  the  process  used. 

' The  following  table  gives  the  results  of  tests  made  by  different  methods 
of  treating  wood  at  Saint  Elroy,  France,  and  recorded  in  1890: 

Tests  of  Preservatives  for  Mine  Timber. 


Name  of  Preservative. 

Relative  Preservative  Effect. 

Oak. 

Fir. 

Pine. 

Beech. 

Birch. 

Poplar. 

Tar 

27.8 

263.5 

87.5 

105.4 

26.2 

150.5 

Chloride  of  zinc 

10.5 

50.0 

26.3 

18.6 

52.5 

34.7 

Sulphate  of  copper 

42.1 

12.0 

8.0 

1.8 

2.5 

15.5 

Sulphate  of  iron 

18.0 

12.5 

4.2 

4.7 

3.7 

2.9 

Creosote  

1.7 

2.5 

4.4 

0.6 

3.3 

1.3 

The  simple  removing  of  the  bark,  under  some  circumstances,  seems  to  be 
advantageous,  but,  in  some  woods,  if  the  bark  is  removed,  the  sap  wood 
should  also  be  removed.  In  many  cases,  the  sap  wood  of  coniferous  trees 
is  as  strong  or  stronger  than  the  heart  wood,  and  for  this  reason  it  should 
not  be  removed.  Also,  in  the  case  of  many  coniferous  trees,  the  bark  seems 
to  act  as  a protection  to  the  timber  in  the  underground  workings.  If  it 
becomes  necessary  to  reduce  the  size  of  the  individual  sticks,  it  is  usually 
better  to  split  them  than  to  saw  them,  especially  in  the  case  of  wood  from 
coniferous  trees,  as  this  does  not  destroy  the  sap  wood  or  unduly  injure  the 
grain  or  fibers  of  the  stick.  Generally  speaking,  mine  timbers  last  longer 
when  kept  wet,  and,  on  this  account,  some  of  the  mines  in  Europe  have 
introduced  a system  of  pipes  for  spraying  the  timbers  in  dry  portions  of  the 
mine.  When  timbers  are  alternately  wet  and  dry,  they  are  destroyed  with 
amazing  rapidity.  Timber  should  be  probed  from  time  to  time  to  ascertain 
its  condition,  as  timbers  may  appear  sound  on  the  outside  when  the  heart  is 
completely  destroyed  by  dry  rot.  In  selecting  props,  the  principal  points  to 
be  observed  are:  Straightness,  slowness  of  growth  as  indicated  by  narrow 
annular  rings,  freedom  from  knots,  indents,  resin,  gum,  and  sap.  They 
should  also  be  well  seasoned  before  use.  With  these  precautions  and  proper 
mine  ventilation,  fungus  growth  may  generally  be  obviated  and  durability 
insured. 

Placing  of  Timber.— The  individual  sticks  should  never  be  weakened  by 
cutting  mortise  and  tenon  joints.  The  pressure  should  be  evenly  distributed 
over  a number  of  sticks,  and  not  concentrated  or  centered  at  one  point. 
Centers  of  revolution  should  be  avoided.  The  individual  sticks  should  be 
placed  in  the  direction  of  the  strain  that  they  are  to  resist,  so  that  they  will 
be  subject  to  compression  along  their  length  rather  than  to  a transverse 
strain.  The  individual  sticks  should  be  so  placed,  and  the  joints  so  formed, 
that  the  pressure  tends  to  strengthen  rather  than  weaken  the  structure  up  to 
the  crushing  strength  of  the  timber.  In  the  case  of  large  slopes,  the  timber- 
ing should  be  done  according  to  some  regular  system,  while,  at  the  face  of 
coal  mines,  single  props  or  posts  are  usually  found  better,  owing  to  the  fact 
that  their  duty  is  only  to  support  the  loose  portion  of  the  roof  for  a limited 
time.  Probably  the  most  important  point  is  to  timber  in  time,  before  the 
rock  becomes  broken  or  begins  to  settle. 


MINE  TIMBER  AND  TIMBERING, 


267 


It  seems  generally  agreed  that  the  main  weight  in  mines  comes  nearly  at 
right  angles  to  the  bedding,  and  that  the  props  should  be  mainly  set  in  that 
direction.  If  the  deposit  is  horizontal,  the  weight  generally  comes  vertically; 
but  if  the  deposit  is  inclined,  the  weight  comes  at  a right  angle  to  the  inclina- 
tion. Some  authorities  hold  it  as  a principle  that  all  props  should  be  set  at  a 
rectangle  against  the  main  pressure.  Others,  in  order  to  guard  against 
possible  side  thrusts  and  a tendency  of  the  ordinary  weight  to  ride  to  the  dip 
in  inclined  deposits,  purposely  cause  a sufficient  number  of  props  to  be  set 
slightly  deviating  from  the  common  axis. 

Sawyer  fixes  a maximum  and  minimum  slope  for  the  props,  varying  with 
the  rate  of  dip.  He  makes  this  maximum  slope  of  the  props  one-sixth  that 
of  the  dip,  and  the  minimum  slope  one-third  of  the  one-sixth. 

Props  are  usually  set  with  the  butt  end  downwards,  but  not  always.  Hav- 
ing the  butt  end  upwards  adds  a trifle  to  the  weight  on  the  lower  end,  but 
the  larger  size  at  the  top  should  lessen  the  liability  of  its  being  split  by  a 
coupling  resting  on  it,  and  also  gives  more  surface  for  abrasion  in  hammer- 
ing up  against  a rough  roof.  Both  ways  may  therefore  have  advantages 
according  to  the  circumstances.  The  butt  end  downwards,  with  air  circu- 
lating, is  the  way  Molesworth  recommends  for  stocking. 

Size  of  Timber. — The  general  tendency  at  all  metal  mines  at  present  is 
toward  the  use  of  systematic  frames  composed  of  small  sizes  of  timber,  rather 
than  toward  the  use  of  large  individual  sticks.  The  advantages  are:  (1)  the 
small  timber  is  cheaper  and  easier  to  procure;  (2)  it  is  easier  to  handle,  and 
hence  costs  less  to  place  in  position.  By  making  the  frames  according  to 
some  regular  system,  the  individual  sticks  can  be  framed  on  the  surface  by 
machinery  so  that  better  joints  are  secured.  The  setting  of  timber  can  be 
done  by  less  experienced  help  when  it  is  all  alike. 

Joints  in  Mine  Timbering.— In  all  mine  timbering,  the  object  is  to  so  form 
the  joints  that  no  fastenings  will  be  necessary  and  that  the  shape  of  the 
pieces  will  be  such  that  the  pressure  from  the  surrounding  material  will 
keep  the  joints  tight.  The  reason  for  this  is  that  any  metal  joints  usually 
corrode  rapidly  in  mines,  and  that,  when  it  becomes  necessary  to  replace 
timbering,  this  can  be  done  with  greater  ease  if  the  sticks  are  so  framed 
that,  by  relieving  them  temporarily  of  the  pressure  from  the  sides  and  top, 
they  can  be  simply  lifted  out  of  place  and  new  ones  substituted.  The  use 
of  a framing  machine  renders  it  possible  to  frame  the  joints  more  exactly 
than  with  hand  framing.  With  hand-framed  timbers,  the  joints  are  always 
cut  a little  free  to  allow  for  any  unevenness  in  the  surface,  but,  if  machine- 
framed,  they  are  sure  to  be  of  the  same  size.  As  timber  does  not  shrink  in 
the  direction  of  its  grain,  it  is  evident  that  where  the  posts  meet,  if  the 
caps  shrink  slightly,  they  will  become  loose  in  the  space  between  the  shoul- 
ders; hence,  if  timbers  are  cut  green  and  framed  to  the  exact  size,  subse- 
quent shrinking  may  open  some  of  the  joints.  This  may  be  obviated  by 
keeping  the  timber  moist. 

The  method  of  taking  timbers  into  a mine  depends  on  the  size  and 
number  of  timbers  used  and  on  the  character  of  the  opening  into  the  mine. 
In  drift  or  tunnel  mines,  timbers  are  sent  in  on  flat  cars  built  especially  for 
the  purpose,  or  in  the  regular  mine  cars.  In  vertical  shafts,  they  are  usually 
stood  on  end  on  the  floor  of  the  cage,  and  lashed  together  and  also  to  the 
supports  of  the  cage.  Where  the  opening  is  an  incline,  it  is  the  common 
practice  to  load  the  timbers  into  a skip  and  thus  lower  them  into  the  mine. 
Timber  should,  wherever  possible,  be  framed  on  the  surface. 

Undersetting  of  Props. — Props  at  the  working  face  should  not  be  set  at 
right  angles  to  the  inclined  floor  of  the  seam,  but  should  be  underset,  and 
the  greater  the  inclination,  the  greater  the  underset.  The  amount  of  under- 
set should  vary  with  the  inclination  of  the  seam,  and  should  not  be  so 
great  that  the  props  will  fall  out  before  the  roof  has  tightened  them. 

Forms  of  Mine  Timbering  and  Underground  Supports.— The  timbering  of  a mine 
may  be  divided  into  two  heads:  (1)  timbering  the  working  faces;  (2)  tim- 
bering the  roads. 

The  roof  may  be  supported  (a)  by  packing  the  waste  places  entirely 
where  sufficient  material  is  obtainable  for  the  purpose,  and  timbering  the 
faces  and  roads;  (6)  by  partially  packing  the  waste,  by  buildings  or  stone 
pillars  with  intervening  spaces,  and  by  timbering  the  face  and  roads;  (c) 
by  timbering  the  face  and  roads  and  supporting  the  roof  in  the  waste  places 
])y  wooden  or  stone  pillars,  but  without  any  packing;  (d)  by  timbering  alone 
without  any  packs  or  walls  whatever;  (e)  by  supporting  the  main  roads 
with  brick  arching,  or  by  steel  or  iron  supports. 


268 


MINE  TIMBER  AND  TIMBERING, 


The  accompanying  plates  include  all  the  common  forms  of  mine  timber- 
ing and  underground  supports. 

Fig.  1 shows  a post  a and  breast  cap  h.  The  breast  cap  h is  also  sometimes 
called  cap,  head-block,  headboard,  lid,  or  bonnet.  Sometimes  the  posts  are 
placed  upon  blocks  of  wood  similar  to  the  head-blocks  or  headboards,  the 
block  being  called  a sole;  at  other  times,  two  or  more  posts  may  be  set  upon 
one  long  block  of  timber  called  a sill.  When  posts  are  used,  in  inclines, 
they  should  not  be  set  perpendicular  to  the  foot  and  hanging  walls,  but 
should  be  underset  slightly,  so  that  any  tendency  of  the  hanging  wall  to 
settle  will  bring  the  posts  nearer  at  right  angles  to  the  walls,  and  so  tighten 
them;  the  amount  of  underset  should  never  be  more  than  one-sixth  the 
pitch  of  the  deposit.  Where  posts  are  set  at  an  angle,  they  are  usually 
placed  on  wedges,  and,  as  the  pressure  comes  on,  the  wedges  are  tightened. 

Fig.  2 represents  a stull  a,  which  is  used  either  to  keep  the  walls  of 
perpendicular  or  steeply  inclined  beds  or  veins  apart,  to  support  planking 
or  lagging  as  a working  platform,  or  as  a platform  upon  which  to  pile 
ore  or  rock. 

Fig.  3 represents  cockermegs,  which  are  simply  timber  frames  employed 
in  coal  mines  for  holding  the  face  of  the  coal  in  place  while  it  is  being 
undercut.  They  are  composed  of  a pole  c extending  along  the  face  and 
supported  by  short  stulls  or  braces  a,  the  whole  being  tightened  into  place 
by  the  long  stulls  b. 

Fig.  4 shows  a crib,  cog,  chock,  pillar,  or  shanty  built  up  of  timbers  and 
filled  with  waste  rock.  It  is  intended  to  serve  as  a pillar  and  to  withstand 
great  vertical  pressure,  doing  away  sometimes  with  the  necessity  of  leaving 
pillars  of  ore. 

Fig.  7 is  a cribbing  framed  from  round  timbers  laid  skin  to  skin,  and  used 
in  raises  or  ore  chutes. 

Gangway  or  Level  Timbers.— Fig.  5 is  a set  employed  in  the  case  of  an  extra- 
wide  gangway,  there  being  a center  post  under  the  middle  of  the  cap.  This 
form  of  set  may  be  provided  with  a sill  when  the  floor  of  the  drift  or 
gangway  is  soft. 

Fig.  6 shows  a form  of  drift  set  surrounded  by  bridging  and  used  where 
such  bad  ground  is  encountered  as  to  necessitate  forepoling.  A are  the 
posts,  B the  caps,  and  C the  sill  of  the  regular  set;  D are  upright  bridge 
pieces;  E a horizontal  bridge  piece  separated  from  the  set  proper  by  blocks 
Fso  as  to  provide  spaces  H around  the  regular  set  through  which  the  spiles 
or  forepoles  can  be  driven. 

Fig.  8 shows  a form  of  drift  set  sometimes  employed  in  very  heavy  or 
swelling  ground.  This  method  of  framing  the  timbers  shortens  each  piece 
and  reduces  the  transverse  strain  on  all  the  timbers. 

Fig.  9 shows  an  ordinary  drift  set  provided  with  a sollar  for  ventilation 
purposes.  An  additional  brace  b is  placed  parallel  to  the  cap  c,  and  this  is 
covered  with  plank  lagging  a,  so  as  to  provide  a passage  above  the  regular 
drift,  which  may  be  used  as  a return  air-course. 

Fig.  10  is  a simple  form  of  drift  set  employed  when  the  roof  and  walls  are 
(')f  soft  material,  but  the  floor  material  firm.  It  is  composed  of  posts  I,  upon 
which  is  placed  the  cap  c.  The  joggle  cut  into  the  cap  to  receive  the  heads 
of  the  post  should  never  be  less  than  1 in.  nor  more  than  one-third  the 
thickness  of  the  cap.  The  cap  is  usually  made  of  such  a length  that  the 
posts  I have  an  inclination  or  batter  as  shown  in  the  illustration,  thus  giving 
greater  strength  to  resist  side  pressure  without  decreasing  the  floor  area  of 
the  drift,  which  may  be  necessary  for  drains,  ditches,  water  pipes,  etc.  at  the 
sides  of  the  track.  When  the  floor  is  not  composed  of  solid  material,  the 
posts  I may  be  set  upon  a sill  that  is  framed  to  fit  the  legs  in  a manner 
similar  to  that  shown  for  the  cap.  The  joggle  cut  in  the  sill  should  never  be 
less  than  1 in.  nor  more  than  one- third  the  thickness  of  the  sill.  The  sill  is 
usually  composed  of  lighter  material  than  the  cap,  is  flattened  on  one 
or  both  sides,  and  is  sometimes  used  as  one  of  the  ties  to  receive  the 
track. 

Fig.  11  shows  a post  I and  the  cap  or  collar  c,  used  where  one  wall  is  of 
firm  material.  On  one  end  the  cap  is  placed  in  a hitch.  When  the  collar 
is  supported  in  a hitch,  it  is  sometimes  said  to  be  needled,  the  operation  being 
called  “ needling.’^  The  bottom  of  the  post  a is  also  secured  in  a hitch,  in 
case, there  is  any  side  pressure.  To  keep  the  surrounding  material  in  place, 
lagging  is  necessary,  as  shown  behind  the  timbers  in  Figs.  5,  10,  and  11.  In 
the  case  of  running  ground,  the  lagging  is  usually  made  from  sawed  material 
and  driven  close  together. 


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MINE  TIMBER  AND  TIMBERING. 


Fig.  13  illustrates  a method  of  spiling  or  forepoling.  a are  the  posts  of  the 
regular  set,  h the  caps,  and  e the  top  bridging.  The  front  ends  of  the  spiles 
from  any  given  set  rest  on  the  bridging  of  the  next  advanced  set,  and  the 
spiles  for  advancing  the  work  are  driven  between  the  bridging  and  the  set, 
as  shown  in  the  illustration.  To  force  the  spiles  out  into  the  ground,  so  as 
to  provide  room  for  the  placing  of  the  next  set,  tail-pieces  i are  employed; 
these  are  placed  behind  the  back  end  of  the  spiles  as  they  are  being  driven. 
After  the  spiles  have  been  driven  forward  the  desired  amount,  another  set 
is  placed,  the  tail-pieces  knocked  out,  and  the  front  end  of  the  spiles  allowed 
to  settle  against  the  bridging  of  a new  set.  Where  the  face  is  composed  of 
extremely  bad  material,  it  may  be  necessary  to  hold  it  in  place  with  hreast 
hoards,  as  shown  at  k,  the  breast  boards  being  held  in  place  by  props  I,  which 
rest  against  the  forward  set.  When  breast  boards  are  used,  it  is  usually 
necessary  to  employ  foot  and  collar  braces  between  the  sets,  so  as  to  transfer 
the  pressure  of  the  breast  back  through  several  sets. 

Fi^.  14  shows  a method  of  placing  drift  sets  in  the  case  of  very  heavy  or 
swelling  ground,  a are  the  posts,  c the  sills,  h the  caps,  d are  the  collar 
braces  that  bear  against  both  the  caps  and  the  posts,  while  e are  foot  or  heel 
braces  that  bear  against  both  the  sills  and  the  posts;  / are  diagonal  braces  that 
are  halved  together  and  placed  as  shown. 

Shaft  Timbering. — Fig.  12  shows  square-set  timbering,  sometimes  employed 
for  shaft  lining.  A are  the  wall  plates,  B the  end  plates,  C the  buntons, 
and  D the  posts.  The  method  of  framing  the  different  parts  is  plainly 
shown. 

Fig.  15  represents  cribbing  sometimes  employed  for  shafts.  It  is  composed 
of  heavy  sawed  material  halved  together  at  the  ends,  as  shown.  The  long 
pieces  a are  called  wall  plates,  and  the  short  pieces  b,  end  plates.  Between  the 
compartments  a partition  is  built  up  of  pieces  c called  buntons.  The  ends  of 
the  buntons  are  let  into  the  wall  plates  an  inch  or  so,  as  shown  in  the 
illustration,  and  should  be  so  placed  that  they  will  break  joints  with  the 
individual  pieces  of  the  wall  plates,  thus  preventing  the  timbers  of  any 
single  set  from  bulging  into  the  shaft. 

Fig.  16  shows  another  method  of  framing,  sometimes  employed  for  the 
end  and  wall  plates  where  square-set  timbering  is  used  in  shafts.  .The  end 
and  wall  plates  are  halved  together  as  shown.  A beveled  face  is  often 
formed  at  D.  This  construction  necessitates  the  cutting  of  a tenon  on  the 
end  of  the  post  F as  shown.  S is  a 2"X  2"  strip  nailed  along  the  center  of 
the  back  of  the  wall  and  end  plates  as  a support  for  the  lagging  that  is 
placed  outside  of  the  sets.  The  lagging  is  usually  composed  of  2"  or  3" 
plank. 

Fig.  18  shows  the  use  of  hangers  between  the  individual  square  sets.  The 
hangersare  bolts  provided  with  hooks  on  the  ends,and  are  employed  to  support 
the  sets  as  the  work  progresses,  the  posts  serving  to  keep  the  sets  properly 
spaced,  while  the  hangers  keep  the  sets  tight  against  the  posts.  Hangers  are 
not  always  left  in  permanently,  but  may  be  removed  after  a considerable 
section  of  the  shaft  has  been  completed. 

Fig.  19  shows  a method  of  applying  rough  square  sets,  made  from  round 
timber,  to  the  sinking  of  a small  prospecting  shaft  by  the  use  of  forepoling. 
A is  the  first  set  of  timbers  and  J the  second.  The  hangers  are  made  from 
2''X  4"  timbers  F spiked  to  the  sets  and  to  the  supports  G.  The  supports  G 
from  which  the  sets  are  hung  are  placed  over  sills  H,  which  are  situated  at 
a convenient  distance  from  the  collar  of  the  shaft.  D represents  the  lagging 
of  the  first  set  that  is  usually  spiked  to  the  set.  K is  the  forepoling  that 
becomes  the  lagging  between  the  second  and  third  sets,  and  C the  tail-pieces 
employed  for  forcing  the  lagging  out  into  the  ground.  The  hangers  between 
the  next  two  sets  would  be  spiked  to  the  other  two  timbers  of  the  sets. 
Where  the  bottom  of  the  shaft  is  very  bad,  it  may  be  necessary  to  use  breast 
boards,  as  illustrated  in  Fig.  20,  in  which  the  shaft  is  being  put  down  by 
means  of  square  sets  and  forepoling  with  the  use  of  breast  boards. 

Square  Sets. — Fig.  21  illustrates  one  method  of  framing  square-set  timbers 
from  sawed  material  for  use  in  stopes  in  mines.  A are  the  posts,  B the  caps 
and  sills,  while  C are  the  sprags  or  studies.  The  method  of  framing  the  joints 
is  clearly  shown  in  the  illustration.  Sometimes  both  caps  and  sprags  are 
made  of  the  same  sized  material  and  are  framed  alike. 

Fig.  17  shows  a method  of  framing  round  timbers  for  square  sets.  The 
dimensions  / and  c are  usually  made  about  10  in.,  d,  e,  and  i,  each  2 in.: 
a depends  on  the  diameter  of  the  post;  b is  usually  cut  down  to  an  angle  of 
about  45°. 


MINE  TIMBER  AND  TIMBERING. 


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MINE  TIMBER  AND  fiMBERINCf, 


Landings,  Plats,  or  Stations.— Fig.  22  is  one  method  of  timbering  a plat  or 
station.  The  regular  square-set  timbering  of  the  shaft  is  continued  past 
the  station  and  the  heavy  stull  or  reacher  a put  across  at  the  bottom  of  the 
station.  The  i)osts  h are  bolted  against  the  posts  of  the  sets  and  the  cap  c 
placed  on  top  of  them.  After  this,  the  wall  plates  are  cut  out  between  the 
posts  &,  and  the  station  opened  and  timbered  as  shown  in  the  illustration. 
The  height  of  the  station  is  gradually  reduced  to  that  of  the  drift  or  level 
connecting  with  it. 

Fig.  23  represents  a method  of  timbering  a level  in  a slope  where  the 
ground  is  so  firm  that  only  stulls  are  employed  in  the  slope  and  at  the 
station,  the  timbers  all  being  secured  in  hitches  or  by  stulls.  a represents 
the  stulls  and  c the  timbers  that  are  spiked  to  the  stulls  and  carry  the 
stringers  for  the  car  track,  h represents  the  car  track  from  the  level  that  is 
brought  across  above  the  skip  track. 

Special  Forms  of  Supports.— Fig.  24  shows  a stone  arch  which  as  a stull 
supports  the  waste  material  in  the  level. 

Fig.  25  show^s  a stone  arch  when  one  wall  of  the  formation  requires 
support. 

Fig.  26  illustrates  a passage  lined  by  a combination  of  stone  or  brick  walls 
with  w^ooden  caps  and  lagging  for  the  roof. 

Fig.  27  illustrates  the  lining  of  a drift  or  level  supported  by  means  of  iron 
or  steel  shapes  bent  into  the  form  of  an  arch  and  employed  for  the  support  of 
lagging. 

Fig.  28  illustrates  a cast-iron  post  or  stull  that  has  been  successfully  used 
as  a support  in  mines.  It  is  composed  of  tw  o pieces  a and  6,  held  together 
by  a collar  c.  By  driving  c down  on  the  post,  the  two  pieces  can  be  taken 
apart  and  the  post  moved. 

Fig.  29  illustrates  a masonry  shaft  lining  supported  by  means  of  cast-iron 
plates  C set  in  bell-shaped  cavities  cut  in  the  w'alls  of  the  shaft.  As  the 
masonry  of  a section  from  below  is  built  up  tow^ard  that  above,  the  over- 
hanging portion  D is  cut  out  a little  at  a time,  and  the  masonry  from  below 
built  up  under  the  plate  so  that  the  lining  becomes  continuous. 

Fig.  30  illustrates  masonry  shaft  linings,  supported  by  artificial  stone  or 
cement  foundations  built  in  bell-shaped  cavities  cut  in  the  w^alls  of  the  shaft. 
The  blocks  of  artificial  stone  are  provided  with  inclined  bearings  C,  which 
serve  to  transmit  a portion  of  the  (downward  thrust  of  the  Lining  in  the 
direction  of  the  arrow. 

Iron  and  Steel  Supports.— The  use  of  iron  or  steel,  either  for  vertical  or 
horizontal  supports  in  mines,  has  not  become  at  all  general.  In  America, 
timber  is  as  yet  comparatively  cheap  in  most  mining  localities,  but  this  situ- 
ation is  fast  changing  and  the  timber  reserves  are  being  rapidly  cut  off, 
so  that  many  mines  now^  using  w’ood  must,  in  the  comparatively  near 
future,  resort  to  some  other  form  of  support.  Some  of  the  disadvantages  of 
metal  supports  are  their  greater  initial  cost,  and  on  this  account  it  is  essen- 
tial that  all  such  supports  should  be  recovered.  As  very  little  timber  is 
recovered  in  American  mining,  this  objection  is  one  that  wfill  probably  con- 
tinue. The  mine  water  is  often  of  such  a character  that  it  will  dissolve  iron 
or  steel;  particularly  is  this  the  case  in  copper  mines,  and  in  any  mines 
where  there  is  much  pyrites.  Metal  mines  keep  their  shaft  sets  open  but  a 
short  time  compared  with  the  pit  bottoms  of  large  coal  mines,  and  hence 
the  extra  cost  of  metal  construction  is  frequently  not  w'arranted.  The  dis- 
tricts in  which  metal  mines  are  located  are  more  likely  to  be  disturbed  thar. 
is  the  ground  over  a coal  mine,  and  if  timbering  is  crushed,  it  is  much  easier 
to  repair  than  iron  or  steel.  Another  objection  to  metal  supports  is  the  fact 
that  they  cannot  be  as  easily  framed  aiid  w^orked  as  timber. 

On  the  other  hand,  the  life  of  metal  is,  under  ordinary  circumstances, 
much  greater  than  that  of  timber,  and  w hile  the  inital  cost  may  be  greater, 
whenever  the  metal  can  be  recovered  it  can  be  used  over  and  over  again, 
and  it  ahvays  has  a certain  value  as  scrap  iron  or  steel.  After  a metal  beam 
has  bent,  it  can  still  be  used  by  simply  turning  it  upside  dowm.  Another 
advantage  for  steel  is  that  it  occupies  less  space  than  timber  or  masonry, 
and  thus  gives  a larger  effective  area  of  roadway  for  the  same  cost  of  driving, 
or  else  the  amount  of  excavation  may  be  reduced. 

Although  metal  has  not  been  greatly  used  for  props  or  upright  supxx)rts, 
it  has  been  quite  extensively  used,  both  in  America  and  abroad,  for  sup- 
porting shaft  bottoms  and  landings,  and  in  England  it  has  been  quite 
successfully  used  for  cross-bars  in  tunbering  roads,  the  bar  being  set  upon 
w ooden  legs.  In  some  of  the  European  mines,  a complete  metal  casing  has 


MINE  TIMBER  AND  TIMBERING, 


273 


been  used.  In  locations  where  a constantly  increasing  pressure  comes  upon 
the  roof,  an  elastic  bending  material  must  be  used,  and  in  such  case,  sofc 
steel  is  greatly  to  be  preferred  to  cast  iron. 


3Q 


274 


MINE  TIMBER  AND  TIMBERING, 


Trestles.— Figs.  31  and  33  illustrate  the  various  timbers  and  methods  of 
cutting  the  joints  for  ordinary  railroad  trestles.  In  Fig.  33  the  portion  (a)  at 
the  left  illustrates  the  manner  of  framing  a pile  trestle,  while  the  portion  {h) 
at  the  right  represents  the  manner  of  placing  timbers  and  cutting  the  joint 
for  the  framed  trestle.  Fig.  31  represents  bents  of  a frame  and  pile  trestle 


HEAD  FRAMES. 


275 


and  the  side  elevation  of  a low  pile  trestle.  The  various  pieces  in  the  figures 
are  numbered,  and  the  accompanying  table  gives  the  names  of  the  parts. 


Bent,  Framed,  1. 

Bent,  Pile, 

Cap,  S. 

Cross-Tie,  4. 

Dapping,  5. 

Gaining,  see  Dapping,  5. 
Guard-Rail,  6. 

Jack-Stringer,  7. 

Longitudinal  Brace,  8. 

Mortise,  9. 

Mud  Sill,  10. 

Notchmg,  Gaining,  Dapping,  5. 


Packing  Block,  11. 

Packing  Bolts,  12. 

Piles,  Batter,  Inclined,  Brace,  13. 


Sill,  17. 

Stringer,  18. 

Sway-Brace,  19. 

Tenon,  20. 

Waling  Strip,  see  Longitudinal 


Brace,  8. 


Fig.  32  illustrates  a bent  of  a frame  trestle  that  is  fastened  together  entirely 
by  means  of  drift  bolts,  no  joints  whatever  being  cut. 

Figs.  34  and  35  illustrate  one  manner  of  cutting  the  tenons  and  mortises 
on  the  ends  of  the  batter  braces  and  posts  and  frame  bents,  and  also  the  drain 
holes  that  are  bored  in  the  mortise  to  prevent  the  timber  from  rotting.  Usually 
the  sills  are  notched  or  boxed  to  receive  the  ends  of  the  timbers,  in  addition 
to  having  mortises  formed  in  them.  Figs.  36  and  37  show  such  joints  for 
receiving  the  batter  brace  and  post. 

Fig.  38  illustrates  the  manner  in  which  a tenon  is  sometimes  formed  on 
the  top  of  the  pile  to  secure  the  cap.  When  the  cap  is  secured  by  a tenon, 
the  two  are  united  by  a wooden  pin  shown  in  the  lower  part  of  the  figure, 
and  known  as  a treenail. 

Fig.  39  illustrates  a manner  in  which  the  cap  may  be  placed  upon  a pile 
trestle  by  splitting  the  cap  into  two  pieces,  a and  h with  the  tenon  c the  full 
width  of  the  pile  between  them. 

Fig.  40  illustrates  the  manner  in  which  the  cap  is  sometimes  secured  to  a 


pile  by  means  of  a drift  bolt,  and  Fig.  41  shows  the  manner  in  which  the 
same  thing  may  be  accomplished  with  the  use  of  a dowel. 

Figs.  42  and  44  show  two  methods  of  longitudinal  bracing  between  the 
bents  of  the  trestles  for  inclined  planes,  such  as  are  used  at  breakers  or 
concentrating  mills. 

Fig.  43  is  an  elevation  of  a high  trestle,  showing  the  cross-bracing  and 
framing  of  the  structure. 

Timber  Head-Frames  or  Head-Gears.— Fig.  45  is  the  simplest  form  of  head- 
gear,  which  consists  of  a vertical  post  to  carry  the  weight  of  the  sheave,  etc., 
and  a diagonal  post  that  approximately  bisects  the  angle  between  the  rope 
from  the  drum  and  the  rope  hanging  down  the  shaft,  thus  taking  the 
resultant  pull  upon  the  axle  of  the  sheave.  There  is  usually  some  extra 
timbering,  as  shown,  to  support  the  cage  guides  and  form  a platform  about 
the  sheave  for  convenience  in  oiling. 

Fig.  46  shows  a modified  form  of  the  same  type  of  frame,  in  which  the 
main  upright  leg  is  vertical  and  in  which  there  is  also  another  vertical 


276 


MINE  TIMBER  AND  TIMBERING. 


member  on  the  opposite  side  of  the  shaft.  The  inclined  leg  is  also  braced 
and  connected  to  the  main  vertical  member. 

Fig.  47  is  a head-frame  for  an  inclined  shaft  where  the  ore  pocket  is  in  the 
structure  carrying  the  sheaves.  Such  head-frames  are  sometimes  enclosed 


in  their  upper  portions  in  a building  so  as  to  protect  the  men  during  winter. 

Fig.  48  is  a form  of  framing  quite  common  in  the  anthracite  coal  fields  of 
Pennsylvania,  in  which  the  timbers  are  further  braced  by  tie-rods,  as  shown. 

Steel  Shaft  Bottoms.— Fig.  49  is  a shaft  bottom  fitted  with  steel  supports, 
the  posts  being  Z-bar  columns  and  the  caps  being  replaced  by  I beams, 
which,  in  the  station  proper,  are  supported  on  stone  or  brick  walls.  This 
metal  construction  is  employed  throughout  all  the  portion  of  the  bottom 
landing  and  passages  where  the  cars  are  handled  after  they  are  brought 
from  the  workings  or  before  they  are  returned  to  the  workings. 

Undersetting  of  Props.— The  following  table,  from  Sawyer’s  “Accidents  in 
Mines,”  gives  the  maximum  and  minimum  angles  at  which  props  should  be 
set  for  varying  inclinations.  This  table  can  be  taken  as  a general  guide, 
but  it  does  not  talce  account  of  the  length  of  prop  nor  the  varying  amounts 
ot  movement  ot  the  top  rock  under  different  conditions. 


METHODS  OF  WORKING, 


277 


Undersetting  of  Props. 


Rate  of  Inclination  of 
Seam. 

Degrees. 

Angle  or  Underset  of  Props. 

Minimum 

Degrees. 

Maximum 

Degrees. 

6 

0 

1 

12 

0 

2 

18 

1 

3 

24 

1 

4 

30 

2 

5 

- 36 

2 

6 

42 

2 

7 

48 

3 

8 

54  and  upwards 

3 

9 

METHODS  OF  WORKING. 


No  definite  rules  can  be  ^ven  for  the  selection  of  a method  of  mining 
that  will  cover  all  the  conditions  that  may  exist  at  any  given  mine.  Each 
mine  is  a distinct  and  separate  proposition,  and  each  superintendent  must 
judge  how  he  will  adapt  the  general  principles  here  given  to  the  local 
conditions  at  his  own  mine.  Every  system  of  mining  aims  to  extract  the 
maximum  amount  of  the  deposit  in  the  best  marketable  shape  and  at  a 
minimum  cost  and  danger.  


OPEN  WORK. 

open  work  applies  to  the  working  of  all  deposits  that  have  no  overburden, 
or  to  those  in  which  the  overburden  or  overlying  material  is  stripped  from 
the  portion  of  the  deposit  to  be  removed  by  hand,  steam  shovels,  scrapers, 
etc.  It  includes  particularly  all  quarries  and  placer  workings,  and  can  be 
applied  to  many  mineral  and  coal  deposits. 

The  advantages  of  this  system  are  that  no  timber  is  required;  unprofitable 
underground  workings  do  not  have  to  be  kept  open  and  in  repair;  when 
required,  a simple  hoisting  plant  is  used;  there  is  less  danger  to  the  work- 
men from  falls  of  roof  and  from  blasting:  there  is  practically  no  danger 
from  fire;  artificial  lights  are  not  required;  mining  can  be  done  more 
economically,  as  larger  faces  are  open,  larger  blasts  can  be  used,  and  the 
amount  of  work  accomplished  per  miner  is  greater,  and  better  superintend- 
ence can  be  had;  the  health  of  the  men  is  usually  much  better  when 
working  in  the  open;  the  deposits  can  be  more  easily  extracted  and  the  ore 
more  easily  and  more  perfectly  selected,  and,  under  proper  conditions,  the 
output  can  be  increased  almost  indefinitely. 

The  disadvantages  of  open  work  are:  A large  amount  of  overburden  often 
has  to  be  removed  and  a place  for  sorting  this  waste  material  provided;  the 
workmen  are  exposed  to  the  weather;  the  expense  of  open  work  increases 
rapidly  with  depth  of  covering. 

Open  work  may  be  divided  into  two  general  classes:  First,  where  the 
whole  or  a greater  part  of  the  deposit  is  of  value  and  has  to  be  removed,  as 
in  quarries  and  in  ordinary  mines;  second,  where  the  valuable  portion  is  but 
a small  part  of  th®  whole,  as  in  placers  or  fragmental  deposits  carrying  gold, 
platinum,  etc. 

Deposits  of  the  first  class  may  be  worked  as  follows:  (a)  The  deposit  is 
stripped,  if  necessary,  and  the  material  is  removed  by  hoisting  with  derricks 
or  a cableway,  or  by  drawing  out  in  cars  with  the  use  of  underground 
passages.  This  class  includes  practically  all  quarries  for  building  or  orna- 
mental stone,  slate  quarries,  and  most  of  the  open-pit  and  steam-shovel 
iron,  phosphate,  and  similar  mines,  (b)  The  deposit  is  stripped,  and  drifts 
or  tunnels  are  extended  through  the  material  below  the  surface,  either  from 
adjacent  valleys  or  from  shafts  sunk  outside  of  the  deposit.  The  material» 


278 


METHODS  OF  WORKING. 


after  being  mined  in  the  open  pit,  is  thrown  through  openings  to  these  drifts 
or  tunnels,  through  which  it  is  trammed  to  the  surface  or  to  the  foot  of  the 
hoisting  shaft. 

Steam -shovel  mines  are  those  in  which  the  material  is,  when  necessary, 
first  shaken  loose  by  big  blasts  of  low-grade  powder,  and  then  loaded  into 
railroad  cars  with  steam  shovels,  which  lift  the  ore  from  its  natural  bed  and 
deposit  it  in  cars  to  be  taken  directly  to  market  or  to  a concentrating  or 
washing  plant.  Mining  is  thus  done  very  cheaply,  but  the  steam  shovel, 
from  a mechanical  standpoint,  is  not  an  economical  machine  and  the  costs 
of  repairs  are  high.  The  expense  for  hauling  material  from  the  steam  shovel 
increases  rapidly  with  adverse  grades.  Economy  in  steam-shovel  mining 
depends  on  the  shovel  being  kept  constantly  at  work.  An  output  of  2,000 
tons  per  day  for  a steam  shovel  and  one  locomotive  has  been  reached  and 
even  surpassed,  but  this  cannot  be  taken  as  an  average  for  a season’s  work. 
Under  favorable  conditions,  there  is  probably  no  cheaper  method  of  mining. 
The  cost  of  removing  97,854  yd.  of  material  over  a seam  of  anthracite  coal 
was  fl  per  ton  of  material  stripped,  and  $0,516  per  ton  of  coal  obtained.  The 
average  depth  of  the  stripping  was  75  ft.  and  about  two-thirds  of  the 
material  removed  was  rock.  The  cost  of  stripping  a bank  15  to  18  ft.  high  in 
Western  Pennsylvania  was  $0.30  per  cu.  yd.  of  stripping. 

By  milling  system,  the  deposit  is  stripped,  shafts  are  sunk  outside  of  the 
boundaries,  and  drifts  are  extended  through  the  ore  some  distance  from 
the  surface.  From  these  drifts,  raises  are  put  up  to  serve  as  chutes,  after 
which  the  material  is  simply  blasted  loose  and  worked  into  these  raises, 
through  which  it  passes  to  the  underground  passages,  and  is  trammed  to  the 
shafts  and  hoisted  to  the  surface.  The  advantages  of  this  system  over  the 
steam-shovel  methods  are:  It  is  not  necessary  to  make  any  long  cut  through 
the  overburden  to  bring  the  cars  on  the  surface  of  the  ore  body.  The 
mining  force  can  be  employed  underground  in  extending  drifts  and  driving 
new  raises  in  bad  or  stormy  weather.  Very  little  handling  of  the  material 
by  manual  labor  is  required,  the  men  simply  working  the  loosened  ore  into 
the  chutes  by  means  of  bars  or  shovels,  without  having  to  lift  any  of  it. 
Some  of  the  soft-ore  iron  mines  have  used  this  system  very  advantageously. 

Cableways  in  Mining.— Cableways  are  extensively  used  for  stripping 
deposits,  for  transporting  material  after  it  has  been  quarried,  and  also  for 
mining  soft  or  loose  deposits,  such  as  clays,  phosphates,  and  gravels.  The 
cost  of  removing  the  overburden  varies  greatly  with  the  nature  of  the 
ground,  and  depends  largely  on  the  distance  to  which  it  is  necessary  to 
carry  the  waste  material  before  dumping.  Frequently,  a cableway  can  be 
installed  spanning  both  the  place  of  mining  and  the  dumping  ground.  In 
other  cases,  one  end  of  the  cableway  is  fixed  and  attached  to  a washing  or 
gold-saving  plant,  while  the  other  end  revolves  about  this  fixed  point  in  a 
circle  until  all  of  the  material  within  this  circumference  has  been  exca- 
vated; the  entire  plant  is  then  moved  to  another  location.  The  advantages 
of  cableways  over  steam  shovels  or  dredges  are  that  the  load  may  be 
delivered  at  a considerable  distance  from  the  point  of  excavation,  while  the 
entire  apparatus  rests  on  banks  entirely  clear  of  the  excavation. 

Cableways  have  been  constructed  with  single  spans  up  to  1,650  ft.,  han- 
dling 25-ton  loads,  and  delivering  an  average  daily  capacity  (10  hours)  of  617 
yd.  of  rock.  Mr.  Spencer  Miller  places  the  following  limitations  on  the 
practical  applications  of  cableways:  Span  (single),  2,000  ft.;  load,  25  tons; 
speed  of  travel,  1,800  ft.  per  minute;  speed  of  hoist,  900  ft.  per  minute.  The 
average  practice,  however,  is  about  as  follows:  Span,  600  to  1,200  ft.;  loads, 
3 to  7 tons;  speed  of  travel,  500  to  1,000  ft.  per  minute;  speed  of  hoist,  150  to 
300  ft.  per  minute. 

Placer  or  fragmental  deposits  may  be  worked  by  means  of  a stream  of  water 
from  a pipe  or  nozzle  directed  against  the  bank  (hydraulic  mining),  or  the 
material  may  be  excavated  by  hand  or  by  mechanical  means,  such  as 
dredges,  steam  shovels,  etc. 

Hydraulic  Placer  Mines.— The  material  is  broken  down  by  water  flowing 
over  the  bank,  as  flume  waterfalls,  or  along  the  ground  so  as  to  ground-sluice 
the  material.  The  material  is  frequently  just  loosened  by  means  of  picks  or 
shovels,  the  current  being  depended  on  to*  carry  it  away.  This  js  commonly 
called  ground  sluicing.  Another  method  of  excavating  the  niaterial  is  to 
direct  a stream  of  water  against  the  bank  from  a pipe  or  nozzle.  This  is 
true  hydraulicking.  After  the  material  has  been  loosened  by  the  water,  it  is 
allowed  to  flow  through  sluices  and  over  undercurrents  or  gold-saving 
tables  so  as  to  recover  the  valuable  portions. 


CLOSED  WORK. 


279 


Placer  Mines  Worked  by  Mechanical  Means.— Where  water  is  scarce,  the 
material  may  be  excavated  by  steam  shovels  or  other  excavators,  such  as 
grab,  or  scooping,  buckets,  operated  by  cableways.  The  material  is  then 
washed  by  a limited  supply  of  water  that  is  frequently  used  over  and  over, 
or  it  may  be  passed  over  a dry  washer  or  concentrator.  Both  the  steam 
shovel  and  the  cable  excavator  have  proved  very  efficient  means  for 
working  certain  classes  of  deposits. 

Dredge  Mining.— Where  the  gold-bearing  material  lies  below  the  water 
level,  or  where  water  can  be  introduced  so  as  to  float  a boat,  a dredge  may 
be  employed. 

For  gold  dredging,  a dredge  should  fulfil  the  following  conditions: 
(1)  Speed  and  readiness  in  moving  and  taking  up  different  positions;  (2)  an 
adaptability  for  cleaning  up  rock,  and  for  digging  to  a maximum  depth; 
(3)  feasibility  of  working  and  of  the  banking  or  disposing  of  the  tail- 
ings; (4)  cheapness  in  working,  as  most  of  the  dredging  propositions  are  of 
low  grade. 

Three  types  of  dredges  have  been  used:  the  hydraulic  suction  dredge,  the 
shovel  dredge,  and  the  continuous-bucket  ladder  dredge.  The  first  of  these 
is  well  adapted  for  digging  very  small  gravel  and  sand,  but  is  not  suited  for 
boulders  or  even  large  stones  without  a great  loss  of  efficiency.  The  con- 
tinuous-bucket dredge  has  proved  the  most  successful  under  ordinary  cir- 
cumstances, as  it  is  controlled  by  lines  and  not  by  spiles  or  spuds,  and  hence 
can  be  shifted  more  rapidly  and  made  to  conform  to  irregularities  in  the  bed 
rock  more  readily  than  the  dipper  type.  Also,  the  continuous-bueket 
dredge  furnishes  a constant  supply  of  material  to  the  apparatus  used  for 
recovering  the  gold. 

A continuohs-bucket  dredge  can  operate  to  a depth  of  60  ft.  Aecording 
to  Mr.  R.  H.  Postlethwaite,  of  San  Franciseo,  Cal.,  a decided  advocate  of 
continuous-bucket  dredges,  the  cost  of  working  a shovel  dredge  runs  from 
7 cents  per  eubic  yard  upwards;  but  he  claims  that  ther bucket  dredge  can  be 
worked  at  a cost  of  from  3 to  5 cents  per  cubic  yard,  including  a charge  of 
^100  per  week  for  depreciation.  The  cost  of  running  a small  gold  dredger 
should  not  average  over  $200  per  week— that  is  allowing  $125  for  wages,  $50 
for  fuel,  and  $25  for  repairs,  etc.  If  the  dredger  handles  10,000  cu.  yd.  per 
week,  that  would  be  at  a cost  of  2 cents  per  cubic  yard.  If  the  material 
averaged  6 eents  per  cubic  yard,  there  should  be  an  approximate  profit  of 
$400  per  week  on  an  investment  of  from  $25,000  to  $40,000.  18  cu.  ft.  of  gravel 
in  place  will  weigh  2,000  lb.;  a cubic  yard  will  weigh  1^  short  tons. 


CLOSED  WORK. 

Under  this  general  heading  it  is  eustomary  to  divide  the  methods  of 
mining^  into  coal-mining  methods  and  metal-mining  methods.  This  classifi- 
cation is  not  entirely  logical,  for  identical  methods  are  applied  to  flat  bedded 
deposits  of  coal,  iron  ore,  clay,  salt,  etc.,  and  identical  or  very  similar 
methods  to  highly  inclined  coal  seams  and  mineral  veins.  A more  logical 
classification  is  one  based  on  the  position,  character,  and  thickness  of  the 
deposit,  but  the  older  classification  has  become  so  firmly  established  that  it 
is  not  advisable  to  give  it  up  entirely  in  a pocketbook. 

Bedded  Deposits.— The  typical  and  most  extensive  bedded  mineral  dei)osits 
are  of  coal  and  iron  ore,  and  of  these  the  former  is  by  far  the  more  extensively 
mined.  A description  of  the  several  methods  of  mining  coal  beds  will 
therefore  comprise  not  only  all  of  the  essential  points  in  the  mining  of  other 
bedded  deposits,  but  will  include  a number  of  points  not  usually  considered 
in  mining  sueh  deposits.  The  chief  of  these  is  the  presence  of  explosive  gas 
in  such  quantities  as  to  influence  the  choice  of  a method  of  mining.  From 
the  descriptions  of  the  methods  of  coal  mining  here  given  it  will  therefore 
be  a comparatively  simple  matter  for  the  miner  of  clay,  iron  ore,  etc.  to 
adapt  a method.  


COAL  MINING. 

General  Considerations.— The  elementary  causes  affecting  the  extraction  of 
coal  are  (1)  weight  of  overlying  strata  or  depth  of  the  deposit;  (2)  strength 
and  character  of  roof;  (3)  character  of  floor;  (4)  texture  of  bedded  material; 
(6)  inclination  and  tliickness  of  bed;  (6)  presence  of  gas  in  the  seam  or  in 
adjoining  strata. 


280 


METBODS  OF  WORKING. 


Roof  Pressure. — Of  these  causes,  the  roof  pressure  is  the  most  important, 
and  a number  of  the  other  causes  are  directly  affected  by  it.  The  weight  of 
the  overlying  cover  will  give  a maximum  roof  pressure,  but  this  may  be  so 
variously  modified  that  the  determination  of  the  actual  pressure  is  practically 
impossible,  and  estimates  of  this  pressure  must  be  based  largely  on  practical 
experience;  hence,  rules  for  its  calculation  are  of  comparatively  little  value. 
One  very  essential  point,  however,  must  be  borne  in  mind,  i.  e.,  that  the 
direction  of  pressure  is  perpendicular  to  the  bedding  plane. 

Strength  and  Character  of  Roof.— The  strength  of  roof  refers  to  the  power  of 
being  self-supporting  over  smaller  or  larger  areas.  A strong  roof  permits 
larger  openings,  but  increases  the  load  on  the  pillars,  thereby  necessitating 
larger  pillars.  A weak  roof  requires  smaller  openings,  and  permits  smaller 
pillars  when  the  floor  is  good.  A strong  roof  may  yield  and  settle  gradu- 
ally, giving  good  conditions  for  long  wall  work,  or  it  may  be  hard  and 
brittle,  and  difficult  to  manage. 

The  character  of  floor  influences  largely  the  size  of  pillars.  A soft  bottom 
requires  large  pillars  and  narrow  openings,  especially  when  the  roof  is  strong. 

Texture  of  Coal  and  Inclination  and  Thickness  of  Seam. — Soft,  friable  coal 
requires  large  pillars,  while  a hard,  compact  coal  requires  only  small  pillars. 
The  inclination  and  thickness  of  the  deposit  increase  the  size  of  pillars 
required,  and  also  influence  the  haulage,  drainage,  timbering,  method  of 
working,  arrangement  of  breasts,  etc. 

The  presence  of  gas  in  the  seam  or  in  the  enclosing  strata  affects  the  system 
of  working,  as  ample  air  passages  must  be  provided,  and  provision  must  fre- 
quently be  made  for  ventilating  separately  the  different  sections  of  the  mine. 
Where  the  gas  pressure  is  strong,  and  outbursts  are  of  frequent  occurrence, 
narrow  openings  are  necessitated  that  render  the  workings  safe  until  the 
gas  has  escaped.  


SYSTEMS  OF  WORKING  COAL. 

There  are  two  general  systems  of  working  coal  seams:  (1)  room-and-pillar, 

and  (2)  longwall.  There 
are,  however,  a great  num- 
ber of  modifications  of 
each,  and  it  is  often  diffi- 
cult to  exactly  classify  a 
given  method  under  either 
of  these  two  systems. 

The  room-and-pillar  sys- 
tem, also  known  as  the  pil- 
lar-and-chamher  or  hord- 
and-pillar,  and  which  may 
include  the  piUar-and-stall, 
system,  is  the  oldest  of  the 
systems,  and  the  one  very 
generally  used  in  the  mines 
of  the  United  States.  By 
this  system,  coal  is  first 
mined*  from  a number  of 
comparatively  small  places 
called  rooms,  chambers, 
stalls,  bards,  etc.,  which  are 
driven  either  square  from 
or  at  an  angle  to  the  haul- 
ageway. These  openings 
may  be  wide  or  narrow, 
and  may  be  either  a road- 
way, incline,  or  chute, 
according  to  existing  con- 
ditioijs.  The  pillars  that 
are  left  between  the  open- 

ings  in  the  original  work- 

A A ings  support  the  roof,  and 

1 are  usually  subsequently 

removed.  All  forms  of 
room-and-pillar  workings  become  impracticable  when  the  thickness  of  the 
pillars  necessary  to  support  the  roof  pressure  much  exceeds  double  the 
width  of  the  breast  openings. 


LONG  WALL  METHOD, 


281 


The  pillar-and-stall  system  is  similar  to  the  room-and-pillar  system,  but  in 
the  former  the  stalls  are  opened  off  from  the  entry  their  full  width,  while  in 
the  latter  the  rooms  or  chambers  are  turned  narrow,  and  widened  inside  to 
their  regular  width.  Fig.  1 shows  a typical  room-and-pillar  method  for 
working  an  approximately  horizontal  seam  of  coal  of  moderate  thickness 
(4  to  10  ft.),  and  with  a fairly  good  roof  and  bottom.  Main  headings  A are 
usually  driven  perpendicular  to  the  strike,  unless  this  direction  is  changed 
by  the  cleat  in  the  coal,  as  explained  later.  Cross-headings,  or  entries  B,  B, 
are  turned  off  at  regular  intervals,  and  at  an  angle  of  90°  to  these  main 
headings,  the  distance  between  any  two  pairs  of  cross-entries  being  deter- 
mined, in  flat  seams,  by  twice  the  length  to  which  a room  can  be  driven, 
which  in  turn  is  determined  by  the  character  of  the  roof,  floor,  and  seam. 
The  rooms  are  turned  to  the  right  and  left  of  each  pair  of  butt  headings,  and 
driven  until  they  meet,  or  one-half  the  distance  between  two  pairs  of  entries. 
After  the  rooms  are  driven  up,  the  pillars  between  the  rooms  are  drawn,  and 
later  the  room  stumps  along  these  entries,  and  the  entry  pillars  themselves, 
are  drawn,  unless  it  should  be  necessary  to  keep  some  of  these  cross-entries 
open  for  purposes  of  ventilation.  A large  chain  pillar  is  left  to  protect  the 
main  headings. 

When  cross-entries  have  been  extended  a considerable  distance,  roads  are 
often  driven  between  them  parallel  to  the  main  heading  A.  The  object  of 
these  subroads  is  to  reduce  to  a minimum  the  air-courses  and  roadways  to  be 
maintained;  or  such  a subroad  may  be  necessary  on  account  of  a squeeze 
crossing  any  pair  of  cross-entries.  The  extent  of  the  territory  worked  out  to 
the  right  and  left  of  each  main  entry  is  a matter  for  local  determination. 

The  room  openings  are  made  suitable  to  prevailing  conditions,  and  Fig.  1 
shows  several  of  the  common  methods.  The  width  of  the  room  and  the  form 
of  the  opening  depend  on  the  character  of  the  roof  and  the  extent  to  which 
it  is  necessary  to  leave  a pillar  to  support  the  cross-heading,  it  being  advan- 
tageous, of  course,  to  open  out  the  room  to  its  full  width  at  the  earliest 
possible  moment. 

Longwall  Method  of  Mining.— The  longwall  system  contemplates  the  extrac- 
tion of  the  entire  seam  or  bed,  and  the  original  significance  of  the  term 
“longwall”  was  a continuous  line  of  breast.  No  portion  of  the  seam  is 
allowed  to  remain  after  leaving  the  vicinity  of  the  shaft.  The  method 
depends  on  producing  a uniform  and  gradual  settlement  of  the  roof  a few 
yards  behind  the  working  face.  Pack  walls  are  built  on  each  side  of  the 
roadways,  and  at  regular  intervals  in  the  gob  or  waste  area,  and  the  roof 
settles  firmly  on  these  packs,  pressing  them  into  the  bottom,  or  compressing 
them  until  the  roof  subsidence  is  complete.  The  height  of  the  main  road- 
way is  maintained  by  “brushing”  the  roof  or  lifting  the  bottom.  Longwall 
may  be  advancing  or  retreating.  In  longwall  advancing,  mining  begins  at  oi 
near  the  foot  of  tb^.  shaft  and  advances  outwards,  forming  a gradually 
widening  and  incre;j,sing  length  of  face  to  the  boundary.  The  passages  are 
made  through  the  excavated  portions  of  the  mine,  and  are  maintained  by 
pack  walls  built  either  of  the  refuse  secured  in  mining  or  sometimes  from 
material  brought  in  from  the  surface.  In  longwall  retreating  or  withdraw- 
ing, entries,  gangways,  or  headings  are  first  driven  to  the  boundary  or  to 
other  convenient  distances  inbye,  and  the  pillars  between  these  entries  are 
then  drawn  back  toward  the  shaft;  this  is  also  called  working  home. 

Fig.  2 shows  a plan  of  combined  longwall  advancing  and  retreating.  In 
the  upper  arrangement,  or  Scotch  longwall,  the  face  is  semicircular  and  the 
roads  are  turned  off  at  angles  of  45°.  This  plan  is  suitable  for  seams  up  to 
3 ft.  thick  with  a weak  top,  and  which  pitch  less  than  20°,  and  situated  at 
almost  any  depth.  It  is  the  one  from  which  most  of  the  longwall  practice 
in  the  central  coal  basins  of  the  United  States  is  taken.  In  the  lower  por- 
tion, which  shows  one  method  of  longwall  retreating,  narrow  parallel 
headings  are  driven  in  pairs  to  the  boundary,  being  from  200  to  300  ft.  apart. 
Such  a combination  of  longwall  advancing  and  retreating  insures  an 
unvarying  supply  of  coal,  for  while  one  side  continually  leaves  the  shaft,  the 
other  approaches  it. 

Longwall  is  specially  adapted  to  flat  seams  or  those  having  a regular  and 
moderate  pitch,  and  wnich  are  free  from  faults;  to  hard  rather  than  to  soft 
coal;  and  to  the  use  of  undercutting  machines.  It  is  also  easy  of  venti- 
lation and  economical  in  timber,  explosives,  and  track. 

In  all  longwall  work,  the  weight  of  the  roof  is  made  to  act  upon  the  coal 
face,  which  is  undercut,  according  to  the  ability  of  the  miner  and  the  con- 
ditions of  the  seam,  from  2\  to  3 ft.  deep.  This  weighing  action  of  the  rooi 


282 


METHODS  OF  WORKING. 


performs  the  work  of  the  powder  and  breaks  the  coal  in  a few  hours  or  less, 
after  the  sprags  have  been  removed.  The  time  required  to  break  the  coal 
will  be  greater  or  less,  according  to  conditions.  The  success  of  the  entire 
system,  as  will  be  readily  seen,  depends  on  a uniformly  regular  advance  of 
the  line  of  the  face  or  breast,  and  a uniform  system  of  setting  and  drawing 
timber  at  the  face;  also,  uniformity  in  the  pack  walls  along  the  roads,  and  in 
the  amount  of  gob  packing.  This  system  does  not  permit  of  long  idle  spells 
induced  by  strikes  or  other  causes.  The  coal  does  not  break  well,  either, 
when  some  of  the  men  are  out  a portion  of  the  time,  and  their  places  lie  idle. 
The  life  of  the  whole  system  consists  in  maintaining  what  miners  call  a 


Fig.  2. 

traveling  weight  upon  the  coal  face,  which  can  only  be  accomplished  satis- 
factorily by  uniformity  in  every  part  of  the  work. 

Longwall  advancing  is  better  suited  to  thin  seams  than  to  thick  ones,  to 
flat  rather  than  pitching,  and  to  good  roofs  and  hard  floors. 

Longwall  retreating  is  better  adapted  to  thicker  beds;  to  those  liable  to  gob 
fires;  to  seams  of  hard  coal  having  a considerable  pitch;  to  pockety,  or 
irregular  seams:  and  to  a soft  and  treacherous  top.  The  air-course  is  also  less 
broken  along  the  face,  and  better  haulage  installations  can  be  made.  Its 
chief  disadvantage  is  the  large  amount  of  dead  work  necessitated  before 
returns  are  received.  With  this  system  there  is  no  expense  in  keeping  up 
the  haulage  road  so  far  as  creep  or  falling  roof  is  concerned,  as  the  roads  are 
all  in  solid  coal,  nor  is  there  any  trouble  from  gob  fires  or  water;  and  little 


STAR  TING  LONG  WALL. 


283 


detriment  to  the  working  face  is  caused  by  the  mine  having  to  stand  idle 
for  a time.  If  the  seam  is  high  enough  for  the  mules  or  horses,  no  rock 
whatever  will  need  to  be  taken  down.  The  coal  seam  will  be  proved  before 
of  it  is  extracted. 

The  ventilation  in  the  retreating  plan  is  as  near  perfect  as  it  is  possible  to 
get  it  in  practice.  All  the  airways  are  tight,  a thing  impossible  to  get  in  the 
advancing  plan;  and  it  is  a comparatively  easy  matter  to  shut  off  fire  or  to 
allow  a portion  of  the  working  face  to  remain  idle. 

Longwall  retreating  is  frequently  used  for  working  quite  limited  sections 
of  a mine  in  which  the  seam  of  coal  is  16  to  20  ft.  thick,  and  inclined  not 
more  than  10°.  A series  of  8 or  10  pairs  of  headings  are  turned  off  the  butt 
entry  and  driven  a distance,  dependent  on  local  conditions,  where  the 
working  face  is  formed  by  driving  cross-cuts  from  one  to  the  other.  This 
face  is  carried  back  on  the  retreating  plan,  allowing  the  roof  to  cave  in  or 
settle  on  the  gob  as  the  work  approaches  the  butt  entry.  In  this  way,  any 
extra  weight  that  would  crush  and  ruin  the  adjacent  coal  is  avoided.  This 
method  is  also  used  in  lower  seams  in  which  the  coal  is  soft,  or  the  roof,  or 
bottom,  or  both,  are  of  such  a nature  as  to  give  trouble  in  working  the  room- 
and-pillar  system.  Sometimes,  instead  of  driving  pairs  of  headings  at 
considerable  distances  apart,  a number  of  single  headings  are  driven  com- 
paratively close  together,  and  connected  by  cross-cuts  from  10  to  20  yd. 
apart.  When  the  limit  of  the  section  is  reached,  the  working  face  is  formed 
and  carried  back,  as  in  the  other  plan.  This  latter  method  is  more  suita- 
ble for  tender  roof,  or  a coal  in  which  the  face  and  butt  cleats  are  not 
prominent. 

Starting  Longwall. — There  are  two  methods  of  starting  longwall  workings. 
In  the  first,  the  work  of  extraction  begins  at  the  shaft  itself,  the  coal  being 
taken  out  all  around  and  its  place  filled  with  solid  packs,  leaving  only  space 
for  the  roadways.  In  the  second  method,  a pillar  of  solid  coal  is  left  to  sup- 
port the  shaft,  cut  only  by  the  roadways.  The  longwall  work  is  then 
started  uniformly  all  around  this  pillar.  Great  care  is  needed  in  building 
the  first  pack  walls  around  the  shaft  pillar,  to  see  that  they  are  solidly  built 
and  well  rammed,  in  order  to  break  the  roof  over  the  coal.  The  system  will 
not  work  rightly,  however,  until  the  breast  has  been  advanced  some  dis- 
tance from  the  pillar,  so  as  to  secure  the  benefit  from  the  weighing  action  of 
the  roof  upon  the  coal  face.  The  mining  will  be  more  difficult  in  the  start, 
and  in  some  exceptional  cases  it  may  even  be  necessary  to  place  some  light 
shots;  which,  however,  should  be  avoided,  if  possible. 

The  panel  system  divides  a mine  into  districts  or  panels  by  driving  entries 
and  cross-entries  so  as  to  intersect  one  another  at  regular  intervals  of,  usually, 
about  100  yd.  Large  pillars  are  left  surrounding  the  workings  within  each 
panel,  and  any  method  of  development  may  be  used  for  each  panel.  This 
system  presents  the  following  advantages:  (1)  Better  control  of  the  ventila- 
tion, since  the  air  in  any  panel  may  be  temporarily  increased  or  decreased, 
as  required.  An  explosion  occurring  in  one  panel  is  less  liable  to  affect  the 
other  workings.  (2)  Coal  may  be  extracted,  pillars  drawn,  and  the  panels 
closed  and  sealed  off  independently  of  each  other.  (3)  Greater  security  is 
afforded  against  creep  and  squeeze.  (4)  Coal  that  disintegrates  on  standing 
can  be  quickly  worked  out. 

Bearing  In,  or  Undercutting. — In  any  method  of  mining  where  the  coal  is 
undermined,  advantage  should  be  taken  of  the  roof  pressure  to  assist  in 
both  breaking  down  the  coal  and  also  in  bearing  in.  The  fact  is  often 
overlooked  that  the  roof  pressure  upon  the  face  coal  makes  it  brittle  and 
more  susceptible  to  the  pick,  and  the  good  miner  starts  a shallow  mining  in 
the  under  clay,  or  lower  coal,  and  carries  it  the  entire  width  of  the  face. 
By  the  time  he  returns  to  the  side  of  the  breast  at  which  he  started,  the  roof 
pressure  has  made  the  coal  more  tender  and  susceptible  to  the  pick.  Such  a 
gradual  system  of  mining  throws  the  pressure  on  the  coal  face  gradually, 
and  the  coal  breaks  in  larger  pieces.  The  depth  of  the  undercut  depends 
on  the  thickness  of  the  seam  and  the  other  conditions.  Undercutting  by 
mining  machines  is  rapidly  replacing  hand  work  wherever  these  machines 
can  be  used. 

Buildings,  Pack  Walls,  and  Stowing.— Pack  walls  should  be  built  large  enough 
at  first  and  kept  well  up  to  the  face,  to  prevent  the  weight  coming  upon  the 
timber  and  also  to  permit  the  roof  to  settle  rapidly  when  the  timber  is 
taken  out  of  the  face.  Often  the  roof  will  not  stand  this  second  movement 
without  breaking,  and  possibly  closing  in  the  entire  face.  The  face  should 
therefore  be  kept  in  shape,  and  just  as  soon  as  there  is  room  for  a prop  or 


284 


METHODS  OF  WORKING. 


chock,  it  should  be  put  in  immediately,  and  the  pack  walls  likewise  should 
be  extended  after  each  cut  or  web  is  loaded  out. 

As  a general  thing,  the  pack  walls  in  the  gob  are  not  so  wide  as  the  road- 
side ones,  particularly  when  the  seam  produces  enough  waste  material 
to  stow  the  “marches,”  “cundies,”  or  “gobs,”  between  these  pack  walls. 
Usually  about  50fo  of  the  cubical  contents  of  the  solid  seam  taken  out  will 
stow  the  spaces  between  the  pack  walls  in  thick  pitching  seams,  where  the 
entire  gob  must  be  completely  filled  or  nearly  so.  No  waste  material,  except 
such  as  will  hasten  spontaneous  combustion,  should  be  taken  out  of  the 
mine  to  the  surface. 

Timbering  a Longwall  Face.— The  method  of  timbering  the  working  face 
depends  on  the  nature  of  the  roof,  floor,  coal,  etc.  The  action  of  the  roof  on 
the  coal  face  is  regulated  almost  entirely  by  timber;  consequently,  when  the 
coal  is  of  such  a nature  as  to  require  little  weight  to  make  it  mine  easily,  the 
roof  must  be  timbered  with  rows  of  chocks  and,  if  necessary,  a few  props. 

Control  of  Roof  Pressure.— The  working  face  of  a longwall  working  should 
advance  up  grade,  but  this  face  cannot  always  be  kept  parallel  with  the 
strike.  When  the  angle  at  the  line  of  face,  made  with  the  line  of  strike,  is 
less  than  90°,  the  greater  j^ressure  of  the  covering  rocks  is  thrown  on  the 
gob,  and,  when  this  angle  is  more  than  90°,  the  greater  pressure  comes  on 
the  coal.  The  angle  made  by  the  working  face  with  the  line  of  pitch  varies 
inversely  as  the  vertical  angle  of  pitch,  or  for  a high  pitch  this  angle  is 
small  and  for  a low  pitch  it  is  large.  Where  longwall  is  worked  in  adjacent 
sections,  care  must  be  taken  to  prevent  the  advancing  of  one  section  throw- 
ing a crushing  weight  on  any  of  the  others,  and  thus  producing  a crush  or 
an  uncontrollable  cave.  Where  the  rocks  are  pitching,  and  a greater  portion 
of  the  cracks  that  cut  them  run  in  lines  parallel  to  the  strike,  neither  stone 
nor  timber  can  efficiently  support  the  roof,  which  frequently  breaks  off  close 
to  the  working  face. 

The  ends  of  all  stone  packs  nearest  the  face  of  the  coal  should  be  in  line, 
and  the  ends  of  these  pack  walls  should  form  a line  parallel  to  the  face  of 
the  coal.  Timbers  set  at  equal  distances  and  in 
line  along  a longwall  face  are  much  more  efficient 
in  supporting  the  roof  than  irregularly  set  tim- 
bers. Fig.  3 shows  the  proper  way  of  locating 
the  pack  walls  and  the  face  timber. 

Number  of  Entries.— The  entries  in  a mine  may 
be  driven  single^  double,  triple,  etc. 

The  single-entry  system  is  only  advisable  under 
certain  conditions  and  for  short  distances,  since 
the  ventilation  must  be  maintained  along  the 
face  of  the  rooms,  and  there  is  but  one  haulage- 
way, which  may  easily  be  closed  by  a fall  or  creep.  Rooms  are  turned  off 
one  or  both  sides  of  the  entry. 

The  double-entry  system  is  most  commonly  used.  Two  parallel  entries 
are  driven,  separated  by  an  entry  pillar  whose  thickness  varies  with  the 
depth  of  the  seam,  and  connected  at  intervals  of  about  20  yd.  by  cross-cuts 
or  breakthroughs  to  maintain  ventilation. 

The  triple-entry  system  is  used  particularly  in  very  gaseous  seams  requir- 
ing separate  return  airways;  or,  at  times,  in  mines  where  the  large  output 
requires  ample  haulage  roads.  It  is  usually  applied  to  the  main  entries  only, 
but  sometimes,  also,  to  the  cross-entries.  In  gaseous  mines,  the  middle 
entry  is  usually  made  the  haulage  road  and  intake  airway,  and  the  outside 
entries  the  return  air-courses  for  either  side  of  the  mine,  respectively. 

A still  larger  number  of  entries  even  has  been  suggested  for  deep 
workings  where  it  is  difficult  to  keep  open  broad  passages,  but  these  have 
not  been  generally  adopted  or  tried  experimentally  to  any  great  extent. 

Direction  of  the  Face. — The  typical  room-and-pillar  plan.  Fig.  1,  shows  the 
main  headings  and  the  rooms  driven  parallel  to  the  direction  of  the  dip,  and 
the  cross-headings  parallel  to  the  strike,  but  in  most  coal  seams  there  are 
vertical  cleavages,  called  cleats,  which  cross  the  coal  in  two  directions  about 
at  right  angles  to  each  other.  Face  cleats,  as  they  are  called,  are  the  more 
pronounced,  while  the  end  or  butt  cleats  are  the  shorter,  less  pronounced 
joints.  The  direction  of  the  face  with  respect  to  the  cleats  is  of  prime 
importance  as  greatly  facilitating  or  retarding  the  mining  of  the  coal. 

Fig.  4 shows  the  different  positions  that  the  face  may  occupy  with  respect 
to  the  direction  of  the  cleats.  The  angle  of  the  breast  depends  on  the  hard- 
ness of  the  coal  and  freedom  of  the  cleats,  and  each  method  has  its  peculiar 


Fig.  3. 


PILLARS. 


285 


adaptation  to  the  varying  conditions  of  a coal  seam.  When  the  face  cleats 
are  working  free  and  the  coal  is  very  soft,  it  may  be  necessary  to  drive  “ end 
on.”  The  end-on  method  is  best  adapted  to  a very  heavy  roof  pressure, 
while  for  a light  roof  pressure  the  short-horn  method  assists  in  breaking  the 
coal.  If  the  “face  ” cleats  are  free  and  the  coal  breaks  readily  along  them, 
and  it  is  reasonably  hard,  the  long-horn  method  is  adopted,  for  when  the 
coal  is  undercut  it  needs  more  support  than  it  gets  from  the  cleats,  and  its 
weight  must  be  thrown  somewhat  upon  the  end  cleats.  “Face  on”  is 
adopted  when  the  face  cleats  are  not  as  free  or  numerous  as  the  butt  cleats. 
Unless  the  coal  at  the  face  re- 
ceives sufficient  support,  the 
undercutting  or  bearing  in  can- 
not be  thoroughly  done,  or  else 
the  amount  of  spragging  and 
the  risk  to  the  miner  are  in- 
creased. When  the  end  cleats 
are  less  pronounced  and  nu- 
merous, and  the  roof  pressure 
great,  the  coal  will  probably 
break  better  by  carrying  wide 
breasts  upon  the  ends  of  the 
coal,  and  it  is  then  an  advan- 
tage to  drive  double  rooms  with 
large  ;^illars  between  them.  In  pitching  seams,  the  pillar  should  have  very 
long  sides  perpendicular  to  the  strike,  if  the  principal  cleats  in  the  coal 
are  parallel  to  the  strike,  or  nearly  so. 

The  short-horn  method  is  adapted  to  heavy  roof  pressure  and  wide  room 
pillars,  as  the  face  cleats  are  here  quite  pronounced,  and  the  pillars  between 
the  rooms  thereby  weakened  to  a large  extent;  hence,  wide  pillars  are  more 
often  employed  when  working  on  the  ends  of  the  coal.  When  the  face 
cleats  are  less  pronounced,  and  the  end  cleats  are  working  freely,  a good 
breast  of  coal  is  carried  on  the  face,  and,  unless  other  conditions  require  it, 
a great  width  of  room  pillars  is  not  needed.  If  this  can  be  done  consistently, 
and  good  lump  coal  secured  at  the  same  time,  the  room  should  cross  the  pitch 
as  little  as  possible,  as  a side  pressure  upon  the  pillars  having  very  long  sides 
running  diagonally  across  the  pitch  is  destructive. 


PILLARS. 

Size  of  Pillars.— It  is  impossible  to  give  exact  rules  or  formulas  for  deter- 
mining the  proper  size  of  pillars.  Each  case  in  practice  recjuires  special 
consideration,  and  in  laying  out  the  pillars  in  a virgin  field  it  is  well  to  find 
out  what  the  current  practice  is  in  similar  fields.  In  general,  the  thicker 
the  seam  and  the  greater  its  depth  from  the  surface,  the  greater  should  be 
the  thickness  of  the  pillar.  Some  coal  deteriorates  rapidly  when  subject  to 
weight  and  to  the  disintegrating  effect  of  the  atmosphere,  and  pillars  of 
such  coal  must  be  larger  than  when  composed  of  a hard,  compact  coal. 
Permanent  pillars,  or  those  that  are  to  remain  for  a considerable  length  of 
time,  must  be  larger  than  those  that  are  to  be  promptly  removed.  Pillars 
about  the  bottom  of  a shaft,  or  along  main  haulage  roads,  should  be  left  large 
enough  to  provide  for  increasing  developments,  for  when  landings  are 
enlarged  or  when  haulage  systems  are  introduced,  the  original  pillars  fre- 
quently have  to  be  reduced  in  size  by  taking  a skip  off  of  them  or  by  taking 
out  chambers  for  engines  and  pumps. 

Shaft  Pillars. — Various  formulas  have  been  given  to  determine  the  size  of 
shaft  pillars,  and  the  results  given  by  these  several  formulas  are  very  diverse. 

Merivale.—  S = 22,  where  S equals  the  length  of  the  side  of  the 

pillar  in  yards,  and  D equals  depth  of  shaft  in  fathoms. 

Andre.— Up  to  150  yd.  depth,  have  the  pillar  35  yd.  square,  and  for  greater 
depths  increase  5 yd.  on  each  side  for  every  25  yd.  of  increased  depth. 

Dron.— Draw  lines  enclosing  all  surface  buildings  that  it  is  necessary  to 
erect  about  the  head  of  the  shaft,  and  make  the  shaft  pillar  so  that  solid 
coal  will  be  left  outside  these  lines  all  around  for  a distance  equal  to  one- 
third  the  depth  of  the  shaft. 

Wardle. — Shaft  pillars  should  not  be  less  than  40  yd.  square  down  to  a 
depth  of  60  fathoms,  and  should  increase  10  yd.  on  a side  for  every  20 
fathoms  increase  in  depth, 


Fig.  4. 


286 


METHODS  OF  WORKING. 


Hughes.— Leave  1 yd.  in  width  of  pillar  for  every  yard  in  depth  of  shaft. 

Pa mely.— Allow  a pillar  40  yd.  square  for  any  depth  up  to  100  yd.;  for 
greater  depths,  increase  the  pillar  5 yd.  for  every  20  yd.  in  depth. 

Calculating  the  size  of  pillar  from  each  of  these  authorities,  we  find  the 
following  variations: 


Authority. 

For  Shaft  300  Ft.  Deep. 

For  Shaft  600  Ft.  Deep. 

Merivale 

22  yd.  square. 

31  yd.  square. 

Andre  

35  yd.  square. 

45  yd.  square. 

Wardle 

40  yd.  square. 

60  yd.  square. 

Pamely 

40  yd.  square. 

65  yd.  square. 

Dron 

33i  yd.  square.* 

66f  yd.  square.* 

Hughes  

100  yd.  diameter. 

200  yd.  diameter. 

^Outside  of  buildings. 

None  of  these  formulas  takes  account  of  the  thickness  of  the  seam,  and 
the  following  formula,  which  takes  account  of  this  very  important  element, 
was  suggested  by  Mr.  R.  J.  Foster,  in  “ Mines  and  Minerals”: 

Radius  of  pillar  = ^\/ DXt, 
in  which  D = depth  of  shaft;  t = thickness  of  seam. 

Pitching  seams  require  smaller  pillars  on  the  low  side  than  on  the  rising 
side  of  the  shaft. 

Room  Pillars. — The  relative  width  of  pillar  and  breast  is  dependent  on 
the  weight  of  cover,  as  compared  with  the  character  of  the  roof  and  floor, 
and  the  crushing  strength  of  the  coal.  These  relative  widths  are  deter- 
mined largely  by  practice.  Speaking  generally,  the  narrower  the  rooms 
or  chambers,  the  higher  the  cost  in  yardage,  the  greater  the  production  of 
slack  and  nut  coal,  the  greater  the  consumption  of  powder,  track  iron,  ties, 
etc.,  and  the  greater  the  cost  of  dead  work. 

For  bituminous  coal  of  medium  hardness  and  good  roof  and  floor,  a rule 
often  used  is  to  make  the  thickness  of  room  pillars  equal  to  l<fo  of  the 
depth  of  cover  for  each  foot  of  thickness  of  the  seam,  according  to  the 

expression  ^ X in  which  Wp  = pillar  width;  t = thickness  of 

seam;  D = depth  of  cover,  and  then  make  the  width  of  breast  or  opening 
equal  to  the  depth  of  cover  divided  by  the  width  of  pillar  thus  found, 

according  to  the  expression  Wo  = where  Wo  — width  of  room. 

f'y  p 

Frail  coal  and  coal  that  disintegrates  readily  when  exposed  to  the  air,  and 
a soft  bottom,  may  increase  the  width  of  pillar  required  as  much  as  50^  of 
the  amount  found  above;  also,  a hard  roof  may  increase  the  same  as  much 
as  25^;  while  on  the  other  hand,  a frail  roof  or  a hard  coal  or  floor  may 
reduce  the  width  of  pillar  required  25^.  The  hardness  of  the  roof  affects 
both  the  width  of  pillar  and  width  of  opening  alike,  which  is  not  the  case 
with  any  of  the  other  factors. 

Dunn’s  Tables  of  Size  of  Room  Pillars  for  Various  Depths. 


The  following  table  is  for  first  working,  with  the  design  of  afterwards 
taking  out  the  pillars,  the  width  of  the  principal  workings  being  5 yd.,  and 
cross-holings  2 yd. 


Depth. 

Feet. 

Size  of 
Pillars. 
Yards. 

Proportion 

in 

Pillars. 

Depth. 

Feet. 

Size  of 
Pillars. 
Yards. 

Proportion 

in 

Pillars. 

120 

20  X 5 

.41 

1,080 

26  X 14 

.69 

240 

20  X 6 

.50 

1,200 

26  X 16 

.71 

360 

22  X 7 

.52 

1,320 

28  X 18 

.73 

480 

22  X 8 

.57 

1,440 

28  X 20 

.75 

600 

22  X 9 

.59 

1,560 

30  X 21 

.77 

720 

22  X 12 

.61 

1,680 

30  X 22i 

.78 

840 

26  X 15 

.63 

1,800 

30  X 24 

.79 

960 

28  X 16 

.66 

— V 

ROOM  PILLARS. 


287 


Extremely  large  pillars  must  often  be  left  as  a precautionary  measure  to 
protect  permanent  haulageways  and  surface  buildings,  or  to  avoid  any  pos- 
sibility of  a break  in  the  roof  that  would  cause  an  inflow  of  water. 


Table  Showing  Distance  From  Center  to  Center  of  Breasts  or 
Chambers  Measured  on  the  Entry  or  Gangway,  for 
Different  Angles. 


cj  ' cc 
r H d O 


Distance  Measured  on  the  Entry  in  Feet,  When  Width  of 
Breast  -f  Width  of  Chamber  Is: 


20 

25 

30 

35 

40 

45 

50 

55 

60 

65 

70 

75 

90 

20.0 

25.0 

30.0 

35.0 

40.0 

45.0 

50.0 

55.0 

60.0 

65.0 

70.0 

75.0 

85 

20.0 

25.1 

30.1 

35.1 

40.2 

45.2 

50.1 

55.2 

60.2 

65.3 

70.3 

75.3 

80 

20.3 

25.4 

30.5 

35.5 

40.6 

45.7 

50.6 

55.8 

60.9 

66.0 

71.1 

76.2 

75 

20.7 

25.9 

31.1 

36.2 

41.4 

46.6 

51.2 

56.9 

62.1 

67.3 

72.5 

77.7 

70 

21.2 

26.6 

31.9 

37.2 

42.6 

47.9 

53.1 

58.5 

63.9 

69.2 

74.5 

79.8 

65 

22.0 

27.6 

33.1 

38.6 

44.1 

49.6 

55.1 

60.7 

66.2 

71.7 

77.2 

82.8 

60 

23.0 

28.9 

34.6 

40.4 

46.2 

52.0 

57.6 

63.5 

69.3 

75.1 

80.8 

86.6 

55 

24.4 

30.5 

36.6 

42.7 

48.8 

54.9 

60.9 

67.1 

73.3 

79.4 

85.5 

91.6 

50 

25.a 

32.6 

39.2 

45.7 

52.2 

58.7 

65.1 

71.8 

78.3 

84.9 

91.4 

97.9 

45 

28.2 

35.4 

42.4 

49.5 

56.6 

63.6 

^0.6 

77.8 

84.9 

91.9 

99.0 

106.1 

40 

31.1 

38.9 

46.7 

54.5 

62.2 

70.0 

77.6 

85.6 

93.4 

101.2 

109.0 

116.7 

35 

34.9 

43.6 

52.3 

61.0 

69.7 

78.5 

87.0 

95.9 

104.6 

113.4 

122.1 

130.8 

30 

40.0 

50.0 

60.0 

70.0 

80.0 

90.0 

100.0 

110.0 

120.0 

130.0 

140.0 

150.0 

25 

47.3 

59.2 

71.0 

82.8 

94.6 

106.5 

118.1 

127.2 

142.0 

153.8 

165.7 

177.5 

20 

58.5 

73.1 

87.7 

102.4 

117.0 

131.6 

145.9 

160.8 

175.5 

190.1 

204.7 

219.3 

15 

77.4 

96.6 

115.9 

135.3 

154.5 

173.9 

192.8 

212.5 

231.9 

251.2 

270.5 

289.8 

10 

115.2 

144.0 

172.8 

201.6 

230.4 

259.2 

287.3 

316.7 

345.6 

374.4 

403.1 

432.0 

5 

229.5 

286.9 

344.2 

401.6 

459.0 

516.3 

572.5 

631.1 

688.5 

745.8 

803.2 

860.5 

In  the  following  table,  the  weight  thrown  upon  pillars  at  different  depths 
by  the  removal  of  different  proportions  of  coal  is  given: 

Weight  on  Pillars  in  Pounds  per  Square  Inch. 


Percentage  of  Coal  Left  in  Pillars. 


^11 

90^ 

80/. 

70/ 

60/ 

50/ 

40/ 

30/ 

20/ 

10/ 

100 

111 

125 

142 

166 

200 

250 

333 

500 

1,000 

500 

555 

625 

710 

830 

1,000 

1,250 

1,665 

2,500 

5,000 

1,000 

1,111 

1,250 

1,428 

1,666 

2,000 

2,500 

3,333 

5,000 

10,000 

1,500 

1,666 

1,875 

2,138 

2,496 

3,000 

3,750 

4,998 

7,500 

15,000 

2,000 

3.000 

4.000 

5.000 
10,000 

2,222 

3,333 

4,444 

5,555 

11,110 

2,500 

3,750 

5,000 

6,250 

12,500 

2,956 

4,384 

5,912 

7,340 

3,333 

4,999 

6,666 

4.000 

6.000 
8,000 

5,000 

7,500 

6,666 

Chain  and  barrier  pillars  vary  in  size  even  more  than  shaft  pillars,  and  their 
widths  are  almost  entirely  determined  by  local  considerations.  In  some 
States,  the  minimum  width  of  barrier  pillars  is  regulated  by  law. 

Barrier  Pillars.— For  finding  the  width  of  barrier  pillars  in  anthracite 
seams,  the  following  formula,  adopted  conjointly  by  the  chief  mining  engi- 
neers of  the  Lehigh  & Wilkes-Barre  Coal  Co.,  Susquehanna  Coal  Co.,  D.,  L.  & 
W.  R.  R.  Co.,  Delaware  & Hudson  C?inal  Co.,  and  the  State  mine  inspectors 
of  Eastern  Pennsylvania,  is  recommended: 

Formula  for  width  of  barrier  pillars:  (Thickness  of  workings  X l^of  depth 
below  drainage  level)  + (thickness  of  workings  X 5). 

Thus,  for  a seam  6 ft.  thick,  400  ft.  below  drainage  level,  the  barrier  pillar 
should  be  (6  X 4)  p (6  X 5)  = 54  ft. 


288 


METHODS  OF  WORKING. 


^ % 


ft  + 


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Thickness  Mined 
From  Seam. 

•••!**tJ»J***«*«!*!**J! 

j»l!**«I**Ij*»***;*II*I 

: i : : i i : : : i i i i i i i i : ! : : i : 

: : • J : • i • : ' 5 J i 2 : ; 5 I 5 • t ! ! 







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>^«v^Tii^~CVJCVJCVJC\iCV|OiJ 

Each  adjoining  owner  is  to  leave  one-half  of  the  pillar  thickness  required. 


PILLAR  DRAWING. 


289 


Compressive  Strength  of  Anthracite.— Attention  has  recently  been  called  by 
Mr.  William  Griffith,  of  Scranton,  Pa.,  to  the  advisability  of  testing  the 
strength  of  the  different  coals  and  of  using  this  data  as  a basis  for  the  proper 
proportioning  of  the  pillars  and  for  determining  the  probability  of  a squeeze. 
In  some  crude  experiments,  which  Mr.  Griffith  carried  on,  he  found  that 
different  coals  from  even  the  same  locality  varied  greatly  in  their  strengths. 
If  attention  were  given  to  this  matter,  probably  the  sizes  of  pillars  could 
be  calculated  on  a much  more  certain  basis  than  is  possible  at  present, 
and  the  liability  to  squeeze  lessened. 

The  table  on  page  290  gives  the  results  of  some  preliminary  and  crude 
tests  made  by  Mr.  Griffith,  which  supply  the  only  data  available  as  to  the 
crushing  strength  of  anthracite  coal. 

Drawing  pillars  is  about  the  most  dangerous  work  the  miner  has  to  perform, 
but  the  fact  of  its  being  so  is  no  doubt  the  reason  why,  comparatively 
speaking,  so  few  serious  accidents  happen  in  it.  It  is  not  so  much  that  the 
best,  most  skilled  workmen  are  chosen  to  perform  pillar  drawing,  as  that 
the  men,  being  alive  to  the  dangers,  are  more  on  the  alert  and  careful  to 
protect  themselves. 

Sometimes,  if  not  very  often,  in  chamber  or  room-and-pillar  working  it  is 
the  custom  to  work  out  the  rooms  or  chambers  and  leave  pillars  all  the  way 
from  the  shaft  to  the  boundary  line  over  large  areas;  in  other  words,  the 
portion  of  the  roof  left  standing  on  pillars  is  very  extensive.  Mines  so 
worked  have  sometimes  been  spoken  of  as  mines  on  stilts.  To  this  mode  of 
proceeding  there  are  several  serious  objections.  By  leaving  the  pillars  until 
the  boundary  has  been  reached,  a large  number  of  airways  and  roadways 
have  to  be  kept  open  and  in  repair,  and  this  number  is  constantly  increasing 
until  the  limits  of  the  workings  have  been  reached.  This  circumstance 
renders  the  ventilation  more  difficult,  and  thereby  increases  risks  of 
accident.  Moreover,  the  length  of  time  during  which  the  old  rooms  and 
pillars  are  left  open  and  standing  increases  the  danger  of  squeeze  and  creep 


Fig.  5.  Fig.  6. 


setting  in,  by  which  a large  area  may  in  a short  time  be  overrun.  Also,  by 
this  method,  the  pillars  first  formed  are  last  removed,  and  hence  it  happens 
that  a large  number  of  them  crack  and  give  way  under  the  combined  action 
of  atmospheric  agencies  and  great  pressure.  Even  if  they  resist  these  actions 
well,  the  quality  of  the  coal  greatly  deteriorates  by  the  long  exposure. 

For  the  above  reasons,  it  is  the  best  practice  to  carry  on  the  two  workings 
(working  the  rooms  and  drawing  the  ribs  and  pillars)  simultaneously.  By 
so  doing,  the  length,  mean  duration  of  the  roadways,  etc.  are  reduced,  and 
the  pillar  coal  obtained  in  much  better  condition;  and,  in  order  to  concen- 
trate the  workings  as  much  as  possible,  the  two  operations  should  go  on  as 
closely  together  as  practicable.  With  fairly  thick  and  very  soft  coals,  the 
rapid  working  up  of  the  rooms  and  equally  quick  drawing  of  the  ribs,  as 
soon  as  the  rooms  are  driven  their  full  distance,  is  essential  to  economical 
working;  for  delay  in  extracting  ribs  and  pillars  in  such  circumstances 
results  in  their  getting  crushed  and  the  coal  lost  or  largely  ground  to  slack, 
waste  of  props  and  material,  disordered  ventilation,  and  shortened  life  of 
the  mine. 

Methods  of  drawing  pillars  vary  according  to  the  inclinations  of  the 
seams,  the  nature  of  the  roof  and  fioor,  and  the  character  of  the  coal.  Figs. 
5 and  6 show  the  common  methods.  In  Fig.  b,  A,  B,  and  C,  the  drawing 
begins  by  cross-cutting  the  fast  ends  of  the  pillars  to  obtain  a retreating 
face.  A shows  a method  for  soft  coal  and  narrowing  pillars,  B for  wide 


Tests  of  Compressive  Strength  of  Sawed  Pieces  of  Anthracite  Coal. 


290 


METHODS  OF  WORKING. 


Remarks. 

Checker  coal  from  Exeter. 

Checker  coal  M.  W.  coal  pile. 

Checker  coal  bottom  of  Clear  Spring  colliery. 

Clear  Spring  Pittston  vein  glassy  coal. 

Clear  Spring  Marcey  checker  coal. 

Clear  Spring  Marcey  checker  coal. 

Clear  Spring  Marcey  checker  coal. 

Clear  Spring  Marcey.  Very  good  test.  Checker  coal. 
Clear  Spring  Marcey.  Knot  in  block.  Not  fair  test. 
Clear  Spring  reddish  glassy  coal. 

Clear  Spring  reddish.  Not  fair  average  test. 

Crushing 
Weight.  Tons. 
Deduced. 

Per 
Cu.  In. 

I>T-lC<JOO«Dl>l>05C<l^ 

GO  OS  rH  Ca  O rH  rH  rH  <M  Oi  ^ 

Ci  TjH  Tji  Tl?  GO  lO  CO  lO  CO 

4.67 

Per 
Sq.  In. 

GO 

T}HOCOGOCOl'-'^Tt<GOTH(--. 

cic4rHOrHr-5iHCOOitH'^ 

Breaking 
Weight.  Tons. 
Deduced. 

Per 
Cu.  In. 

C5  O O <N 
c^c^c^.  05  lO  00  CO  tJH  O 

'CO  ci  c4  c4  c4  th  CO 

2.70 

Per 
Sq.  In. 

CD 

.^-^..-vCO  05  uo  00  O O 

C-.  I>.  c^.  C-.  lO  05  rH  GO  lO  Tfl  tH 

j j ,_| 

Average 

Weight 

Sustained. 

Crush- 

ing. 

Tons. 

I>iQlOOlOlOI>OOOC<lO 

CO(NCOCOI>COOII>»OCOw 

Break- 

ing. 

Tons. 

28(?) 
17  ?) 
30  (?) 
28(?) 
30 

20 

22 

38 

32 

22 

30 

Dimensions  of  Test 
Piece. 

’53 

W 

-.la 

r-l(M(MiCCDCO(MrHi-HCOC<l 

A 

Ha*’ESrt|+  -.iM-l't-'Iet-'letrtk 

COC0rt<COl>'^'«f«^-^l>u0 

Length. 

nlwoH-  -I*  H«-'le<-‘l«-'lo«-ila-Ic» 

TftCOiOCDOOTfTfrtlTtt^iO 

•^isax  JO 
J8quin>^ 

iHC<JC0^iOCDl>00  05O^  1 

rH  tH  1 

pillars,  the  end  being 
taken  in  two  lifts,  while 
C is  for  harder  coal  and 
shows  it  taken  in  three 
lifts.  D and  E show  the 
pillars  cut  into  stocks  to 
be  drawn  by  side  or  end 
lifts,  according  to  the 
character  of  the  coal,  the 
inclination  of  the  seam, 
thickness  of  the  cover, 
and  the  strength  or  weak- 
ness of  the  roof  and  floor. 
Fig.  6 shows  some  of  the 
methods  used  in  robbing 
the  pillars  in  steep  pitch- 
ing, thick  beds  of  anthra- 
cite. To  get  the  coal  out 
of  the  pillar  at  the  left 
of  A,  a skip  is  taken  off 
the  side,  as  shown.  Suc- 
cessive skips  are  thus 
taken  off  until  the  whole 
is  removed,  the  miner 
keeping  the  manway 
open  to  the  heading  be- 
low as  a means  of  retreat. 
The  pillar  between  A 
and  B is  very  similarly 
worked.  To  remove  that 
between  B and  C,  a nar- 
row chute  or  heading  is 
driven  up  the  middle, 
and  cross-cuts  put  to  the 
right  and  left  a few  yards 
from  the  upper  end. 
Shots  are  placed  in  the 
four  blocks  of  coal  thus 
formed,  as  shown,  and 
they  are  fired  simultane- 
ously by  battery.  This 
operation  is  repeated  in 
each  descending  portion 
unless  the  pillar  begins 
to  run.  A pillar  from 
which  the  coal  has 
started  to  run  is  shown 
to  the  right  of  C. 

To  secure  the  highest 
percentage  of  pillar  coal, 
a method  should  be 
adopted  that  will  pre- 
vent squeezing  or  crush- 
ing, if  possible.  All  the 
pillars  in  a panel  may  be 
taken  out  at  the  same 
time  by  end  lifts  in  such 
a way  as  to  keep  the  face 
of  all  the  lifts  in  line  and 
perpendicular  to  the 
sides  of  the  pillars,  or 
the  pillars  are  drawn  in 
lifts  of  three  or  more 
pillars  each,  the  centers 
of  the  face  of  the  lifts 
lying  in  a straight  line 
that  makes  an  angle  of 
about  40°  with  the  sides 


ROOM-AND-PILLAR  METHODS. 


291 


of  the  pillars.  (See  also  “ Flushing  of  Culm,”  which  is  described  fully  on 
page  314.) 

Gob  fires  are  due  to  the  spontaneous  ignition  of  coal,  and  are  most  likely 
to  occur  in  pack  walls  and  gobs  where  there  is  an  insufficiency  of  air.  Ample 
ventilation  is  the  best  preventive. 

Spontaneous  Combustion.— According  to  Prof.  Able,  Dr.  Percy,  and  Prof. 
Lewes,  the  causes  of  the  spontaneous  ignition  of  coal  are:  Urst,  and  chiefly, 
the  condensation  and  absorption  of  oxygen  from  the  air  by  the  coal,  which 
of  itself  causes  heating,  and  this  promotes  the  chemical  combination  of  the 
volatile  hydrocarbons  in  the  coal  and  some  of  the  carbon  itself  with  the 
condensed  oxygen.  This  process  may  be  described  as  self-stimulating,  so 
that,  with  conditions  favorable,  sufficient  heat  may  be  generated  to  cause 
the  ignition  of  portions  of  the  coal.  The  favorable  cond^itions  are:  A mod- 
erately high  external  temperature;  a broken  condition  of  the  coal,  affording 
the  fresh  surfaces  for  absorbing  oxygen;  a supply  of  air  sufficient  for  the 
purpose,  but  not  in  the  nature  of  a strong  current  adequate  to  remove  the 
heat;  a considerable  percentage  of  volatile  combustible  matter  or  an 
extremely  divided  condition.  Second,  moisture  acting  on  sulphur  in  the 
form  of  iron  pyrites.  The  heating  effect  of  this  second  cause  is  very  small, 
and  it  acts  rather  by  breaking  the  coal  and  presenting  fresh  surfaces  for  the 
absorption  of  oxygen. 

Coal  Storage.— Prof.  Lewes  gives  the  following  recommendations  for  the 
storage  of  coal:  “The  coal  store  should  be  well  roofed  in,  and  have  an  iron 
floor  bedded  in  cement;  all  supports  passing  through  and  in  contact  with 
the  coal  should  be  of  iron  or  brick;  if  hollow  iron  supports  are  used,  they 
should  be  cast  solid  with  cement.  The  coal  must  never  be  loaded  or  stored 
during  wet  weather,  and  the  depth  of  coal  in  the  store  should  not  exceed 
8 ft.,  and  should  only  be  6 ft.  where  possible.  Under  no  condition  must  a 
steam  or  exhaust  pipe  or  flue  be  allowed  in  or  near  any  wall  of  the  store, 
nor  must  the  store  be  within  20  ft.  of  any  boiler,  furnace,  or  bench  of  retorts. 
No  coal  should  be  stored  or  shipped  to  distant  ports  until  at  least  a month 
has  elapsed  since  it  was  brought  to  the  surface.  Every  care  should  be  taken 
during  loading  or  storing  to  prevent  breaking  or  crushing  of  the  coal,  and 
on  no  account  must  a large  accumulation  of  small  coal  be  allowed.  These 
precautions,  if  properly  carried  out,  would  amply  suffice  to  entirely  do 
away  with  spontaneous  ignition  in  stored  coal  on  land.” 

When  the  coal  pile  has  ignited,  the  best  way  to  extinguish  the  fire  is  to 
remove  the  coal,  spread  it  out,  and  then  use  water  on  the  burned  part.  The 
incandescent  portion  is  invariably  in  the  interior,  and  when  the  fire  has 
gained  any  headway  usually  forms  a crust  that  effectually  prevents  the 
water  from  acting  efficiently. 


MODIFICATIONS  OF  ROOM-AND-PILLAR  METHODS. 

Some  modifications  of  the  room-and-pillar  plan  shown  in  Fig.  1 can 
usually  be  applied  to  seams  whose  dip  does  not  exceed  3°.  When  the  pitch 
is  greater,  rooms  are  often  turned  ofl*  toward  the  rise  only,  and  the  cross- 
entries driven  correspondingly  closer  together.  When  the  pitch  is  from 
5°  to  10°,  the  cars  may  still  be  taken  to  the  face  if  the  rooms  are  driven 
across  the  pitch,  thus  making  an  oblique  angle  with  an  entry  or  gangway, 
the  rooms  being  known  as  room  breasts. 

Buggy  Breasts.— For  inclinations  between  10°  and  18°,  that  is,  after  mule 
haulage  becomes  impossible  and  until  the  coal  will  slide  in  chutes,  buggies 
are  often  used.  Fig.  8 shows  a buggy  breast  in  plan  and  section.  Coal  is 
loaded  into  a small  car  or  buggy  c,  which  runs  to  the  lower  end  of  the  breast 
and  there  delivers  the'  coal  upon  a platform  I,  from  which  it  is  loaded  into 
the  mine  car.  The  refuse  from  the  seam  is  used  in  building  up  the  track, 
and  if  there  is  not  sufficient  refuse  for  this,  a timber  trestle  is  used. 

Another  form  of  buggy  breast  is  shown  in  Fig.  7.  Here  the  coal  is 
dumped  directly  into  the  mine  car  from  the  buggy.  If  the  breast  pitches 
less  than  6°,  the  buggy  can  be  pushed  to  the  face  by  hand,  but  in  rooms  of 
a greater  pitch,  a windlass  is  permanently  fastened  to  timbers  at  the  bottom 
of  the  breast,  while  the  pulleys  at  the  face  are  temporarily  attached  to  the 
props  by  chains,  so  that  they’  can  be  advanced  as  the  face  advances.  The 
rope  used  is  from  i in.  to  | in.  in  diameter,  and  any  form  of  ordinary 
horizontal  windlass  can  be  used.  With  the  windlass  properly  geared,  one 
man  can  easily  haul  a buggy  to  Ihe  lace  of  a breast  in  a few  minutes  time. 
The  buggy  runs  upon  20-lb.  T rails  spiked  with  2U'  X I"  spikes  upon  2"  X 4" 


892 


METHODS  OF  WORKING, 


hemlock  studding  sawed  into  lengths  of  14  ft.  This  system  has  been 
thoroughly  tested  by  the  Delaware  & Hudson  Canal  Co.,  Scranton,  Pa., 
und  has  proved  a very  successful  and  economical  one. 

Chute  Breasts.— Seams  pitching  more  than  15°  are  usually  worked  by 
chutes,  or  self-acting  inclines.  When  the  pitch  is  between  15°  and  30°,  sheet 
iron  is  laid  to  furnish  a good  sliding  surface  for  the  coal.  On  inclinations 
of  less  than  18°  to  20°,  it  is  usually  necessary  to  push  the  coal  down  the 
chute.  Sheet  iron  is  not  required  on  pitches  above  30°.  It  must  be  remem- 
bered that  these  pitches  are  only  fair  averages,  as  much  depends  on  the 
character  of  the  coal.  Anthracite  slides  more  easily  than  bituminous.  To 
secure  the  best  returns  from  a coal  seam,  the  slope  or  shaft  should  be  driven 
the  basin,  and  the  lowest  gangways  or  levels  first  driven  to  the  property 
■imits,  and  the  coal  then  worked  retreating  toward  the  slope  or  shaft. 
Practice  is,  however,  usually  contrary  to  this,  and  the  upper  levels  or  gang- 
ways are  turned  off  first,  and  working  places  opened  out  as  rapidly  as  the 
gangway  is  driven.  Fig.  9 shows  a method  of  grouping  rooms  that  may  be 


Fig.  7. 


used  where  the  pitch  is  from  8°  to  20°,  the  straight  heading  being  driven  on 
the  strike  and  the  other  headings  at  such  angles  as  will  give  a good  grade 
for  haulage  purposes. 

, T^®.P!l'3r-and-5tall  system  is  a modification  of  the  room-and-pillar,  to 
which  It  is  similar  in  all  respects  excepting  in  the  relative  size  of  the  pillars 
and  breasts.  The  stalls  are  usually  opened  narrow  and  widened  inside, 
according  to  conditions  of  roof,  floor,  coal,  depth,  etc.,  being  from  4 to  6 yd. 
in  the  single-stall  method,  with  the  pillars  about  the  same  width.  Fig.  10, 
A and  B,  shows  single  and  double  stalls.  This  system  is  adapted  to  weak  roof 
and  floor,  or  strong  roof  and  soft  bottom,  to  a fragile  coal,  or  wherever 
ample  support  is  required,  and  is  particularly  useful  in  deep  seams  with 


CONNELLSVILLE  METHOD, 


293 


great  roof  pressure.  Double  stalls  are  often  driven  from  12  to  15  yd.  wide, 
with  an  intervening  pillar  of  sometimes  30  yd. 

The  following  are  a few  of  the  applications  of  the  pillar-and-stall  method 
of  working  as  they  are  carried  out  in  some  of  the  leading  coal  fields  of 
America: 

Connellsville  Region  (if.  L.  Auchmuty), — Fig.  11  shows  the  common  method 
used  in  the  Connellsville,  Pa.,  region.  The  average  dip  is  about  5^.  The 
face  and  butt  headings  are  driven,  respectively,  at  right  angles  to  each 
other  on  the  face  and  the  butt  of  the  coal.  The  face  headings  leave 


the  main  butts  about  1,000  ft.  apart,  while  from  these  face  headings,  and 
400  ft.  apart,  secondary  butts  are  driven,  and  again  from  these  butts  on 

the  face  of  the  coal  the 
rooms  or  wide  work- 
ings are  excavated  to  a 
length  of  300  ft.,  this 
having  proved  the  most 
convenient  length  for 
economical  working. 
Room  pillars  have  a 
thickness  of  30  to  40 
ft.,  while  the  rooms  are 
12  ft.  in  width  and  are 
spaced  42  to  52  ft. 
between  centers,  de- 
pending on  depth  of 
strata  over  the  coal. 
The  headings  are  8 ft. 
wide,  and  in  all  main 
butts  and  faces  the  dis- 
_ tance  between  centers 

Fig.  9.  of  parallel  headings  is 

_ . 60  ft.,  leaving  a. solid 

rib  of  52  ft.  A solid  rib  of  60  ft.  is  also  left  on  the  side  of  each  main 

beading  The  «average  thickness  of  cover  at  tlie  I.eith  mine,  which 


294 


METHODS  OF  WORKING, 


is  here  described  and  which  may  be  considered  as  a type  of  the  region, 
is  250  ft.,  the  overlying  measures  being  alternated  layers  of  soft  shale 

and  coal  for  4 ft.  The  bottom  is 
an  18"  layer  of  hard  fireclay 
and  slate.  These  floor  and  roof 
materials  are  soft,  and  are  easily 
disintegrated  by  air  and  water. 
At  some  mines,  cover  will  reach 
as  much  as  700  ft.,  and  the  dip  of 
55^  (as  at  Leith)  is  much  heavier 
at  some  points  on  eastern  out- 
crop, and  will  run  as  high  as  12^, 
flattening  off  as  the  synclinal  line 
of  the  basin  is  reached,  until  it  is 
almost  level.  In  some  localities, 
the  material  below  coal  is  hard 
limestone,  requiring  blasting  to 
remove  it,  and  at  other  places 
the  roof  slates  are  much  more 
solid  than  at  Leith,  and  not  read- 
ily disintegrated.  The  method 
of  drawing  ribs  is  one  of  the  beauties  of  the  system,  since  it  is  harder  to  do 
successfully  in  a soft  coal  like  the  Connellsville  coal  than  in  hard  coal.  The 


Fig.  11. 


CLEARFIELD  METHOD. 


295 


coal  iiself  is  firm.  When  necessary  to  protect  the  top  or  bottom,  4 to  6 in.  of 
coal  are  left  covering  the  soft  material. 

The  method  as  given  above  is  often  applied  to  a whole  series  of  butts 
(4  or  5)  at  once  instead  of  to  butt  by  butt,  as  shown  in  Fig.  11.  In  this  case, 
work  IS  started  at  the  upper  end  of  the  uppermost  butt  and  progresses,  as 
shown  in  Fig.  11;  but,  after  cutting  across  the  butt  heading  from  which  the 
rooms  were  driven,  the  butt  heading  itself  and  the  upper  rooms  from  the 
second  butt,  or  that  just  before,  are  likewise  drawn  back  by  continuous 
slices  being  removed  from  the  rooms  of  the  upper  butt,  and  on  across  the 
next  lower  butt,  etc.,  all  on  an  angle  to  the  butts,  and  so  continued  as  the 
operations  progress,  until  another  butt  is  reached,  etc.,  thus  gradually 
making  a longer  and  longer  line  of  fracture,  which  is  only  limited  by  the 
number  of  butts  it  is  desired  to  include  at  one  time  in  the  section  thus 
mined.  This  works  very  nicely  and  makes  long  even  lines  of  fracture,  the 
steps  of  the  face  of  the  workings  (in  the  rib  drawing)  being  about  30  ft. 
ahead  of  one  another. 

Pittsburg  Region  {H.  L.  Auchmuty). — The  coal  is  worked  in  much  the  same 
way  as  in  the  Connellsville  region,  except  that  a different  system  of  drawing 
ribs  is  used.  The  coal  is  worked  on  the  room-and-pillar  system,  with  double 
entries,  with  cut-throughs  between  for  air,  and  on  face  and  butt,  entries  are 
about  9 ft.  wide,  and  the  rooms  21  ft.  wide  and  about  250  ft.  long;  narrow  (or 
neck)  part  of  room,  21  ft.  long  by  9 ft.  wide;  room  pillars,  15  to  20  ft.  wide, 
depending  on  depth  of  strata  over  the  coal,  which  is  from  a few  feet  to 
several  hundred  feet.  The  mining  is  done  largely  by  machines  of  various 
types.  Coal  is  hard,  of  course,  and,  in  many  places,  the  roof  immediately 
oVer  the  coal  is  also  quite  hard.  There  are  about  4 ft.  of  alternate  layers  of 
hard  slate  and  coal  above  the  coal  seam.  Rooms  are  mined  from  lower  end 
of  butt  as  fast  as  butt  is  driven,  the  ribs  being  drawn  as  mining  progresses. 
As  the  coal  is  harder  than  in  the  Connellsville  region,  thickness  of  coal 
pillar  between  parallel  entries  is  somewhat  less. 

Clearfield  Region  {G.  F.  Duck). — The  butt  and  face  are  not  strongly  marked 
in  the  B or  Miller  seam,  the  one  chiefly  worked  in  this  region.  Where 
possible,  these  cleavages  are  followed  in  laying  out  the  workings,  but  the 
rule  is  to  drive  to  the  greatest  rise  or  dip  and  run  headings  at  right  angles  to 
the  right  and  left,  regardless  of  anything  else.  The  main  dip  or  rise  heading 
is  usually  driven  straight,  and  is  raised  out  of  swamps  or  cut  down  through 
rolls — very  common  here — unless  they  are  too  pronounced,  when  the  head- 
ing is  curved  around  them.  The  same  is  true  of  room  headings,  except  that 
they  are  more  usually  crooked,  not  being  graded  except  over  very  minor 
disturbances. 

As  the  B seam  rarely  runs  over  4 ft.  in  thickness,  and  is  worked  as  low  as 
2 ft.  8 in.  in  the  haulage  headings,  the  roof  is  taken  down  to  give  5 ft.  to 
5 ft.  2 in.  above  the  rail,  or  5 ft.  8 in.  to  5 ft.  10  in.  in  the  clear.  Where  the 
resulting  rock  is  taken  outside,  the  headings  are  driven  10  ft.  wide  with 

24  ft.  of  pillar,  roof  taken  down  in  haulage  heading  but  not  in  air-course. 
Where  the  rock  is  gobbed  underground,  the  haulage  heading  is  18  to  24  ft. 
wide,  air-course  10  ft.,  pillar  24  ft.,  and  roof  taken  down  in  haulage  heading 
only.  The  thinner  the  coal,  the  wider  the  heading.  It  is  more  economical 
to  haul  the  rock  to  daylight.  The  bottom  generally  consists  of  3 ft.  to  5 ft.  of 
hard  fireclay,  frequently  carrying  sulphur  balls. 

In  numerous  places,  the  sand  rock  is  immediately  over  the  coal,  but  in 
most  cases  there  is  from  3 to  5 ft.  of  slate  before  the  sand  rock  is  reached. 
Room  headings  are  driven  280  ft.  apart,  haul  rock  to  daylight,  heading  10  ft. 
wide  with  24  ft.  pillar  to  10  ft.  air-course,  in  which  roof  is  left  up.  A 15  ft.  to 

25  ft.  chain  pillar  is  left  between  air-course  and  faces  of  rooms  from  the  lower 
heading,  every  fourth  to  eighth  of  which  is  driven  through  to  the  air-course 
to  shorten  the  travel  of  the  air.  The  rooms  are  therefore  180  to  200  ft. 
long,  and  the  men  push  the  cars  to  the  face,  an  important  economical  item 
in  this  thin  coal. 

Rooms  are  21  ft.  wide  with  a 15  ft.  pillar,  and  a 15  ft.  chain  pillar  is  left 
between  the  first  room  on  any  room  heading  and  the  main  heading,  and 
roof  is  not  taken  down  in  rooms.  Main-heading  track  is  usually  30-lb.  iron, 
room  heading,  12  lb.,  and  2"  X strap  iron  set  on  edge  is  used  in  the  rooms 
in  low  coal.  Mine  cars  hold  from  600  to  800  lb.  in  low  seams,  and  1,500  to 
2,000  lb.  in  the  so-called  thick  seams,  i.  e.,  3 ft.  8 in.  to  4 ft.  thick. 

Reynoldsville  Region.— The  measures  are  very  regular,  and  the  method 
employed  the  typical  one  shown  in  Fig.  1.  The  average  thickness  of  the 
principal  seam  is  6^  ft.  and  the  pitch  is  3°  to  4°.  The  coal  is  hard  and  firm, 


296 


METHODS  OF  WOBKINQ, 


and  contains  no  gas;  the  cover  is  light,  and  on  top  of  the  coal  there  are 
3 or  4 ft.  of  bony  coal;  the  bottom  is  fireclay.  Drift  openings  and  the  double- 
entry system  are  used.  Both  main  and  cross-entries  are  10  ft.  wide,  with  a 
24-ft.  pillar  between.  The  cross-entries  are  600  ft.  apart,  and  a 24  ft.  chain 
pillar  is  left  along  the  main  headings.  The  rooms  are  about  24  ft.  wide 
and  open  inbye,  the  necks  being  9 ft.  wide  and  18  ft.  long.  The  pillars  are 
from  18  to  30  ft.  thick. 

West  Virginia  {James  W.  Paul).—T\iQ  general  plan  of  working  the  Pitts- 
burg coal  in  the  northern  part  of  West  Virginia  is  as  follows.  The  coal 
measures  vary  from  7 to  8 ft.  in  thickness,  and  have  a covering  varying 
from  50  to  500  ft.  The  coal  does  not  dip  at  any  place  over  5^.  In  most  places  the 
coal  is  practically  level,  or  has  just  sufficient  dip  to  afford  drainage.  The  usual 
method  of  exploitation  is  to  advance  two  parallel  headings,  30  ft.  apart,  on  the 
face  of  the  coal.  At  intervals  of  500  to  600  ft.,  cross-headings  are  turned  to  right 
and  left,  and  from  these  headings  rooms  are  turned  off.  These  cross-headings 
are  driven  in  pairs  about  20  or  30  ft.  apart.  Between  the  main  headings  and 


Fig.  12. . 


the  first  room  is  left  a block  of  coal  about  100  ft.,  and  on  the  cross-headings 
there  is  often  left  a barrier  pillar  of  100  ft.  after  every  tenth  room. 

The  headings  are  driven  from  8 to  12  ft.  wide,  and  the  rooms  are  made 
24  ft.  wide  and  250  to  300  ft.  long.  A pillar  is  left  between  the  rooms 
about  15  to  20  ft.  wide.  These  pillars  are  withdrawn  as  soon  as  the  panel 
of  rooms  has  been  finished.  The  rooms  are  driven  in  from  the  entry  about 
10  ft.  wide  for  a distance  of  20  ft.,  and  then  the  room  is  increased  in  width  on 
one  side.  The  track  usually  follows  near  the  rib  of  the  room.  Cross-cuts 
on  the  main  and  cross-headings  are  made  every  75  to  100  ft.,  and  in  rooms 
about  every  100  ft.  for  ventilation. 

The  double-heading  system  of  mining  and  ventilation  is  in  vogue.  Over- 
casts are  largely  used,  but  a great  many  doors  are  used  in  some  of  the 
mines.  Rooms  are  worked  in  both  directions.  This  is  the  general 
practice  when  the  grades  are  slight.  When  the  coal  dips  over  1^,  the 
rooms  are  driven  in  one  direction  only.  In  this  case,  the  rooms  are 
made  longer,  as  much  as  350  ft.  It  is  the  custom  then  to  break  about 
every  third  room  into  the  cross-heading  above  (a  practice  ill  advised), 
floor  of  this  bed  of  coal,  being  composed  of  shale  and  fireclay,  ofteu 


ALABAMA  METHODS. 


297 


heaves,  especially  when  it  is  made  wet.  Some  trouble  is  at  times  experi- 
enced by  having  the  floor  heave  by  reason  of  the  pillars  being  too  small  for 
the  weight  they  support. 

The  dimensions  of  rooms  and  pillars  given  are  for  a mine  (with 
covering  300  to  500  ft.  thick)  having  a fairly  good  and  strong  roof.  Where 
roof,  bottom,  and  thickness  of  cover  change,  these  dimensions  are  altered  to 
suit  the  requirements.  The  main-heading  pillars  may  be  reduced  to  30  or 
40  ft.;  the  rooms  may  be  made  15  ft.  wide  with  12  ft.  pillars,  and  no  barrier 
pillars  may  be  left  on  the  cross-headings. 

The  foregoing  plan  is  very  much  followed  in  other  parts  of  the  State;  at 
least  an  attempt  is  made  to  do  so,  but  local  disturbances  often  require 
changes  in  the  plan.  This  plan  is  followed  on  some  parts  of  New  River, 
and  also  in  the  Flat  Top  field. 

Alabama  Methods  (J.  E.  Strong).— Fig.  12  shows  the  common  methods  used 
in  working  the  Alabama  coals.  The  seams  now  working  vary  from  2 to 
6 ft.  thick,  and  they  pitch  from  2°  to  40°.  Where  the  seams  are  thin,  the 
coal  is  hard,  and  pillars  of  about  20  to  30  ft.  are  used  to  support  the  roof. 


Fig.  13. 

The  thick  seams  are  soft  and  easily  broken,  and  much  larger  pillars  are  left. 
The  character  of  bottom  and  top  varies;  fireclay  bottom  and  slate  roof  are 
usually  found  with  the  thick  seams,  and  hard  bottom  and  sandstone  roof 
with  the  thin  seams.  The  general  plan  of  laying  out  the  mine  is  to  drive 
the  slope  straight  with  the  pitch  of  the  seam;  this  is  usually  on  the  butts  of 
the  coal.  A single-track  slope  is  8 ft.  wide,  and  a double-track  slope  16  It. 
Cross-headings  are  driven  or  turned  from  the  slope  water  level  every 
300  ft.;  air-courses  are  driven  parallel  on  either  side  of  the  slope.  Where 
an  8 ft.  slope  is  driven,  30  ft.  of  pillar  are  left  between  the  slope  and  airway, 
and  for  a 16  ft.  slope,  30  ft.  of  pillar.  The  size  of  pillar,  however,  depends 
largely  on  the  character  of  the  roof  and  thickness  and  strength  of  coal.  On 
the  lower  side  of  the  headings,  pillars  from  20  to  60  ft.  are  left  on  the 
entry  before  turning  the  first  room.  The  rooms  are  worked  across  the  pitch 
on  an  angle  of  about  5°  on  the  rail.  Fig.  12,  A,  when  the  coal  does  not 
pitch  greater  than  20°;  where  the  pitch  is  greater,  chutes  are  worked  and 
the  rooms  are  driven  straight  up  the  pitch  (Fig.  12,  R).  In  a few  cases, 
where  the  pitch  is  not  greater  than  15°,  double  rooms  are  worked  with  two 
roadways  in  each  room  (Fig.  12,  C).  A rope  with  two  pulleys  is  used,  and 
each  track  keeps  the  rib  side  of  the  room,  the  loaded  car  pulling  up  the 
empty  on  the  opposite  side  of  the  room;  distance  between  room  centers, 
about  42  ft.  Where  single  rooms  are  worked,  the  room  is  driven  narrow 
(8  ft.  wide)  for  21  ft.,  when  connections  are  made  with  the  room  outside  of 
it;  the  room  is  then  widened  out  to  about  25  ft.,  sloping  gradually  until  this 
width  is  at  tained;  pillars  of  from  10  to  20  ft.  thick  are  left  between  the 
rooms,  and  cross-cuts  for  ventilation  are  made  about  every  50  ft.;  every  third 
or  fourth  room  is  driven  through  to  the  entry  above;  pillars  are  then  drawn 
back  to  the  entry  stumps  or  pillars.  The  average  cover  over  the  coal  now 
workiim  is  from  100  to  600  ft.  Air-courses  usually  have  an  area  of  30  ft., 
and  sumcient.coal  is  taken  out  to  give  this  area,  the  roof  and  bottom  being  left. 

George’s  Creek  District,  Md. — Fig.  13  shows  the  method  used  in  the  George’s 
Creek  field,  Maryland.  The  coal  shows  no  indication  of  cleats,  and  the 
butts  and  headings  can  be  driven  in  any  direction.  The  main  heading  is 
driven  to  secure  a light  grade  for  hauling  toward  the  mouth.  Cross- 
headings making  an  angle  of  35°  to  40°  are  usually  driven  directly  to  the 


298 


METHODS  OF  WORKING. 


rise,  and  of  the  dimensions  shown.  Pillars  are  drawn  as  soon  as  the  rooms 
are  completed,  being  attacked  on  the  ends  and  from  the  rooms  on  either 
side,  the  coal  being  shoveled  to  the  mine  car  on  a track  in  the  room.  Very 
wide  pillars  are  split.  No  effort  is  made  to  hold  up  the  overlying  strata,  and 
the  entire  bed  is  removed  as  rapidly  as  possible.  An  extraction  of  85^  of  the 
bed  is  considered  good  work.  A section  of  the  seam  is  as  follows:  Roof 
coal,  10  in.;  coal,  7 ft.;  slate,  i in.;  coal,  10  in.;  slate,  i in.;  coal,  10  in.;  fireclay; 
slate.  The  top  bench  is  bony  and  frequently  left  in  place  to  prevent 


disintegration  of  the  roof  by  the  air.  Above  this  coal  is  from  8 to  10  ft.  of 
“rashiiigs,”  consisting  of  alternating  thin  beds  of  coal  and  shale,  that  is  very 
brittle,  and  requires  considerable  timber  to  keep  it  in  place.— (“Mines  and 
Minerals,”  Vol.  19,  page  422.) 

Blossburg  Coal  Region,  Pa.— Coal  is  generally  mined  from  drifts,  but  in  a 
few  cases  by  slopes.  Fig.  14  shows  the  general  method  adopted;  the  breasts 
are  run  at  right  angles  to  the  slips;  the  breast  pillars  are  split  by  a center 
heading  and  taken  out  as  soon  as  the  breasts  are  finished.  The  gangway 
pillars  are  taken  out  retreating  from  the  crop  or  boundaries  of  the  property. 


Fig.  15. 

The  general  average  of  the  coal  seams  is  not  over  3^  ft.,  accompanied  by 
fireclay  and  some  iron  ore.  The  dip  of  the  veins  is  about  3^. — (“  Mines  and 
Minerals,”  Vol.  19,  page  126.) 

Indiana  Coal  Mining.— Fig.  15  shows  the  double-entry  room-and-pillaT 
method  as  used  in  Indiana.  The  entries  are  generally  6 ft.  high,  8 ft.  broad, 


IOWA  METHOD. 


299 


the  minimum  height  required  by  law  being  4 ft.  6 in.  The  rooms  are  from 
21  to  40  ft.  in  width.  The  mines  are  generally  shallow.  The  rooms  in  Fig.  15 
are  shown  as  widened  on  both  ribs,  but  a more  usual  method  in  this  locality 
is  to  widen  the  room  on  the  inbye  rib,  leaving  one  straight  rib  for  the  protec- 
tion of  the  road  in  the  room. — (“Mines  and  Minerals,”  Vol.  20,  page  202.) 

Iowa  Coal  Mining. — The  coal  lies  at  a depth  of  200  ft.  below  the  surface,  and 
is  geologically  similar  to  that  of  the  Missouri  and  Illinois  fields.  It  lies  in 
lenticular  basins  extending  northwest  and  southeast  and  outcropping  in  the 
larger  river  beds.  The  seams  are  practically  level,  non-gaseous,  and  gen- 
erally underlaid  by  fireclay  and  overlaid  by  a succession  of  shales,  sand- 
stones, and  limestones,  which  are  generally  of  a yielding  nature,  giving  a 
strong,  good  roof  for  mining.  There  are  three  distinct  seams,  the  lower  one, 
which  varies  from  4 to  7 ft.  in  thickness,  being  the  only  one  worked.  The 
coal  is  a hard,  brittle,  bituminous  coal  that  shoots  with  difficulty,  but  is 
excellent  for  steam  and  domestic  uses.  About  Centerville,  the  coal  has  a 
distinct  cleat,  but  elsewhere  in  the  State  this  is  lacking. 

The  entry  pillars  along  the  main  roads  are  6 to  8 yd.  thick,  for  the 
cross-entries  5 to  6 yd.,  and  for  the  rooms  3 to  5 yd.  Room  pillars  are 
drawn  in  when  approaching  a cross-cut.  Both  room-and-pillar  and  longwall 
methods  are  in  use,  with  modifications  of  each.  In  the  room-and-pillar 
system,  the  double-entry  system  is  almost  invariably  used  in  the  larger 
mines.  Rooms  are  driven  off  each  entry  of  each  pair  of  cross-entries  at 
distances  of  30  to  40  ft.,  center  to  center;  the  rooms  are  8 to  10  yd.  in  width, 
and  pillars  3 to  4 yd.  The  rooms  are  narrow  for  a distance  of  3 yd.,  and  then 
widened  inbye  at  an  angle  of  45°  to  their  full  width.  They  vary  from  50  to 
100  yd.  in  length,  and  the  road  is  carried  along  the  straight  rib. 

When  double  rooms  are  driven,  the  mouths  of  the  rooms  are  40  to  50  ft. 
apart,  and  they  are  driven  narrow  from  the  entry  a distance  of  4 or  5 yd. 


Mdhwav 


Fig.  16. 


A cross-cut  is  then  made  connecting  them,  apd  a breast  16  yd.  wide  is  driven 
up  50  to  60  yd.  The  pillar  between  each  pair  of  rooms  is  12  to  15  yd. 

In  pillar-and-stall  work,  the  stalls  are  usually  turned  off  narrow  and 
widened  inside,  the  pillar  varying  from  5 to  8 yd.  The  stalls  are  30  to  40  yd. 
in  length,  and  the  pillars  are  drawn  back.  When  the  stalls  are  driven  in 
pairs,  the  pillar  8 to  10  yd.  in  width  is  carried  between  them. 

Longwall.— main  haulage  road  runs  in  each  direction  from  the  foot  of 
the  shaft,  and  on  both  sides  of  this  diagonal  roads  are  turned  at  an  angle  of 
45°,  or  parallel  to  the  main  haulageway.  These  are  spaced  10  yd.  apart  and 
driven  50  to  60  yd.,  when  they  are  cut  off  by  another  diagonal  road.  Panel 
breasts  are  used  where  the  conditions  are  such  as  to  induce  a squeeze. 
Rooms  are  turned  narrow  off  entries  and  are  arranged  in  sets  of  6 to  12 
rooms,  with  a pillar  10  to  20  yd.  wide  between  the  sets  of  rooms.  When  the 
rooms  have  progressed  a short  distance  from  the  entry,  they  are  connected 
by  cross-cuts,  and  the  longwall  face  is  carried  forward  from  this  point. 
Packs  are  built  and  the  roof  allowed  to  settle,  as  in  longwall.  The  wide 
pillars  are  taken  out  after  the  roof  has  settled. 


300 


METHODS  OF  WORKING. 


Ventilation.— system  of  ventilating  the  workings  usually  employed  is 
that  of  conducting  the  air  to  the  inside  workings  by  means  of  an  air-course 
forming  the  back  entry  of  each  haulage  road.  From  this  point  it  is  carried 
along  the  face  of  the  rooms,  through  the  breakthroughs  or  cross-cuts  in  the 
room  pillars,  returning  thence  to  the  haulage  road,  which  is  usually  made 
the  return  airway.  When,  however,  the  mine  is  ventilated  by  means  of  a 
furnace  or  an  exhaust  fan,  the  intake  airway  is  usually  made  the  haulage 
road,  in  order  to  avoid  doors  at  the  shaft  bottom. 

The  Tesla,  California,  method  is  shown  in  Fig.  16.  The  coal  seam  averages 
7 ft.  of  clear  coal,  and  pitches  60°.  This  system  was  adopted  in  a portion  of 
the  mine  to  get  coal  rapidly;  for,  at  this  point,  a short-grained,  slate  cap 
rock  came  in  over  the  coal,  making  it  difficult  to  keep  props  in  place.  The 
lioor  is  a close  blue  slate  and  has  a decided  heaving  tendency.  The  roof  is 
an  excellent  sandstone.  There  is  a small  but  troublesome  amount  of  gas. 
Two  double  chutes  are  driven  up  the  pitch  at  a distance  of  36  ft.  apart,  con- 
nected every  40  ft.  by  cross-cuts.  One  side  of  each  chute  is  used  for  a coal 
chute  and  the  other  for  a manway  and  air-course.  At  a distance  of  12  yd. 
apart  small  gangways  are  driven  parallel  with  the  main  mine  gangways. 
These  are  continued  from  each  chute  a distance  of  300  ft.,  if  the  conditions 
warrant  it.  The  top  line  is  then  attacked  from  the  back  end  and  the  coal  is 
worked  on  the  cleavage  planes;  the  breast,  or  room,  therefore  consists  of 
a 12-yd.  face,  including  the  drift  or  gangway  through  which  the  coal  is 
carried  to  the  chutes;  a rib  of  coal  (2  or  3 ft.)  is  left  between  the  breasts  to 
keep  the  rock  from  falling  on  the  breast  below.  Thus  in  each  breast  the 


N9 


Fig.  17. 


miners  have  a working  face  of  about  15  or  16  yd.,  and  as  the  coal  is  directed 
to  the  car  by  a light  chute,  moved  along  as  the  face  advances,  the  coal  is 
delivered  into  the  cars  at  small  cost,  and  but  little  loss  results  from  the 
falling  coal,  as  a minimum  of  handling  is  thus  obtained.  Immediately 
above  each  gangway,  and  starting  from  these  main  chutes,  an  angle  chute  is 
driven  at  about  45°,  connecting  with  the  breast  gangway  above  it,  and  into 
these  chutes  the  coal  from  that  breast  is  delivered,  runs  into  the  main  chute, 
and  from  it  is  loaded  into  the  mine  cars  in  the  main  gangway.  These  angle 
chutes  serve  as  a means  of  keeping  the  main  chute  full,  and  at  the  same 
time  giving  each  breast  an  opportunity  to  send  out  coal  continuously. 
They  also  serve  the  purposes  primarily  intended,  of  saving  the  coal  from 
breakage,  by  giving  it  a more  gradual  descent  into  the  mil  chute.  The 
breast  gangways  are  driven  5 ft.  wide.  No  timbers  are  needed  in  these 
gangways,  as  they  are  driven  in  the  coal,  except  on  the  foot-wall  or  floor 


TESLA  METHOD. 


301 


side,  which,  as  before  stated,  is  a firm  sandstone.  It  is  found  safest  to  leave  a 
rib  of  coal  on  the  top  of  the  breast  2 or  3 ft.  thick,  until  the  working  face  has 
passed  on  12  or  15  ft.,  when  this  rib  is  cut  out  and  thus  all  the  coal  extracted, 
the  roof  caving  behind  and  filling  in  the  opening.  As  cross-cuts  are  driven 
every  36  ft.,  ventilation  is  kept  along  the  worMng  faces,  and  a safe  and 
effectual  means  of  securing  all  the  coal  in  the  seam  is  thus  attained. 

Fig.  17  shows  another  system  used  in  No.  7 vein  at  the  same  place.  The 
seam  averages  7 ft.  of  coal.  The  roof  is  shelly  and  breaks  quickly,  hence 
the  coal  must  be  mined  rapidly. 

In  this  system  the  gangway  chutes  are  driven  at  right  angles  with  the 
strike  of  the  seam,  40  ft.  up  the  pitch;  a cross-cut  5 ft.  X 6 ft.  is  then  driven 


B 0 » 


Fig.  18. 

parallel  with  the  gangway.  From  this  cross-cut,  chutes  are  driven  at  same 
distance  apart  as  the  gangway  chutes  (30  ft.),  at  an  angle  of  35°,  and  cross- 
cuts are  driven  every  40  ft.  between  chutes,  for  ventilation.  After  a panel 
of  five  or  more  chutes  is  driven  up  the  required  distance,  work  is  com- 
menced on  the  upper  outside  pillar  and  the  pillars  on  that  line  are  drawn 
and  the  next  line  is  attacked,  and  this  is  continued  until  the  panel  or  block 
is  worked  down  to  the  cross-cut  over  the  gangway.  About  every  80  ft.  in 
this  level  it  is  found  advantageous  to  build  a row  of  cogs  parallel  with  the 
strike  of  the  seam  as  the  pillars  are  drawn.  This  serves  to  save  the  crushing 
of  the  pillars,  and  prevents  any  accidents  from  falls  of  rock.  But  few 
timbers  are  required  by  this  system.— (“  Mines  and  Minerals,”  Vol.  19, 
page  145.) 


302 


METHODS  OF  WORKING. 


New  Castle,  Colorado,  Method.— The  following  method  as  described  by  Mr. 
R.  M.  Hosea,  Chief  Engineer  of  the  Colorado  Fuel  and  Iron  Co.,  is  used 
at  New  Castle,  Colo.,  for  highly  inclined  bituminous  seams.  The  coals  mined 
are  only  fairly  hard,  contain  considerable  gas,  and  make  much  waste  in 
mining.  Fig.  18  shows  the  method  used  for  extracting  the  Wheeler  or 
thicker  vein  to  its  full  width  of  45  ft.,  and  the  E seam  18  ft.  thick,  excepting 
that  left  for  pillars.  Rooms  and  pillars  are  laid  out  under  each  other  in 
the  two  seams  whenever  practicable.  Entries  are  along  the  foot-wall;  30  ft. 
up  the  pitch  is  an  air-course.  Rooms  and  breasts  are  laid  out  as  shown 
in  B and  C,  Fig.  18.  In  the  Wheeler  vein,  the  manways  go  through  the 
entry  pillars  to  the  air-course  and  thence  along  the  ribs  each  side  of 
the  room,  one  manway  to  the  main  entry  serving  for  two  double  rooms.  A 
lower  bench  of  6 ft.  is  first  mined  the  full  length  of  the  rooms,  120  ft.,  side 
manways  being  protected  by  vertical  or  leaning  props,  bordered  with  3" 
planks  outside,  and  the  chute  or  battery  is  then  put  in.  At  the  top  the  rooms 
are  connected  by  cross-cuts,  and,  occasionally,  intermediate  cross-cuts  are 
required.  The  room  is  kept  full  of  loose  coal,  only  sufficient  being  drawn  to 
keep  the  working  floor  at  the  proper  height  for  the  mining.  When  driven 
to  the  limit  and  with  cross-cuts  connected,  the  coal  is  all  drawn  out  at 
the  chutes,  which  have  receptacles  for  rock  and  waste  at  their  sides,  to  be 
picked  out  by  the  loaders.  The  next  operation  is  to  drive  across  the  seam  at 


Fig.  19. 


the  air-course  until  the  hanging  wall  is  reached,  manways,  called  hack  man- 
ways, being  maintained  as  before.  A triangular  section  of  coal  is  mined  off, 
as  shown  in  A,  Fig.  18,  and  the  room  filled  with  loose  coal.  The  full  thick- 
ness of  the  seam  is  now  taken  off,  shots  being  first  placed  at  S S,  coal  being 
drawn  out  at  the  bottom  as  required.  Section  D,  Fig.  18,  shows  a method  of 
robbing  a pillar.  In  doing  this,  the  manways  are  moved  back  into  the 
pillar  each  side  10  ft.  or  so,  by  mining  on  the  lower  bench  as  before,  and 
holes  are  drilled  into  the  roof  with  long  drills,  which  bring  down  as  much  of 
the  overhanging  part  as  can  be  reached.— (“Mines  and  Minerals,”  Vol.  17, 
page  377.)  


MODIFICATIONS  OF  LONGWALL  METHOD. 

Fig.  19  shows  a good  arrangement  of  the  main  and  temporary  haulage- 
ways  in  a flat  seam.  The  chief  object  in  any  plan  of  longwall  workings  is  to 
have  the  permanent  roadways  the  arteries  of  the  system,  providing  the  most 
direct  route  from  all  sections  of  the  mine  to  the  shaft.  The  temporary 


LONG  WALL  METHOD. 


303 


roads  or  working  places  are  only  maintained  for  a distance  of  60  to  100  yd., 
until  cut  oif  by  subroads  branching  at  regular  intervals  from  the  main 
roads.  In  the  figure,  full  heavy  lines  indicate  the  permanent  haulageways, 

except  only  the  main 
intake  airway  (12  ft. 
wide),  running  west 
from  the  downcast  shaft 
D,  and  the  main  return 
air-course  (12  ft.  wide) 
leading  from  the  face  on 
the  east  side  to  the  man- 
way around  the  upcast  U, 
which  is  the  hoisting 
shaft.  The  full  light 
lines  indicate  the  diag- 
onal subroads,  driven  to 
cut  off*  the  working 

S laces,  shown  by  the 
otted  lines.  The  stables 
are  located  as  shown  in 
the  shaft  pillar,  between 
the  two  shafts,  where 
they  will  not  contami- 
nate the  air  going  into 
the  mine,  but  will  receive 
air  fresh  from  the  down- 
cast and  discharge  it  at 
once  into  the  upcast  cur- 
rent. This  position  also 
affbrds  ready  access  from 
either  shaft  in  case  of 
accident,  and  for  the 
handling  of  feed  and 
refuse.  The  pumps  may 
be  located  in  any  con- 
venient position  at  the 
foot  of  the  upcast.  The 
shaft  bottoms  are  driven 
14  ft.  wide  nearly  through 
the  shaft  pillar,  and  are 


rj  

/ /r > iTT- 


Fig.  21 


continued  10  ft.  wide  north 
and  south  through  the  gob. 
The  width  of  all  other  roads 
and  subroads  is  made  8 ft.  The 
extra  width  of  the  straight 
road  through  the  hoisting  shaft 
is  to  provide  for  the  future  need,  when  the 
size  of  the  workings  will  demand  that  the 
mine  be  ventilated  in  four  sections  or  splits;  and  these  two  roads  will  then 
each  form  the  return  of  two  sections.  This  will  be  accomplished  by  over- 
casting the  main  road  forming  the  shaft  bottom,  and  carrying  half  the  cur- 
rent by  this  means  to  the  east  face,  where  it  is  again  divided.  The  same 
thing  is  done  on  the  west  side.  The  divided  currents,  after  traversing  the 
faces  of  their  own  respective  sections,  unite  and  return  to  the  hoisting  shaft 
by  the  main  haulage  road. 

When  the  roof  is  very  solid,  the  gob  roads  turn  off*  the  entries  at  45°.  and 


304 


METHODS  OF  WORKING, 


may  be  a considerable  distance  apart,  so  that  the  tracks  can  be  turned  in 
along  the  working  face  and  the  mine  cars  loaded  at  the  face.  When  the 
roof  is  tender,  making  it  impossible  to  maintain  sufficient  room  for  the  mine 
cars  to  pass  along  the  face,  gob  roads  are  turned  off  near  together,  and  the 
mine  cars  run  to  the  road  heads,  to  which  ix)ints  the  coal  is  shoveled  or 
hauled  in  buckets.  When  the  working  face  has  reached  such  a distance 
from  the  bottom  of  the  shaft  that  it  becomes  impossible  to  work  rapidly 
enough  to  avoid  the  destructive  weighting  action  of  the  roof,  the  mining 
must  be  divided  into  panels  or  sections,  the  working  face  of  each  of  which 
can  be  advanced  at  the  proper  rate. 

Figs.  20  and  21  show  a plan  and  section,  respectively,  of  two  methods 
largely  used  in  Europe  for  working  thick  pitching,  contiguous  seams  of 
hard,  long-grained  coal.  From  the  foot  of  the  shafts,  levels  are  driven  on 
the  strike,  and  jig  roads  turned  off  these  in  the  top  seam  at  right  angles 
up  the  pitch.  The  working  faces  are  advanced  in  the  same  horizontal 
plane,  the  lower  one  being  always  ahead.  The  coal  from  the  two  lower 
seams  is  run  through  horizontal  passages  to  the  upper  seam,  where  it  is 
lo  vvered  to  the  levels  below  by  means  of  jigs  or  g:ravity  planes.  The  slates 
between  the  seams  and  the  refuse  obtained  in  mining  are  used  to  fill  in  as 
the  faces  advance.  This  gobbing  must  be  done  quite  thoroughly,  in  order  to 
prevent  excessive  settling  of  the  roof  and  consequent  crushing  of  the  coal  at 
the  faces.  Where  spontaneous  combustion  is  liable  to  occur,  it  is  not 
advisable  to  use  this  method,  but  rather  that  shown  in  the  lower  portion  of 
the  figures.  Slopes,  or  inclined  planes,  are  driven  down  the  pitch  from  the 
levels  to  the  basin,  or,  if  possible,  to  the  boundary  line,  where  the  working 
faces  are  formed  by  driving  levels  to  the  right  and  left  of  the  ends  of  the 
slopes.  The  working  faces  are  here  also  kept  in  a horizontal  plane  with 
the  lower  one  farthest  up  the  pitch.  The  coal  from  the  two  upper  seams  is 
taken  through  tunnels  or  flats  to  the  slopes  in  the  lower  seam,  and  hoisted  to 
the  shaft  bottom.  Here  all  the  inclined  planes  or  other  passages  are  in  the 
solid  coal,  and  the  worked-out  places  are  left  behind.  A very  small  amount 
of  coal  is  left  in  the  mine  when  worked  from  the  basin  upwards,  and  the 
eftects  of  squeezes  are  not  felt  to  any  great  extent,  as  the  weight  of  the  roof 
is  thrown  on  the  gob.  Where  there  is  not  sufficient  refuse  material  to  fill  in 
with,  it  is  taken  into  the  mine  from  the  surface,  or  from  another  adjacent 
mine  having  an  extra  amount  of  stowing  material. 

It  is  not  necessary  that  the  slopes  be  sunk  to  the  boundary  line,  in  which 
case  the  main-slope  pillars  should  be  large  and  left  in  so  that  the  dip 
workings,  as  they  are  called,  can  be  continued  downwards  when  desired. 
In  this  way,, the  first  cost  of  opening  up  is  greatly  reduced.  The  ventila- 
tion of  these  workings  is  quite  simple,  the  intake  being  split  at  the  ends  of  the 
main  entries,  or  slopes,  and  the  air  forced  along  the  different  working  faces 
to  the  right  and  left,  and  thence  to  the  upcast  by  way  of  the  main-return 
airways.  If  at  all  possible,  it  is  advisable  to  provide  an  outlet  near  the 
faces  of  the  rise  workings  that  are  advancing  upwards,  because  the  lighter 
gases  cannot  be  forced  down-hill  with  satisfaction  unless  an  excessive 
velocity  of  the  air-current  be  maintained.  These  systems  are  well  adapted 
to  deep  or  shallow  mines,  and  to  give  maximum  outputs  for  minimum 
development,  provided  the  work  is  carried  on  quickly  and  steadily. 

Overhand-Stoping  Method.— Where  several  thick  and  heavily  pitching  . 
seams,  in  which  considerable  firedamp  is  given  off  and  the  roof  falls 
freely,  are  to  be  worked,  a shaft  is  sometimes  sunk  in  the  adjacent  strata, 
and  at  certain  distances  horizontal  tunnels  are  driven  to  the  coal  seams. 
From  these  tunnels,  levels  or  haulage  roads  are  driven  in  each  seam  to 
the  right  and  left,  provided  the  seams  are  not  so  close  together  as  to  make 
it  more  profitable  to  use  rock  chutes  or  tunnels,  through  which  the  coal 
is  run  from  one  seam  into  the  other.  At  certain  intervals,  depending  on  the 
length  of  the  lifts  horizontally,  pairs  of  headings,  usually  called  dips,  are 
driven  up  the  pitch  until  they  intersect  the  levels  and  tunnels  above. 
Headings  are  turned  off  these  dips  to  the  right  and  left,  parallel  to  the  main 
levels  or  haulage  roads,  and  when  they  meet  or  have  reached  their  limit 
horizontally  they  are  holed,  or  cut  through,  by  cross-cuts  driven  on  the 
pitch.  The  working  faces  thus  formed  are  then  carried  back,  as  shown  in 
Fig.  22.  Skips  are  taken  off  the  face  and  the  roof  allowed  to  cave  in  after 
each  operation  and  fill  up  the  gob  behind.  The  order  of  working  is  such 
that  the  top  faces  are  worked  in  advance  of  the  lower  ones.  The  cars, 
which  are  taken  to  the  working  faces,  are  handled  in  the  dips  by  balance 
carriages,  or  back  balances,  as  they  are  termed  in  some  localities.  The 


ANTHRACITE  MINING. 


305 


barney,  or  balance,  runs  on  a narrow  track  in  the  middle  of  the  track  for  the 
carriage  on  which  the  car  is  placed.  The  barney  will  raise  the  carriage  with 
the  empty  car  on  it,  and  the  carriage  and  loaded  car  will  hoist  the  barney. 
These  gravity  planes  are  only  made  one-half  the  length  of  the  dips,  or  about 
150  ft.,  in  order  that  greater  safety  may  be  secured  and  shorter  ropes  used. 
One  is  placed  in  the  lower  half  of  one  of  the  pairs  of  dip  headings,  and 
another  in  the  upper  half  of  the  other,  thus  necessitating  that  the  cars  be 
changed  from  one  gravity  plane  to  the  other  midway  along  the  dips.  This 
is  done  by  taking  the  car  off  one  carriage  and  pushing  it  through  a break- 
through or  cross-cut  to  the  other.  Fig.  22  shows  the  method  of  working  these 
lifts  in  some  parts  of  England  and  Belgium  where  the  seams  are  gaseous,  and 
some  of  them  quite  thick.  The  face  is  stepped  more  or  less  deeply,  depend- 
ing on  the  pitch,  in  order  to  protect  each  miner  from  the  falling  coal  of  his 
neighbor.  The  men  rtiach  the  higher  portion  of  the  working  face  through 
timbered  manways.  The  coal  is  generally  run  down  chutes  to  the  cars 
below,  but  in  some  places  it  is  run  to  the  end  of  the  gangway  below  by 
means  of  inclined  chutes,  or  spouts,  laid  on  the  gob.  The  essential  feature 
for  the  successful  operation  of  this  system  is  the  close  and  careful  stowing  of 
the  gob  between  walls.  In  Belgium,  cord  wood  and  brush  wood  are  very 
largely  used  for  gobbing  material  or  stowing  between  the  regular  timbers. 
All  the  coal,  except  very  thin  vertical  pillars,  is  taken  out.  Where  there  is 


Fig.  22. 


much  firedamp,  the  miners  simply  nick  the  coal  and  leave  it  stand  over 
night,  during  which  time  the  gas  either  forces  it  off  the  solid  or  so  loosens  it 
that  the  miner  can  easily  take  it  off  with  a pick.  (See  also  Highly  Inclined 
Mineral  Deposits.) 


METHODS  OF  MINING  ANTHRACITE. 

A perfectly  flat  seam  of  anthracite  is  seldom  found  in  America,  and  even 
where  a portion  of  the  seam  may  be  found  lying  comparatively  flat,  such 
sudden  changes  in  dip  must  be  expected  that  a system  adapted  to  working 
on  a pitch  is  almost  universally  used.  A breast  may  start  on  a low  pitch  and 
the  pitch  may  increase  gradually  until  it  becomes  vertical,  or  the  reverse 
may  be  the  case.  The  cleat  is  usually  lacking  in  anthracite,  and  the  direc- 
tion of  driving  the  breasts  is  determined  largely  by  the  pitch  and  by  haulage 
considerations. 

For  pitches  up  to  30°,  the  methods  shown  in  Figs.  1,7, 8, 9, 10, 12,  and  13  are, 
in  general,  applicable,  with  certain  changes  due  to  local  considerations. 
There  is  considerable  difference  in  the  methods  of  opening  rooms  in  anthra- 
cite and  bituminous  mines,  owing  to  variations  in  the  characteristics  of  the 
coals  and  to  the  fact  that  anthracite  will  slide  on  chutes  of  less  inclination 
than  bituminous  coal.  Where  the  pitch  does  not  exceed  4°,  the  rooms  are 
turned  off  at  right  angles  to  the  gangway.  In  moderately  thick  coal  seams, 
pitching  between  4°  and  18°,  the  rooms  are  generally  driven  across  the  pitch, 
forming  room  breasts,  thus  securing  a grade  that  permits  the  haulage  of  the 
cars  to  the  face. 


306 


METHODS  OF  WORKING. 


There  are  two  methods  of  mining  thick  coal  in  breasts  when  nearly  flat. 
(1)  The  breasts  are  opened  out  and  driven  to  the  limit  in  the  lower  bench  of 
coal,  and  the  top  benches  are  blown  down  afterwards,  beginning  at  the  face 
and  working  back.  (2)  When  the  roof  is  good  and  there  is  no  danger  of  its 
falling  and  closing  up  the  workings,  the  upper  benches  may  be  worked  in 
the  opposite  direction,  beginning  at  the  gangway  and  driving  towards  the 
limit  of  the  lift,  or  the  working  of  the  upper  bench  may  follow  up  that  of  the 
lower  bench.  When  the  seam  is  less  than  12  ft.,  the  top  is  supported  by 
props;  in  thicker  seams,  the  expense  is  so  great  for  propping  that  but  little 
attempt  is  made  to  support  the  roof.  In  the  thicker  anthracite  seams 
(notably  the  Mammoth),  the  coal  in  the  breasts  is  so  worked  as  to  make  an 
arch  of  the  upper  benches  of  coal,  which  acts  as  a temporary  support  for  the 
roof,  the  coal  in  the  arch  being  extracted  when  the  pillars  are  robbed. 

When  the  inclination  of  anthracite  seams  is  less  than  30°,  the  breasts  may 
be  opened  with  one  chute  in  the  center,  which  ends  in  a platform  projecting 
into  the  gangway,  off  which  the  coal  can  be  readily  loaded  into  the  mine 
car.  When  this  method  is  employed,  the  refuse  is  thrown  to  either  side  of 
the  chute.  If  the  pillars  are  to  be  robbed  by  skipping  or  slabbing  one  rib 
only,  it  is  well  to  keep  most  of  the  refuse  on  one  side.  Sometimes,  when  the 
top  is  good,  and  the  breasts  are  driven  wide,  two  chutes  are  used,  but  the 
cost  of  making  the  second  chute  is  considerable  and  is  therefore  not 
advisable  unless  necessitated  by  the  method  of  ventilation  employed. 

Col.  Brown’s  Method.— Fig.  23  shows  a panel  system  devised  by  Col.  D.  P. 
Brown,  of  Lost  Creek,  Pa.,  which  gives  good  results  in  thick  seams  pitching 
from  15°  to  45°,  where  the  top  is  brittle,  the  coal  free,  and  the  mine  gaseous. 
Rooms  or  breasts  are  turned  off  the  gangway  in  pairs,  at  intervals  of  about 


Fig.  23. 

60  yd.  The  breasts  are  about  8 yd.  wide,  and  the  pillar  between  about  5 yd. 
wide,  which  is  drawn  back  as  soon  as  the  breasts  reach  the  airway  near  the 
level  above.  In  the  middle  of  each  large  pillar  between  the  several  pairs  ot 
breasts,  chutes  about  4 yd.  wide  are  driven  from  the  gangway  up  to  the 
airway  above.  These  are  provided  with  a traveling  way  on  one  side,  giving 
the  miners  free  access  to  the  workings.  Small  headings  are  driven  in  the 
bottom  bench  of  coal,  at  right  angles  to  these  chutes,  and  about  10  or  20  yd. 
apart.  These  headings  are  continued  on  either  side  of  the  chutes  until  they 
intersect  the  breasts.  When  the  chute  and  headings  are  finished,  the  work 
of  getting  the  coal  in  the  panel  is  begun  by  going  to  the  end  of  the  upper- 
most heading  and  widening  it  out  on  the  rise  side  until  the  airway  above  is 
reached  and  a working  face  oblique  to  the  heading  is  formed.  This  face  is 
then  drawn  back  to  the  chute  in  the  middle  of  the  panel.  After  the  work- 
ing face  in  the  uppermost  section  has  been  drawn  back  some  10  or  12  yd., 
work  in  the  next  section  below  is  begun,  and  so  on  down  to  the  gangway, 
working  the  various  sections  in  the  descending  order.  Both  sides  of  the 
pillar  are  worked  similarly  and  at  the  same  time  toward  the  chute. 

Small  cars,  or  buggies,  are  used  to  convey  the  coal  from  the  working  faces 
along  the  headings  to  the  chute,  where  it  is  run  down  to  the  gangway  below 
and  loaded  into  the  regular  mine  cars.  This  system  affords  a great  degree  of 
safety  to  the  workmen,  because  whenever  any  signs  of  a fall  of  roof  or  coal 
occur,  the  men  can  reach  the  heading  in  a very  few  seconds  and  be 
perfectly  safe.  A great  deal  of  narrow  work  must  be  done  before  any  great 


anthhacite  mining. 


307 


quantity  of  coal  can  be  produced.  The  breasts  are  driven  in  pairs  and  at 
intervals,  to  get  a fair  quantity  of  coal  while  the  narrow  work  is  being  done, 
and  they  are  not  an  essential  part  of  the  system.  It  is  claimed  that  the 
facility  and  cheapness  with  which  the  coal  can  be  mined,  handled,  and 
cleaned  in  the  mine  more  than  counterbalance  the  extra  expense  for  the 
narrow  work. 

Battery  Working.— Fig.  24  shows  a method  of  opening  a breast  by  two 
chutes  c,  c,  when  there  is  a great  amount  of  refuse,  or  when  a great  amount 


of  gas  is  given  off.  The  chutes  are  extended  up  along  the  rib  to  within  a 
few  feet  of  the  working  face,  either  by  planking  carried  on  upright  posts,  or 
by  building  a jugular  manway,  as  shown  in  the  sections  (a)  and  (5),  Fig.  25. 
These  chutes,  built  of  jugulars  or  inclined  props  and  faced  by  2"  plank,  are 
made  as  nearly  air-tight  as  possible,  to 
carry  the  air  from  the  heading  a to  the 
working  face.  Fig.  24  shows  a breast 
on  a pitch  too  steep  to  enable  the  miner  to 
keep  up  to  the  face.  In  seams  of  less  than 
35°,  the  platform  / shown  near  the  face  of 
the  breast  is  unnecessary,  and  in  seams 
thicker  than  12  ft.  it  cannot  be  built; 
hence,  this  method  of  working  is  applica- 
ble (1)  to  beds  pitching  more  than  35°, 
and  (2)  to  thin  seams. 

The  coal  is  separated  from  the  refuse 
on  the  platform  /,  and  is  run  down  the 
manway  chutes  and  loaded  into  the  cars 
from  a platform  projecting  into  the  gang- 
way g.  The  refuse  is  thrown  in  the  middle 
of  the  breast  behind  the  platform.  A cer- 
tain amount  of  coal  is  kept  on  the  plat- 
form to  deaden  the  blow  from  the  falling 
coal.  The  chutes  are  timbered  when  the 
character  of  the  coal  requires  it.  This 
plan  can  also  be  employed  in  thick  seams 
having  a heavy  dip,  if  there  is  enough 
refuse  to  fill  the  center  of  the  breast  so  that  the  miner  can  work  without  the 
platform. 

Fig.  25  (a)  is  a section  through  p,  p when  jugulars  a,  a are  used  to  form  the 
manways  b,  b along  the  sides  of  the  breast;  and  (6)  is  a section  through  the 


308 


METHODS  OF  WORKING, 


same  line  when  upright  posts  a,  a are  used  to  support  the  plank  in  forming 
the  manways  h,  h.  The  refuse  in  these  cases  only  partially  fills  the  gob! 

In  working  very  thick  seams  on  heavy  dips,  where  there  is  not  enough 
refuse  to  fill  the  middle  of  the  breast,  the  miner  has  nothing  to  stand  on,  the 


platform  being  impracticable;  therefore,  it  is  necessary  to  leave  the  loose 
coal  in  the  breast.  Loose  coal  occupies  from  50^  to  90^  more  space  than  coal 
in  the  solid.  This  surplus  is  drawn  out  through  a central  chute.  If  the  roof 


ANTHRACITE  MINING, 


309 


is  ix)or,  the  movement  of  the  coal  will  not  in  this  way  cause  it  to  fall  and 
mix  with  the  coal;  and  if  the  floor  is  soft,  the  jugulars,  which  are  stepped 
into  the  floor,  are  not  so  liable  to  be  unseated,  closing  the  manway  and 
blocking  the  ventilation.  The  surplus  is  sometimes  sent  down  the  manways, 
leaving  the  loose  coal  in  the  center  of  the  breast  undisturbed,  until  the  limit 
is  reached. 

Single-Chute  Battery.— To  prevent  the  coal  from  running  out  through  the 
chutes,  the  opening  into  the  breast  is  closed  by  a battery  constructed  by, 
laying  heavy  logs  across  the  openings,  as  shown  at  &,  Fig.  26,  or  else  built  on' 
props,  as  shown  at  b,  Fig.  27;  a hole  is  left  in  the  center,  or  at  one  side  of  the 
battery,  through  which  the  coal  may  be  drawn.  The  battery  closes  all  the. 
openings  into  the  breast,  except  the  space  occupied  by  the  jugular  manways, 
and  is  made  air-tight,  or  as  nearly  so  as  possible,  by  a covering  of  plank. 

Fig.  26  is  a plan  and  section  of  a breast  opened  up  by  a single  chute.  The 
plan  ^ is  taken  on  the  line  m n shown  on  the  section  B,  which  section  is 
taken  on  the  line/^  shown  on  the  plan  A.  The  pitch  is  great  and  the  seam 
is  so  thick  that  the  breast  must  be  kept  full  of  loose  coal  for  the  men  to  work 
upon,  the  surplus  being  drawn  off  at  the  battery  b and  run  into  the  car 
standing  on  the  gangway  g through  the  chute  c.  A manway  w is  made 
along  each  side  of  the  breast,  for 
the  purpose  of  ventilation  and 
affording  a passage  for  the  men 
to  reach  the  working  face.  The 
heading  a is  used  for  an  air- 
course  between  breasts.  The 
main  airway  h is  driven  over 
the  gangway  g,  where  it  will  be 
well  protected. 

By  drawing  the  surplus  coal 
through  a central  chute,  the 
manways  are  not  injured  so 
much  as  when  it  is  drawn  off 
through  side  chutes,  as  the  coal 
will  move  principally  along  the- 
middle  of  the  breast.  When  the 
breast  is  worked  up  to  its  limit, 
all  the  loose  coal  is  run  out  of 
the  breast  and  the  drawing  back 
of  the  pillars  is  commenced, 
unless  for  some  purpose  they 
are  allowed  to  stand  for  a time. 

Double-Chute  Battery.— Fig.  27 
shows  a plan  and  section  pf 
double-chute  breasts  used  in 
very  thick  seams  having  a heavy 
dip.  The  breasts  are  entered  by 
two  main  coal  chutes  c,  c,  each 
of  which  is  provided  with  a battery  6,  through  which  the  coal  is  drawn. 
A manway  chute  m is  driven  up  through  the  middle  of  the  pillar  for  a few 
yards  and  is  then  branched  in  both  directions  until  each  branch  (slant 
chute)  intersects  the  foot  of  a breast  near  the  battery  6,  as  shown.  The  jugu- 
lar manways  n,  n are  started  at  this  point  and  continued  up  each  side 
of  the  breast.  The  main  airway  h is  driven  in  the  solid  through  the 
stump  A above  the  gangway.  By  driving  the  main  gangway  g against  the 
roof,  as  shown,  the  pitch  of  the  chute  is  lessened,  and  the  loading  chute  c 
is  more  readily  controlled. 

When  the  main  gangway  is  not  driven  against  the  roof,  a gate  is  placed 
in  the  chute  below  the  check-battery,  which  enables  the  loader  to  properly 
handle  the  coal.  Coal  in  excess  of  the  amount  necessary  to  keep  the  miner 
up  to  the  face  may  be  drawn  through  the  main  battery,  or  sent  down  the 
manway  chute,  from  which  it  is  loaded  through  an  air-tight  check-battery. 

The  main  chutes  are  usually  8 or  9 ft.  wide,  but  sometimes  only  for  the 
first  6 or  8 ft.;  above  this  they  are  driven  about  6 ft.  square.  The  manway 
and  slant  chutes  are  also  about  6 ft.  square. 

When  the  seam  is  not  thick  enough  to  carry  the  return  airway  h (Fig.  27) 
over  the  gangway,  the  chutes  are  driven  up  in  the  same  manner  as  in 
Fig.  27,  for  a distance  of  about  30  ft.,  where  they  intersect  the  airway.  The 
breast  is  opened  out  just  above  the  airway,  a battery  being  built  in  the  airway 


Fig.  28. 


310 


METHODS  OF  WORKING. 


immediately  above  each  chute.  A manway  is  driven  from  the  gangway 
up  through  the  middle  of  the  stump  until  it  intersects  the  airway,  and  a 
trap  door  is  placed  at  this  point  to  confine  the  air.  This  manway  is  made 
about  4 ft.  X 6 ft.,  or  smaller. 

Fig.  28  shows  a less  complicated  plan  than  Fig.  27.  The  main  chutes  n,  n 
are  driven  up  to  the  heading  c,  from  which  the  breast  is  opened  out;  a log 

battery  is  built  at  the  top 
of  each  chute  at  the  points 
marked  a,  a.  The  chutes 
are  used  for  drawing  the 
batterj’^  coal,  and  for  re- 
ceiving the  manway  coal, 
and  are  also  used  for  trav- 
eling ways.  A check-bat- 
tery h is  placed  in  the  chute 
to  prevent  the  air-current 
from  taking  a short  cut 
from  the  gangway  through 
the  chute  to  the  breast  air- 
ways. This  check-battery 
is  of  great  assistance  to  the 
loader  when  the  chute  has 
a very  steep  pitch,  as  he 
can  readily  control  the  flow 
of  coal  through  the  draw- 
hole. 

All  these  methods  are 
open  to  the  objection  that 
in  case  of  any  accident  to 
the  breast  manway,  by 
which  the  flow  of  air, 


Fig.  29. 


shown  by  the  arrows,  is  obstructed,  there  is  no  means  of  isolating  the  breast 
in  which  .the  accident 
occurs,  and  the  venti- 
lation of  all  the  breasts 
beyond  it  is  entirely 
stopped.  To  overcome 
this,  sometimes  the  pil- 
lar A,  shown  in  left- 
hand  breast.  Fig.  28,  is 
left  in  each  breast  to 
protect  the  airway. 

Rock-Chute  Mining. 

Fig.  29  shows  a section 
of  two  seams,  sepa- 
rated by  a few  yards 
of  rock.  Chutes  from 
4^  to  7 ft.  high  and  7 to 
12  ft.  wide  are  driven 
in  the  rock  from  the 
gangway  or  level  g to 
the  level  I in  the  seam 
above,  at  such  an 
angle  that  the  coal 
will  gravitate  from  the 
upper  seam  into  the 
gangway  g.  The  work- 
ing, otherwise,  is  sim- 
ilar to  that  previously 
described. 

Rock-chute  mining 
contemplates  the  fol- 
lowing sequence  of 
operation; 

1.  The  opening  of 
all  gangways  and  air- 
ways in  the  lower  seam, 
lying  a few  feet  above  it. 


Fig.  30. 

to  develop  coal  as  yet  untouched  in  a thick  seam 


ANTHRACITE  MINING. 


311 


2.  Developing  the  thick  bed  by  a regular  series  of  rock  chutes  driven 
from  the  gangway  below;  workings  being  opened  out  from  chutes  as  in 
ordinary  pillar-and-breast  working— the  panel  system  or  some  other  plan 
may  be  found  better  than  pillar-and-breast  workings. 

3.  Driving  the  breasts  to  the  limit  of  the  lift  and  robbing  out  the  pillars 
from  a group  of  breasts  as  soon  as  possible,  even  if  a localized  crush  is  induced. 

4.  After  one  group  of  breasts  is  taken  out  and  the  roof  has  settled,  open- 
ing a second  series  of  chutes  for  the  recovery  of  coal  from  any  large  pillars 
that  were  not  taken  out  when  the  crush  closed  the  workings. 

5.  While  the  work  of  recovering  the  pillar  coal  is  in  progress,  a second 
group  of  breasts  may  be  worked,  and  the  process  continued  until  all  the 
area  to  be  worked  from  that  gangway  has  been  exhausted.  The  same 
process  is  employed  in  opening  lower  lifts. 

6.  When  all  the  upper  bed  of  coal  has  been  exhausted,  the  lower  seam 
may  be  worked  by  the  ordinary  method.  Workings  in  this  seam  may  be 


Fig.  31. 


carried  on  simultaneously  with  the  upper  bed,  but  to  avoid  the  possibility 
of  a squeeze  destroying  these  workings,  very  large  pillars  must  be  left. 
After  exhausting  tlie  upper  seam,  these  pillars  may  be  advantageously 
worked  by  opening  one  or  two  breasts  in  the  center  of  each,  and  when  these 
are  worked  to  the  upper  limit,  attacking  the  thin  rib  on  each  side,  com- 
mencing at  the  top  and  drawing  back. 

When  the  roof  of  the  lower  bed  is  good,  the  cost  of  timbering  and  keeping 
open  the  gangways  and  airways  will  be  considerably  less  than  if  these  were 
driven  in  the  upper  seam,  and  this  difference,  in  some  cases,  may  be  suf- 
ficient to  pay  for  driving  all  the  rock  chutes. 

There  are  three  undetermined  points  in  this  connection,  viz.;  (1)  The 


312 


METHODS  OF  WORKING. 


maximum  distance  between  the  two  beds,  or  the  length  of  rock  chute  that 
can  be  driven  with  satisfactory  financial  results.  (2)  The  maximum  dip  on 
which  such  working  can  be  successfully  opened.  (3)  The  maximum  thick- 
ness of  the  upper  and  also  of  the  lower  seam,  which  will  yield  results  war- 
ranting the  additional  outlay  when  rock  chutes  are  of  considerable  length. 

Fig.  30  shows  how  one  or  more  seams  are  worked  by  connecting  them  by 
a “stone  drift,”  or  “tunnel,”  driven  horizontally  across  the  measures, 
through  which  the  coal  from  the  adjacent  seams  is  taken  to  the  haulage- 
way leading  to  the  landing  at  the  foot  of  the  slope  or  shaft.  Tunnels  are 
sometimes  driven  horizontally  through  the  measures  from  the  surface,  so  as 
to  cut  one  or  more  seams  above  water  level. 

The  lower  seam  of  coal  is  worked  from  a gangway  or  level  I,  connected 
by  a tunnel,  or  stone  drift  to  the  level  or  gangway  g,  in  the  thick 
seam.  The  stone  drift  may  be  extended  right  and  left  to  open  seams  above 
and  below  the  thick  seam.  This  tunnel,  or  stone  drift,  is  never  driven  under 
a breast  in  the  upper  seam,  but  directly  under  the  middle  of  the  pillar. 

In  the  upper  and  thicker  seam,  when  the  coal  is  very  hard,  a breast  h is 
worked  to  the  limit  and  the  loose  coal  nearly  all  run  out  through  the  chute  s 
into  the  gangway  g.  The  “ monkey  gangway  ” m is  driven  near  the  top  as  a 
return  airway,  and  is  connected  to  the  upper  end  of  the  chute  s by  a level 
heading  n,  and  to  the  main  gangway  ^ by  a heading  v.  These  headings  are 
driven  for  the  purpose  of  ventilation  and  to  provide  access  to  the  battery  in 
case  the  chute  s should  be  closed.  In  the  lower  seam,  the  breast  is  still  being 
worked  upwards  in  the  ordinary  way. 

The*  J.  L Williams  method  of  working  anthracite.  Fig.  31,  has  been  applied 
successfully  by  the  originator  at  the  Richards  Mine,  Mt.  Carmel,  Pa.,  and  by 
it  90^  of  the  available  coal  is  said  to  have  been  obtained.  The  method  is  a pil- 
lar-and-stall  method  with  the  following  distinguishing  points:  (a)  Timbering 
the  gob  with  props  set  not  more  than  6 ft.  apart,  to  keep  up  the  roof  during 
the  extraction  of  the  pillars.  (6)  Making  holes  from  the  crop,  for  the 
delivery  of  timber  into  the  workings,  (c)  Removing  the  pillars  in  shorter 
lifts  than  is  possible  when  the  roof  is  supported  with  culm  pillars,  {d)  Keep- 
ing the  gob  open  with  timber  for  dumping  the  fallen  rock,  that  would  have 
to  be  sent  to  the  surface  if  the  breasts  were  flushed. 

Both  the  floor  and  the  roof  of  the  mine  were  weak,  so  that  it  was  not 
possible  to  make  either  the  breasts  or  the  pillars  wide.  In  some  cases,  the 
floor  consisted  of  3 ft.  of  clod,  and  to  prevent  its  lifting  and  sliding,  every 
alternate  prop  was  put  through  the  clod  and  its  foot  set  in  the  slate  beneath, 
while  the  other  props  were  set  oh  pieces  of  2"  plank  2 ft.  in  length  to  keep 
down  the  bottom.  A small  gangway  X is  driven  to  take  out  the  chain  pillar, 
and  F is  a small  gangway  for  taking  in  timber. 

Running  of  Coal.— In  large  seams,  when  the  coal  is  soft  and  shelly  or  slip- 
pery, and  lies  at  an  angle  of  more  than  50°,  and  generates  large  quantities  of 
firedamp,  a danger  to  be  guarded  against  is  the  sudden  liberation  of  gas 
should  a breast  run;  that  is,  should  the  coal  at  the  face  loosen  and  run  out 
by  its  own  gravity,  only  stopping  when  it  chokes  or  fills  up  the  open  space 
below.  To  meet  these  conditions,  the  air-course  may  be  driven  above  the 
gangway  and  used  as  a return,  the  fan  being  attached  as  an  exhaust,  and 
the  working  breasts  ventilated  in  pairs.  The  inside  manway  of  one  of  a pair 
of  breasts  is  connected  with  the  gangway  for  the  intake,  and  the  outside 
manway  of  the  other  breast  with  the  return  airway,  giving  each  pair  of 
breasts  a separate  split  of  the  current.  In  collieries  where  this  system  of 
working  is  followed,  the  coal  is  soft.  A new  breast  is  worked  up  a few  yards, 
but  as  soon  as  it  is  opened  out,  the  coal  runs  freely  and  the  manways  are 
pushed  up  on  each  side  as  rapidly  as  possible,  to  keep  up  with  the  face.  Two 
miners,  one  on  either  side,  sometimes  finish  a breast  without  being  able  to 
cross  to  each  other.  The  work  is  done  exclusively  with  safety  lamps,  and 
when  a breast  “runs”  the  gas  is  liberated . in  such  quantities  that  it 
frequently  fills  breasts  from  the  top  to  the  airway  before  the  men  can  get 
down  the  manway  on  the  return  side.  When  the  gas  reaches  the  cross-hole, 
it  passes  into  the  return  airway  without  reaching  any  part  where  men  are 
working.  Should  a run  of  coal  block  a breast  by  closing  the  mahway,  it 
affects  the  current  of  one  pair  of  breasts  alone.  As  the  gangway  is  the 
intake,  leakage  at  the  batteries  passes  into  the  breasts,  as  the  cross-holes  are 
above  their  level  and  the  gas  is  thus  kept  above  the  starter  when  at  the 
draw-hole.  The  gangway,  chutes,  and  airway  are  supplied  by  wooden 
pipes,  which  connect  with  a door  behind  the  inside  chute.  If  a breast  runs 
up  to  the  surface,  it  does  not  affect  the  return  airway,  as  it  is  in  the  solid. 


ANTHRACITE  MINING, 


313 


Among  the  disadvantages  urged  against  this  system  of  working  are  the 
following: 

It  increases  the  friction,  as  the  air  must  pass  in  the  airway  all  the  distance 
from  the  breast  to  the  fan,  the  area  of  the  airway  being  small  in  comparison 
to  the  gangway  or  intake. 

As  the  faces  of  the  breasts  are  so  much  higher  than  the  return  airway, 
the  lighter  gas  must  be  forced  down  into  the  return  against  the  buoyant 
power  of  its  smaller  specific  gravity. 

The  reduction  of  friction  obtained  by  splitting  is  neutralized  by  each  split 
running  up  one  small  manway  and  down  another;  the  advantage  of  running 
through  several  pillar  headings  and  thus  securing  a shorter  course  being 
lost.  This  can  be  partly  obviated  by  ventilating  the  breasts  in  groups,  but 
the  dangers  avoided  in  splitting  are  increased. 

Blackdamp,  which  accumulates  in  the  empty  or  partly  empty  breasts, 
works  its  way  down  and  mixes  with  the  intake  current,  as  there  is  no  return 
current  in  the  breast  strong  enough  to  carry  it  away,  the  return  being  closed 
in  the  airway. 

All  things  considered,  when  the  seam  is  soft  and  has  a pitch  of  40°  and 
upwards,  and  emits  large  quantities  of  gas  in  sudden  outbursts,  as  in  running 
breasts,  this  system  is  the  best  that  can  be  adopted. 

When  the  Coal  Is  Hard  and  Gas  Is  Not  Freely  Evolved.— The  reverse  of  the 
system  just  described  is  followed  at  some  collieries  where  the  coal  is  hard 
and  but  little  gas  is  encountered.  The.  airway  is  driven  over  the  gangway 
or  against  the  top,  the  fan  being  used  to  force  the  air  inward  to  the  end  of 
the  airway.  The  air  is  distributed  as  it  returns,  being  held  up  at  intervals 
by  distributing  doors  placed  along  the  gangway. 

Among  the  advantages  claimed  for  this  plan  are  the  following: 

As  the  pressure  is  outward,  it  forces  smoke  and  gas  out  at  any  openings 
that  may  exist  from  crop-hole  falls  or  other  causes. 

The  warm  air  from  the  interior  of  the  mine  returning  up  the  hoisting 
slope  or  shaft  prevents  it  from  freezing. 

As  the  current  is  carried  from  the  fan  to  the  end  of  each  lift  without  pass- 
ing through  working  places,  the  opening  of  doors  as  cars  are  passing,  etc. 
does  not  interfere  with  the  current. 

If  a locomotive  is  used,  the  smoke  and  gases  generated  by  it  are  carried 
away  from  the  men  toward  the  bottom.  Locomotives  are  generally  used 
only  from  the  main  turnout  to  the  bottom. 

An  objection  to  this  system  is  that  the  gangway,  as  the  return,  is  apt  to  be 
smoky.  Starters  and  loaders  are  forced  to  work  in  more  or  less  smoke,  and 
even  the  mules  work  to  disadvantage,  while  if  gas  is  given  off,  it  is  passed 
out  over  the  lights  of  those  working  in  the  gangway. 

However,  in  places  where  there  is  but  little  gas,  and  airways  of  large  area 
can  be  driven,  this  plan  works  very  satisfactorily,  and  some  of  the  best  ven- 
tilated collieries  are  worked  upon  it. 

An  objection  advanced  by  some  against  forcing  fans  is  that  they  increase 
the  pressure,  thus  damming  the  gas  back  in  the  strata.  In  case  the  speed  of 
the  fan  is  slacked  off,  the  accumulated  gas  may  respond  to  the  lessened  pres- 
sure and  spring  out  in  large  volumes  from  its  pent-up  state.  This  argument, 
however,  works  both  ways.  An  exhaust  fan  running  at  a given  speed  is 
taking  off  pressure,  and  if  anything  occurs  to  block  the  intake,  the  pressure 
is  diminished,  and  the  gas  responds  to  the  decrease  on  the  same  principle. 

Hints  for  the  Smaller  Seams  When  They  Are  Small  and  Lie  From  Horizontal  to 
About  10°.— Two  gangways  may  be  driven,  the  lower  or  main  gangway  being 
the  intake.  Branch  gangways  should  then  be  driven  diagonally  or  at  a slant, 
with  a panel  or  group  of  working  places  on  each  slant  gangway.  Large 
headings  should  connect  the  panels.  In  this  system,  the  air  is  carried 
directly  to  the  face  of  the  gangway  and  up  into  the  breasts,  returning  back 
through  the  working  places.  The  intake  and  return  are  separated  by  a solid 
pillar,  the  only  openings  being  the  slant  gangways  on  which  are  the  panels. 

The  advantages  of  this  plan  are  several: 

The  main  gangway  is  solid,  with  the  exception  of  the  small  cross-holes 
connecting  with  the  gangway  above;  these  furnish  air  to  the  gangway  and 
are  small  and  easily  kept  tight.  These  stoppings  should  be  built  of  brick, 
and  made  strong  enough  to  withstand  concussion. 

A full  trip  of  wagons  can  be  loaded  and  coupled  in  each  panel  or  section 
without  interfering  with,  or  detaining  the  traffic  on,  the  main  road;  one  trip 
can  be  loaded  while  another  is  run  out  to  the  main  gangway  for  transpor- 
tation to  the  bottom. 


314 


METHODS  OF  WORKING. 


The  only  break  in  the  intake  current  is  when  a tri^  of  cars  is  taken  out 
from,  or  returns  to,  a panel  or  section;  this  can  be  partially  provided  against 
by  double  doors,  set  far  enough  apart  to  permit  one  to  close  after  the  trip 
before  the  other  is  opened.  This  distance  can  be  secured  by  opening  the 
tirst  three  breasts  on  a back  switch  above  the  road  through  the  gangway 
pillar,  or  by  running  each  branch  over  the  other  far  enough  to  obtain  the 
distance  for  the  double  doors. 

If  it  is  not  desired  to  carry  the  whole  volume  of  air  to  the  end  of  the  air- 
way, a split  can  be  made  at  each  branch  road.  These  will  act  as  unequal 
splits  in  reducing  friction,  and,  although  not  theoretically  correct,  are  prefer- 
able to  dragging  the  whole  current  the  full  length  of  the  workings. 

The  objections  urged  to  this  plan  are  that  it  involves  too  much  expense 
in  the  large  amount  of  narrow  work  at  high  prices  necessary  to  open  out  a 
colliery,  that  it  necessitates  a double  track  the  whole  length  of  the  lift,  and 
that  the  grade  ascends  into  each  panel  or  section.  But  the  latter  criticism 
falls,  because  the  loss  of  powder  hauling  the  empty  wagons  up  a slight  grade 
is  more  than  made  up  by  the  loaded  wagons  running  down  while  the  mules 
are  away  putting  a trip  into  another  panel  or  section. 

For  a large  colliery  this  is  without  doubt  the  best  and  cheapest  system. 

When  the  Seam  is  Small  and  Lies  at  an  Angle  of  More  Than  i0°.— In  small  seams 
lying  at  an  angle  of  more  than  10°,  and  too  small  to  permit  an  airway  over 
the  chutes,  it  is  more  difficult  to  maintain  ventilation.  If  air  holes  are  put 
through  every  few  breasts,  and  a fresh  start  obtained  by  closing  the  back 
holes,  or  if  an  opening  can  be  gotten  through  to  the  last  lift  as  often  as 
the  current  becomes  weak,  an  adequate  amount  of  air  can  be  maintained, 
because  the  lift  worked  can  be  used  as  the  intake,  and  the  abandoned  lift 
above  as  the  return.  To  ventilate  fresh  ground,  the  filling  of  the  chutes 
with  coal  will  have  to  be  depended  on,  or  a brattice  must  be  carried  along 
the  gangway.  This  can  be  done  for  a limited  distance  only,  as  a brattice 
leaks  too  much  air.  As  a rule,  collieries  worked  on  this  plan  are  run  along 
until  the  smoke  accumulates  and  the  ventilation  becomes  poor;  then  a new 
hole  is  run  through  and  the  brattice  removed  and  used  as  before  for  the 
next  section.  This  operation  is  repeated  until  the  lift  is  worked  out.  Some- 
times, to  make  the  chutes  tight,  canvas  covers  are  put  on  the  draw  holes, 
but  as  they  are  usually  left  to  the  loaders  to  adjust,  they  are  often  very 
imperfectly  applied.  Then,  as  the  coal  is  frequently  very  large,  the  air  wdll 
leak  through  the  batteries. 

This  plan  works  very  satisfactorily  if  the  openings  are  made  at  short 
intervals,  say  as  frequent  as  every  fifth  breast,  but  the  distance  is  usually 
much  greater  to  save  expense.  As  the  power  of  the  current  decreases  as  the 
distance  between  the  air  holes  is  increased,  good  ventilation  is  entirely  a 
question  of  how  often  a cut-off  is  obtained. 

An  effective  ventilation  could  be  maintained  in  a small  seam  at  a heavy 
angle  by  working  with  short  lifts,  say  two  lifts  of  50  yd.  instead  of  one  of 
100  yd.,  as  at  present.  The  gangways  should  be  frequently  connected,  and 
one  used  as  an  intake  and  the  other  as  a return.  This  would  necessitate 
driving  two  gangways  where  one  is  now  made  to  do,  but  the  additional 
expense  would  be  made  up  in  the  greater  proportion  of  coal  won. 


FLUSHING  OF  CULM. 

From  15 9^  to  20^  of  the  coal  taken  out  of  an  anthracite  mine,  according 
to  the  methods  used  in  the  past,  became  so  fine  in  the  course  of  preparation 
through  the  breaker  that  it  could  not  be  used  or  sold,  and  had  to  be  piled 
away  as  refuse.  Recently,  the  coarser  portions  of  these  culm  piles  have 
been  screened  out  and  sold  for  use  as  steam  sizes,  while  the  finer  part, 
together  with  the  fine  material  from  the  breaker,  has  been  carried  back  into 
the  mines  with  water  to  fill  the  abandoned  portions  of  the  underground 
workings. 

This  culm  is  carried  through  a system  of  conveyors  to  the  hopper,  usually 
an  old  oil  barrel,  and  the  stream  of  water  is  conducted  into  the  same  hopper 
by  a 3"  pipe.  The  culm  is  then  carried  by  the  water  through  a pipe  from 
4 to  6 in.  in  diameter,  which  passes  into  the  mine  through  the  shaft,  bore 
hole,  or  other  opening,  thence  along  the  gangways  to  the  chambers  through 
the  cross-cuts,  and  to  the  point  where  it  is  desired  to  deposit  the  culm.  The 
bottoms  or  outlets  of  the  chambers  to  be  filled  are  closed  by  board  partitions 
fitted  closely,  or  by  walls  of  slate  or  mine  rubbish.  The  culm,  as  it  issues 


CVLM  FLUSHING. 


315 


from  the  end  of  the  pipe,  takes  a very  flat  slope,  and  it  is  carried  a long  dis- 
tance hy  the  water,  which  ultimately  filters  through  the  deposited  culm  to 
the  lower  portion  of  the  mine,  to  he  pumped  to  the  surface.  When  the 
chamber  is  filled  to  the  roof,  the  pipe  is  withdrawn  and  extended  to  the 
next  place  to  be  filled,  and  so  on.  Wrought-iron  pipe  is  said  to  be  the  best, 
and  the  life  of  the  pipe  depends  on  the  nature  of  the  water  used  and  the 
material  treated.  With  fresh  water  and  small  culm  from  the  buckwheat 
screen,  it  lasts  18  months;  when  carrying  culm  from  the  bank,  ranging  from 
dust  to  pea  coal  and  some  chestnut,  9 months;  and  when  mixed  with  ashes, 
6 months.  The  smaller  the  material  the  better. 

The  amount  of  water  used  depends  on  the  distance  to  which  the  culm  is 
carried  and  the  slope  of  the  pipe. 

From  li  to  If  lb.  of  water  is  required  to  flush  1 lb.  of  culm  to  level  and 
down-hill  places;  3 to  6 lb.  of  water  to  1 lb.  of  culm  to  flush  up-hill  for  heights 
varving  from  10  to  100  ft.  above  the  level  of  the  shaft  bottom.  Any  ele- 
vation of  the  pipe  very  materially  increases  the  amount  of  water  necessary. 
Mr,  James  B.  Davis,  superintendent  of  the  Dodson  and  Black  Diamond 
mines,  has  ascertained  by  experiment  that  1 cu.  ft.  of  anthracite  coal  ground 
to  culm  can  be  flushed  into  a space  of  nearly  li  cu.  ft.,  and  it  is  therefore 
impossible  to  compress  the  culm  more  than  one-third.  In  addition  to  acting 
as  a filling  and  a support,  to  prevent  squeezes  and  crushing,  flushing  has 
been  advantageously  used  for  fighting  and  sealing  off  mine  fires.  No 
instance  has  been  recorded  where  spontaneous  combustion  has  taken  place 
in  the  flushed  culm. 

The  Dodson  culm  plant,  which  was  a pioneer,  cost  S7,473.42,  with  the 
capacity  of  flushing  119  tons  per  day,  while  the  Black  Diamond  culm  plant 
is  capable  of  flushing  287  tons  per  day  and  cost  ^6,280.12,  but  plants  can 
probably  be  put  up  much  more  cheaply  than  this. 

The  saving  from  the  flushing  of  culm  over  depositing  it  on  the  surface 
varies  for  the  ordinary  anthracite  colliery  from  |5  to  ^15  per  day.  The 
average  cost  of  putting  in  stoppings  in  a 9'  vein  is  given  by  Mr.  Davis  as 
^9.50,  including  material. 

To  remove  the  pillars  after  the  intervening  breasts  have  been  filled  with 
culm,  the  face  of  the  pillar  along  the  gangway  is  attacked,  and  a road  driven 
up  through  the  pillar,  splitting  it  {z,  Fig.  32).  This  road  may  be  the  full 
width  of  the  pillar,  but  in  general  it  is  necessary  to  leave  a narrow  stump  of 
coal  on  either  side  to  keep  up  the  fine  flushed  material  in  the  adjoining 
breasts.  The  thickness  of  this  supi)orting  coal 
depends  entirely  on  the  condition  of  the 
flushed  material  behind  it.  If  that  is  fine, 
it  will  set  firmly  and  form  a compact  mass 
that  will  not  run.  In  such  a case,  the  pillar 
may  be  entirely  taken  out,  leaving  a vertical 
wall  of  solidly  packed  flushed  culm.  When 
the  flushed  material  is  of  a size  larger  than 
buckwheat,  it  will  not  set  compactly,  but  will 
run  when  it  is  opened  up,  and  when  such 
material  fills  the  adjoining  breasts,  the  thin 
pillar  of  coal  must  be  left  to  keep  back  the 
culm.  Timbers  are  placed  flush  up  against 
the  culm  or  the  coal  stumps,  as  the  case  may 
be,  and  if  there  is  a tendency  for  the  culm 
to  run,  lagging  is  placed  behind  the  timbers. 

In  some  cases,  as  much  as  700  ft.  of  timber 
have  been  used  per  100  ft.  of  pillar  taken 
out.  As  the  pillar  is  removed,  the  top  settles 
until  it  finally  rests  upon  the  flushed  culm, 
and  as  the  weight  from  the  top  and  the  pres- 
sure from  the  sides  comes  upon  these  props, 
they  are  broken,  while  the  coal  that  has  been 
left  will  also  be  crushed.  At  the  Black  Dia- 
mond colliery,  the  props  us^d  are  16  ft.  long,  ^ . 

and  at  this  colliery  the  top  settles  about  4 ft.  if  the  flushed  material  is 
packed  tightly  before  the  roof  pressure  comes  on  it.  After  this  settling, 
new  props  12  ft.  in  length  are  put  in  close  up  against  the  culm  and  the 
broken  stump  of  the  original  pillar,  and  they  serve  to  keep  the  road  open 
up  to  the  working  face. 


Fig.  32. 


316 


MINING  MINERAL  DEPOSITS, 


METHODS  OF  MINING  MINERAL  DEPOSITS. 

Much  of  what  has  already  been  given  under  the  heading  of  Coal  Mining 
applies  equally  to  the  mining  of  mineral  deposits.  It  will  therefore  not  be 
repeated  under  this  heading,  and  the  only  methods  here  given  will  be  those 
that  have  not  already  been  covered. 

Highly  inclined  deposits  are  mined  out  as  follows:  Horizontal  passages 
called  drifts,  levels,  or  galleries  are  driven  through  the  ore  at  regular  intervals, 
and  connected  by  openings  at  right  angles  to  the  levels,  which,  in  the  case 
of  perpendicular  or  highly  fnclined  deposits,  are  called  winzes  or  raises, 
according  as  they  are  sunk  from  above  or  raised  from  below.  These  parallel 
openings  divide  the  ore  body  into  a series  of  rectangles,  thus  serving  to  test 
its  value.  (See  also  Overhaiid-Stoping  Method,  page  304.) 

Levels.— The  distance  between  the  individual  levels  depends  on  the 
material  being  mined.  They  are  placed  nearer  together  in  high-grade  ore 
than  in  low-grade  material.  The  width  of  the  vein  also  has  considerable 
influence  on  the  distance  between  the  levels.  In  veins  where  it  is  necessary 
to  break  into  walls  to  afford  working  room  in  the  levels,  they  are  usually 
placed  as  far  apart  as  is  consistent  with  the  economical  handling  of  the 
material  in  chutes  and  convenient  access  to  the  working  faces  of  the  stopes. 
The  distance  between  the  levels  varies  from  60  to  100  ft.,  and  should  be 
measured  on  the  dip  and  not  perpendicularly. 

Winzes  or  Raises. — The  distance  between  the  raises  or  winzes  varies  from 
30  to  250  ft.,  depending  largely  on  the  character  of  the  material  and  the 


method  of  getting  it  into  the  chutes  or  winzes.  Where  the  material  at  the 
working  faces  is  shoveled  or  thrown  directly  into  the  chutes,  they  are  often 
placed  as  close  as  30  ft.,  while  if  the  material  is  carried  from  the  working 
face  to  the  chute  or  winze  in  a wheelbarrow,  the  chutes  may  be  much 
farther  apart. 

Sloping.— For  narrow  deposits,  there  are  two  general  styles  of  stoping  in 
regular  use,  called,  respectively,  underhand  and  overhand  stoping.  There  are 
several  minor  divisions  under  each. 

Underhand  stoping  may  be  conveniently  divided  into  underhand  regular 
and  underhand  Cornish. 

The  regular  method  of  underhand  stoping  is  illustrated  in  (a).  Fig.  33,  and 
may  be  described  as  follows:  The  miner  selects  a place  in  any  given  level 
or  on  the  surface  of  the  ore  deposit  from  which  to  commence  stoping.  A 
cut  6 or  7 ft.  in  depth  and  from  6 to  8 ft.  in  length  is  made.  This  forms  the 
first,  or  No.  1,  bench  in  the  stope.  After  this,  he  continues  the  work  in  each 
direction,  supporting  the  track,  if  any  exists  above,  upon  stulls  or  timbering. 
After  this  No.  1 bench  has  proceeded  a sufficient  distance,  he  starts  a similar 
cut  in  the  bottom  of  it,  which  forms  No.  2 bench,  and  is  driven  in 
both  directions  as  before.  At  first  the  ore  can  be  shoveled  to  the  level 
above,  but  after  considerable  depth  has  been  attained,  it  will  be  necessary 
to  provide  a winze,  as  shown  at  /,  through  whfch  the  ore  from  the  lower 
benches  can  be  hoisted.  Stulls  covered  with  lagging  are  placed  across  the 
stope  behind  each  bench  as  platforms,  to  support  the  waste  material.  Under- 
hand stoping  by  the  Cornish  system  is  illustrated  in  (6),  Fig.  33,  and  differs 
from  the  system  just  described  only  in  that  the  level  below  has  to  be  driven 
first,  and  a winze  sunk  to  it.  a is  the  lower  level,  b the  winze,  and  c the 
upper  level.  The  work  is  then  carried  on  in  successive  benches,  as  described. 


OVERHAND  STORING. 


317 


The  advantages  of  the  Cornish  method  are  that  any  water  that  collects 
in  the  stope  flows  to  the  lower  level  and  does  not  have  to  be  taken  care  of  in 
each  individual  stope.  Also,  the  ore  can  be  tumbled  down  through  the  raise 
to  the  lower  level,  thus  avoiding  the  extra  hoisting  with  a windlass, 
or  small  hoist. 

The  advantages  that  apply  to  any  system  of  underhand  stoping  are  as 
follows:  The  ore  can  be  extracted  at  once;  while  the  stope  is  new,  the  miner 
is  protected  from  the  roof  by  stulls  and  stagings;  the  loss  of  fine  and  valuable 
mineral  is  reduced,  owing  to  the  opportunity  for  sorting  afforded  during  the 
handling  of  the  broken  ore. 

The  disadvantages  are  as  follows:  The  manner  in  which  the  ore  must  be 
handled  is  expensive;  an  individual  pumping  plant  will  be  necessary  in  each 
stope  of  a wet  mine  with  the  regular  system;  should  the  mine  be  abandoned 
for  any  length  of  time,  the  stulls  become  loose  and  allow  the  rock  stowed 
upon  them  to  fall  on  the  face  of  the  ore,  rendering  the  mine  unsafe,  and 
burying  the  ore  so  as  to  require  a large  expenditure  of  time  and  money  to 
reopen  the  workings;  in  a wet  stope,  the  water  flows  down  over  the  working 
faces,  interfering  with  the  workmen  and  forcing  them  to  stand  continually 
in  water. 

Overhand  Sloping.— In  this  system  of  stoping,  the  ore  is  broken  down  from 
above  as  the  work  progresses.  Work  is  usually  started  from  the  bottom  of  a 
raise,  as  B,  Fig.  34.  After  the  lower  level  A has  been  driven,  the  miner 
stands  on  top  of  the  lagging  over  the  caps  and  works  out  a slice  (7  5 or  6 ft. 
high,  this  being  followed  by  succeeding  slices,  as  D and  E.  Chutes  are 
timbered  or  cribbed  at  intervals,  through  which  the  material  may  be  thrown 
down  and  any  waste  packed  in  the  space  between  the  chutes,  as  at  F.  In 
cases  where  the  entire  deposit  is  of  value,  a portion  of  the  broken  ore  is 
allowed  to  accumulate  as  a platform  upon  which  the  men  stand  while 


Fig.  34. 


working,  only  enough  being  sent  through  the  chutes  to  provide  working 
room.  After  overhand  stoping  is  started,  the  work  may  be  carried  on  by 
means  of  breast  holes,  as  shown  at  E.  The  force  of  gravity  assists  in  break- 
ing the  rock,  and  reduces  the  powder  necessary  for  blasting. 

Where  rich  ore  is  broken,  platforms  of  planks,  or  sheets  of  canvas  or  bull 
hide  covered  with  plank,  may  be  placed  over  the  filling  to  receive  the  broken 
ore,  thus  preventing  the  loss  of  fine  and  valuable  material  in  the  filling. 
One  argument  which  is  usually  presented  against  overhand  stoping  is  that 
the  roof  is  not  secured  by  timbering,  but  this  is  offset  by  the  fact  that  the 
workmen  are  always  close  to  the  roof  and  thus  examine  its  condition  and 
break  off  any  dangerous  portions  or  give  them  such  support  as  may  be 
needed  with  temporary  timbers. 

Overhand  stoping  may  be  carried  on  in  a number  of  modified  forms,  all  of 
which  involve  the  principle  of  breaking  down  the  material  in  such  a manner 
that  the  work  is  aided  by  gravitation.  Sometimes,  where  practically  the 
entire  deposit  is  removed,  temporary  platforms  supported  on  stulls  are  com 
structed  close  to  the  working  face  for  the  workmen. 

The  advantages  of  overhand  stoping  are  that  no  hoisting  or  pumping  is 
required  in  the  block  of  ore  being  worked,  as  with  underhand  stoping  with- 
out a winze;  water  gives  no  trouble  in  the  stopes;  less  timbering  is  required 
than  in  the  underhand  stoping,  because  no  platforms  are  required  to  store 
waste,  and  the  timbering  in  working  stagings  is  usually  recovered;  where 
the  mine  is  abandoned  for  a time,  the  working  face  is  usually  left  in  better 


318 


MINING  MINERAL  DEPOSITS. 


shape  with  overhand  than  with  underhand  stoping.  In  the  overhand  system, 
gravity  assists  in  the  breaking  of  the  ore. 

The  disadvantages  are  that  the  miner  is  forced  to  work  under  an  unsup- 
ported roof,  though  the  fact  that  he  is  close  to  it  enables  him  to  examine  it 
and  take  care  of  any  dangerous  portions.  There  may  be  greater  loss  of  the 
fine  and  valuable  material  that  becomes  mixed  with  the  waste  than  in 
underhand  stoping,  though  this  may  be  largely  prevented  by  the  use  of 
boards  or  canvas. 

Flat  or  Slightly  Inclined  Deposits.— Where  flat  or  slightly  inclined  ore  bodies 
are  being  worked,  the  working  drifts  (corresponding  to  levels  in  steeper 
deposits)  are  driven  comparatively  close  together  (about  30  ft.  apart)  and 
the  material  between  them  removed  in  successive  steps,  as  in  underhand  or 
overhand  stoping,  the  space  behind  the  miner  being  packed  with  waste  mate- 
rial to  support  the  roof,  or  the  roof  being  supported  by  timbering  until  the  ore 
is  removed.  Sometimes  pillars  of  ore  have  to  be  left  to  aid  in  the  support 
of  the  roof,  and  when  this  is  the  case,  the  miners  try  to  leave  the  pillars 
where  the  ore  is  low  grade.  When  a deposit  of  ore  is  of  uniform  value 
throughout,  and  the  roof  of  a somewhat  flexible  character,  it  may  be  let 
down  without  much,  if  any,  stowing,  as  in  the  longwall  system  of  coal 
mining.  In  other  cases,  the  material  is  removed  like  square  work  or  by  pillars 
and  rooms,  the  pillars  in  either  case  being  robbed  as  closely  as  possible 
before  leaving  the  workings. 


LARGE  DEPOSITS  OVER  8 FEET  THICK. 


With  a deposit  much  over  8 ft.  in 


thickness,  it  is  impossible  to  keep  the 
walls  in  place  by  stulls  or  single  sticks 
of  timber.  Large  masses  of  mineral 
frequently  contain  very  valuable  ma- 
terial, and  engineers  have  developed 
a number  of  methods  for  the  removal 
of  their  valuable  contents.  The 
method  depends  largely  on  the  value 
per  ton  of  the  material  being  removed, 
and  local  conditions  as  to  the  cost  of 
labor,  timber,  filling  material,  char- 
acter of  wall  rock,  etc.  The  methods 
used  for  these  deposits  are  square  work, 
filling,  caving,  and  square-set  timbering 


Fig.  35. 

The  advantages  are  that  it 


Square  work,  also  called  the  cham- 
ber-and-pillar  system,  is  illustrated  in 
Fig.  35.  Galleries  are  driven  through 
the  ore  as  shown,  the  deeper  galleries 
being  smaller  than  the  upper  ones, 
the  object  being  to  leave  larger  pillars 
for  the  support  of  the  material  above 
the  workings.  Galleries  are  then 
driven  at  right  angles  to  these,  to  leave 
square  pillars,  as  shown.  When  this 
svstem  is  applied  to  a bed  that  is  only 
30  or  40  ft.  thick,  from  three-fourths  to 
eight-ninths  of  all  the  material  in  the 
deposit  can  be  removed,  the  remainder 
being  left  as  pillars;  but  where  it  be- 
comes necessary  to  leave  floors  be- 
tween the  succeeding  levels,  as  shown 
in  (6),  Fig.  35,  scarcely  one-half  of  the 
deposit  can  be  removed,  even  when  it 
is  of  such  a firm  nature  that  the  gal- 
leries can  be  driven  considerably 
wider  than  the  thickness  of  the  pil- 
lars. This  system  of  mining  is  applied 
to  the  removal  of  salt,  gypsum,  build- 
ing stone,  and  various  low-grade  ores, 
and  is  very  similar  to  the  room-and- 
pillar  system  (see  page  280). 

3 no  timbering,  and  that,  owing  to  the 


MINING  THICK  DEPOSITS. 


319 


larger  size  of  the  chambers,  the  material  can  he  removed  at  a low  cost  per 
ton.  The  disadvantages  are  that  a large  portion  of  the  deposit  has  to  be  left 
untouched,  and  that  where  the  formation  being  mined  is  at  all  soft,  it  is  not 
safe  to  work  these  large  chambers. 

Filling  Methods.— Sometimes  a filling  of  worthless  material  is  substituted 
for  the  worked-out  ore.  This  system  may  be  carried  on  by  any  one  of  a 
number  of  different  plans. 

Slicing  Method. — In  some  cases,  comparatively  small  drifts  or  chambers 
(from  6 ft.  X 6 ft.  to  10  ft.  X 10  ft.)  are  driven  through  the  ore  across  the 
aeposit,  and  then  tightly  packed  with  broken  rock,  after  which  other  drifts 
or  chambers  are  driven  beside  the  first  ones  and  also  packed  or  filled.  This 

Process  is  continued  until  a slice  has  been  removed  from  under  the  entire 
eposit.  The  process  is  then  repeated  on  top  of  the  filling,  taking  out  suc- 
cessive chambers  and  filling  them,  until  another  slice  has  been  removed. 
This  method  has  been  used  in  the  copper  mines  of  Spain,  and  has  also  been 
tried  at  some  mines  in  the  United  States  with  varying  degrees  of  success, 


Fig.  36. 


Fig.  37. 


depending  principally  on  the  cost  of  the  stowing  material  compared  with 
the  value  per  ton  of  the  deposit  being  removed.  In  this  process,  the  filling 
material  should  be  composed  entirely  of  large  pieces,  so  that  it  can  be 
packed  closely. 

Transverse  Rooming  With  Filling.— In  other  cases,  a filling  system  is  used 
in  which  rooms  or  chambers  are  driven  across  the  deposit  and  then  con- 
tinued upwards  by  overhand  stoping,  the  ore  being  thrown  to  a lower  level 
through  a chute  cribbed  up  as  the  work  progresses,  and  the  excavated 
space  filled  up  with  broken  rock  brought  down  through  a chute  from  above, 
as  shown  in  Fig.  36.  After  the  rooms  are  worked  out  between  two  levels, 
the  pillars  are  removed  in  the  same  manner. 

Longitudinal  Back  Stoping  With  Filling.— In  this  case,  the  deposit  is  worked  as 
a series  of  overhand  stopes,  Fig.  37,  the  space  below  the  workmen  being  filled 
with  broken  rock  a brought  down  through  raises  b from  above,  the  ore  being 
thrown  to  a level  c,  which  has  been  timbered  through  the  filling  material  on 


320 


MINING  MINERAL  DEPOSITS. 


the  first  or  lower  floor  of  the  stope.  This  method  has  been  very  successfully 
applied  to  some  of  the  large  iron  mines  of  the  Lake  Superior  region  of  the 
United  States. 

The  filling  material  used  in  any  one  of  the  various  filling  methods  may  be 
obtained  at  the  surface,  may  be  partially  or  wholly  obtained  from  the  waste 
rock  associated  with  the  vein  material  and  from  drifts  or  passages  that  have 
to  be  driven  in  barren  ground,  or  it  may  be  obtained  by  driving  drifts  into 
the  hanging  wall,  and  opening  chambers  there,  from  which  the  waste  may 
be  obtained.  (See  also  Flushing  of  Culm,  page  314. ) 

Caving  Methods. — The  longwall  method  of  mining  coal  is  really  a caving 
system,  but  where  this  system  is  applied  to  the  mining  of  large  masses,  it 
becomes  necessary  to  introduce  some  special  features.  There  are  two 
general  systems  in  use,  caving  a hack  of  ore  and  caving  the  gob  or  waste  only. 

Caving  a Back  of  Ore. — In  this  system,  drifts  or  levels  are  run  through  the 
ore  a few  feet  below  the  top  of  the  deposit,  as  though  the  material  above  were 
to  be  removed  by  overhand  stoping,  but  in  place  of  breaking  the  m,aterial 
down,  it  is  allowed  to  cave  by  gravity.  When  a back  of  ore  is  thick  (20  ft. 
or  more),  the  entire  stope  is  sometimes  allowed  to  cave  full  and  then  the 
broken  ore  removed  by  driving  heavily  timbered  drifts  through  to  the 
farther  side  and  drawing  the  crushed  material  into  the  face  of  the  drift. 

When  the  overlying  worthless  material  appears,  op-* 
erations  are  continued  by  removing  the  last  set  in 
the  drift  and  drawing  the  ore  from  nearer  the  shaft. 
This  method  is  continued  until  practically  all  the 
broken  ore  has  been  removed.  Where  the  back  of 
the  ore  is  comparatively  thin  (less  than  20  ft.),  the 
caving  is  usually  accomplished  at  the  face  of  the 
drift  only,  the  drift  being  driven  a short  distance 
beyond  the  timbering  without  support.  The  ore 
above  this  unsupported  portion  will  cave  in  and  can 
be  removed.  When  the  waste  rock  and  old  timber 
from  above  appear,  the  operator  retreats,  removing 
one  set  of  timber  from  the  drift,  caving  and  remov- 
ing the  ore  over  it.  In  this 
manner,  operations  are  contin- 
ued until  all  the  ore  over  the 
drift  or  stope  has  been  caved, 
when  another  drift  or  stope  is 
driven  beside  the  first  and  the 
ore  over  it  caved.  In  this 
method,  blasting  has  to  be  re- 
sorted to  only  in  driving  the 
drifts,  from  one-half  to  three- 
fourths  of  the  ore  being  obtained 
without  the  use  of  powder. 

The  advantages  of  this  system 
are  that  little  blasting  is  re- 
quired; practically  the  entire 
deposit  is  recovered;  the  mining 
cost  per  ton  is  very  low. 

The  disadvantages  are  that 
the  ore  is  liable  to  become 
mixed  with  more  or  less  dirt,  which  caves  down  with  it;  only  one  level  of  the 
mine  can  be  operated  at  a time,  and  the  surface  of  the  ground  is  allowed  to 
cave  into  the  openings,  thus  rendering  it  unfit  for  ordinary  surface  uses. 

Caving  the  Waste  Only.— In  this  system.  Fig.  38,  drifts  A and  galleries  B 
are  driven  through  the  top  of  the  ore  body  immediately  under  the  waste 
rock.  After  one  of  these  drifts  or  galleries  is  completed,  the  floor  is  covered 
with  a lagging  of  plank  or  poles,  and  the  waste  material  allowed  to  cave  on 
to  this  platform.  Subsequently,  other  drifts  are  driven  beside  the  first  one, 
the  floor  covered  with  lagging,  and  the  waste  allowed  to  cave.  This  process 
is  continued  until  a slice  has  been  removed  over  the  entire  surface  of  the 
ore  deposit,  when  more  drifts  are  driven  lower  down  and  another  slice 
removed.  After  the  first  slice  has  been  removed,  the  broken  or  waste  mate- 
rial is  supported  on  the  lagging  laid  on  the  floors  of  the  first  drifts,  and  hence 
the  miners  have  only  to  support  this  lagging  in  order  to  support  the  waste. 
The  caving  of  any  individual  drift  crushes  the  ore  on  either  side  to  a con- 
siderable extent,  thus  materially  reducing  the  blasting  expense, 


Fig.  38. 


IRREGULAR  DEPOSITS, 


321 


The  advantages  of  this  system  are  that  the  entire  deposit  is  recovered; 
little  blasting  is  required;  the  ore  obtained  is  clean;  the  mining  expense  is 
comparatively  low  per  ton. 

The  disadvantages  are  that  only  one  level  of  a mine  can  be  producing  at  a 
time;  the  surface  is  allowed  to  cave,  thus  rendering  it  unfit  for  surface  uses. 


SQUARE-SET  SYSTEM. 


Frequently,  large  masses  of  material  are  encountered,  which  it  is  neces- 
sary to  remove,  and  at  the  same  time  support  the  surrounding  material. 
At  times,  it  is  not  desirable  to  fill  the 

TT  l/Xit;  VXi  C XO  UCXXig  iCXXXWVcCl,  

and,  at  the  same  time,  it  is  impossible 
to  support  the  walls  by  single  sticks 
or  Stulls.  To  overcome  these  diffi- 
culties, the  square-set  system  has  been 
evolved,  which  consists  in  the  sup- 
porting of  the  walls  by  means  of  a 
series  of  square  frames,  from  6 to  9 ft. 
square,  which  are  placed  in  position 
as  fast  as  the  ore  is  removed.  The  use 
of  these  frames  reduces  the  length  of 
the  individual  sticks,  and  so  produces 
a firm  structure.  The  timbers  may 
be  square-sawed  material  or  round 
logs.  If  the  walls  are  soft,  the  sides 
and  top  may  require  lagging,  and  if 
the  floor  is  soft  or  composed  of  ore, 
sills  will  be  necessary  under  the  posts. 

The  mining  is  carried  on  by  overhand- 
stoping  system,  removing  one  block  at 
a time  and  replacing  it  with  the  square 
set.  Fig.  39  represents  a stope,  the  Fig.  39. 

walls  and  roof  of  which  are  supported 

by  square  sets  that  are  lagged  from  the  outside.  In  this  case,  the  square 
sets  are  made  from  round  timber. 


IRREGULAR  DEPOSITS. 

Coyoting,  or  Gophering.— Bodies  of  valuable  material  frequently  occur  that 
cannot  be  mined  by  any  regular  system.  These  are  recovered  by  simply 
following  the  ore  throughout  its  irregularities  and  removing  it  with  the  use 
of  as  little  supporting  timber  or  other  material  as  possible.  Owing  to  the 
crooked  and  irregular  passages  that  occur  in  such  mines,  the  work  has  been 
called  coyoting,  or  gophering.  Sometimes  regular  levels  are  driven  at  stated 
intervals,  and  the  coyoting,  or  gophering,  carried  on  from  them.  Many  of 
the  small  gold  and  silver  mines  of  the  West,  the  mines  of  Mexico  and  South 
America,  and  the  Missouri  lead  and  zinc  deposits  are  worked  by  this  system, 
the  object  being  to  remove  as  much  of  the  ore  as  possible  without  the  use  of 
timbering  or  the  driving  of  unnecessary  passages. 

Probably  one  of  the  best  examples  of  working  irregular  deposits  is  the 
mining  practice  in  the  Joplin  zinc  district,  Missouri.  The  deposits  of  zinc 
blende  are  irregularly  distributed  through  a limestone  rock,  and  the  mining 
is  carried  on  in  a very  crude  and  irregular  fashion. 

After  an  ore  body  has  been  found  by  drilling,  a shaft  5 ft.  X 5 ft.  to  6 ft.  X 
9 ft.  in  the  clear  is  sunk  by  the  contractor,  the  price  being  $4  per  foot  for  soft 
and  ^9  per  foot  for  hard  ground  for  the  first  50  to  80  ft.,  the  contractor  doing 
all  the  work  in  sinking  and  timbering.  Through  the  soft  ground,  the  shaft  is 
timbered  by  4"  round  poles  or  by  2"  X 4"  or  2"  X 6"  timbers  laid  flatwise, 
skin  to  skin.  The  mines  are  divided  into  four  kinds.  (1)  Very  hard  mines 
that  require  all  the  ore  to  be  drilled  with  air  drills  and  blasted  out,  and 
require  no  timbering.  (2)  Mines  that  are  hard  but  have  open  crevices 
between  the  strata  where  a hand  drill  can  be  driven  and  a charge  of  dyna- 
mite lodged  and  exploded,  throwing  down  a large  amount  of  dirt  and  so 
jarring  the  surrounding  ground  that  it  may  be  easily  cut  down  with  the 
miner’s  pick.  This  kind  of  ground  needs  no  timber.  (3)  Mines  that  are 
moderately  soft  and  where  the  miner  can  place  a blast  anywhere  by  driving 


322 


COSTS  OF  MINING  ANTHRACITE. 


a spud,  throwing  down  a large  amount  of  ore.  The  drifts  are  carried 
10  ft.  X 12  ft.  in  the  clear,  and  are  cut  ahead  from  6 to  10  ft.  before  putting 
in  the  sets  of  timber  and  laggings  to  hold  the  roof.  (4)  Mines  that  are  very 
soft  and  where  a drift  cannot  be  carried  over  8 ft.  X 10  ft.  in  size,  where  the 
getting  of  the  ore  is  all  performed  by  pick  and  shovel,  and  where  it  is  neces- 
sary to  timber  close  and  drive  spiling  overhead  as  well  as  along  the  sides 
and  to  resort  to  mud -sills  in  the  floor  of  the  drift. 

When  the  shaft  reaches  the  ore  and  the  drift  is  extended  for  some  dis- 
tance to  prove  the  ore  body,  underhand  stoping  is  used  and  15'  holes 
are  drilled  by  hand  in  the  bottom.  A charge  of  50  lb.  of  40^  dynamite  lifts  a 
stope  10  ft.  X 10  ft.  The  cost  of  75  tons  of  ore,  hoisting  it  and  dumping  it  on 
the  mill  platform  during  a shift  of  9 hours  in  the  two  classes  of  hard  mines 
mentioned,  is,  according  to  Mr.  E.  Hedburg,  as  follows: 


1 ground  boss  $ 2.50 

2 miners  at  ^2.00 : 4.00 

2 miners  at  S1.75 3.50 

2 shovelers  at  $1.75 3.50 

1 hoister 1.75 

1 engineer,  who  also  sharpens  picks  and  drills 2.25 

1 engineer  1.50 

Dynamite  6.00 

Fuel 2.50 

Oil  and  supplies 2.50 

Superintendent  3.50 

Total  $33.40 


Or  44.5  cents  per  ton  of  rough  ore;  this  includes  pumping  the  mine. 

In  very  soft  ground,  a drift  8 ft.  to  10  ft.  high  is  driven,  a spiling  put  in 
the  top  and  sides.  When  one  level  is  worked  out,  the  whole  drift  is  then 
caved  from  the  surface  and  allowed  to  settle  down  on  the  floor  of  timbers. 
The  cost  of  mining  in  soft  ground  is  about  the  same  as  in  hard  ore,  as  the 
saving  of  labor  and  dynamite  is  expended  in  timber  and  time.  A typical 
primitive  mining  plant  in  this  region,  which  has  a shaft  150  ft.  deep*  with 
pump,  hoisting  engines,  and  boilers,  and  including  hand  jigs,  screens,  and 
tools,  costs  from  $2,000  to  $3,000;  more  modern  plants  are  however  now 
being  erected,  costing  $8,000  to  $10,000. 


SPECIAL  METHODS. 

Frozen  Ground.— When  the  material  of  placer  deposits  is  frozen,  as  in 
Alaska  and  Siberia,  it  is  mined  by  building  a fire  on  the  surface,  which 
thaws  the  earth  to  a depth  of  from  1 ft.  to  14  in.  The  embers  are  then 
scraped  away  and  the  thawed  material  removed.  By  repeating  this 
operation,  a shaft  can  be  sunk,  and  then,  by  building  a fire  against  one  side, 
a drift  can  be  started  and  continued  by  thawing  the  face,  1 ft.  at  a time. 
It  has  been  found  that  1 ft.  of  timber  piled  against  the  face  of  a drift  will 
thaw  to  a depth  of  about  1 ft.  The  latest  practice  thaws  the  frozen  ground 
by  means  of  a steam  jet  instead  ot  by  fire.  The  openings  have  to  be  securely, 
but  not  heavily,  timbered. 

Leaching  Methods.— Salt,  copper,  and  sulphur  have  been  mined  by  leaching 
methods.  In  the  case  of  salt,  a hole  is  drilled  into  the  salt  formation,  water 
allowed  to  flow  down  and  dissolve  the  salt,  and  is  then  pumped  out  as  a con- 
centrated brine.  For  excavating  upward  in  salt,  a jet  of  water  is  made  to 
play  upon  the  roof  of  the  level  to  be  raised,  and  the  resulting  brine  is  carried 
off  in  launders. 

When  old  workings  containing  the  sulphides  of  copper  are  left  exposed 
to  the  action  of  air  and  to  percolating  waters,  part  of  the  copper  is  converted 
into  soluble  sulphate.  Water  pumped  from  such  mines  may  be  a profitable 
source  of  the  metal,  for  by  passing  it  over  iron  bars  or  scrap  iron  the  copper 
will  be  separated  and  deposited  as  cement  copper  in  the  bottom  of  the 
vessel  containing  the  iron. 

In  the  case  of  sulphur,  superheated  steam  is  forced  down  to  melt  the 
sulphur,  which  is  then  pumped  out. 


LEHIGH  REGION. 


323 


COSTS  OF  MINING  ANTHRACITE. 

The  following  costs  include  only  labor  and  supplies,  and  do  not  include, 
ill  general,  improvements,  royalties,  taxes,  and  other  similar  fixed  charges 
that  independent  of  the  method  of  mining. 


LEHIGH  REGION  (PENNA.). 

The  costs  for  the  Lehigh  region,  though  based  on  the  results  of  a single 
'Company,  are  believed  to  be  very  fairly  representative  of  the  entire  region. 
'They  are  the  mean  costs  of  two  collieries  where  about  2,000  men  were 
employed  inside  and  outside,  and  apply  to  the  year  1897,  when  the  con- 
dition at  all  anthracite  mines  was  very  unfavorable  to  economical  working, 
as  the  mines  were  then  working  on  very  short  time. 

The  tonnage  at  these  collieries  for  the  year  was  as  follows: 

January,  29,775.04  May,  34,090.02  September,  27,406.94  1 

February,  30,872.97  June,  35,761.89  October,  56,710.04  f Total, 

March,  42,827.04  July,  44,409.13  November,  48,177.94  [ 463,672.08. 

April,  38,553.08  August,  37,500.97  December,  37,587.02  J 

The  following  tables  show  the  distribution  of  this  output  by  sizes  during 
the  year,  and  the  costs  per  ton  itemized  under  the  several  headings  given: 

Percentages  of  Different  Sizes. 


Month. 

Lump. 

Broken. 

Egg. 

Stove. 

Chestnut. 

Pea. 

January 

10.56 

23.59 

18.27 

18.69 

14.21 

14.68 

February  

12.34 

22.54 

18.11 

17.98 

14.50 

14.53 

March 

11.85 

19.26 

18.81 

19.69 

13.18 

17.21 

April  

12.81 

19.21 

18.35 

19.48 

11.14 

19.01 

May 

13.81 

19.11 

18.35 

19.01 

11.32 

18.40 

June 

15.29 

18.60 

17.73 

19.08 

11.23 

18.07 

July 

14.26 

19.89 

17.41 

18.30 

11.25 

18.89 

August  

13.56 

20.26 

18.10 

17.72 

11.49 

18.87 

September 

12.31 

20.41 

18.27 

18.28 

11.61 

19.12 

October 

12.21 

18.01 

19.15 

18.89 

12.28 

19.46 

November 

11.40 

18.53 

19.78 

19.79 

12.01 

18.49 

December 

10.78 

19.56 

20.09 

20.32 

12.07 

17.18 

Year 

12.58 

19.71 

18.59 

18.99 

12.15 

17.98 

Costs  of  Mining  and  Preparation. 


Month. 

Outside. 

Inside. 

Total 

Cost. 

Credits. 

Net  Cost 

Labor. 

Supplies. 

Total. 

Labor. 

Supplies. 

Total. 

January ... 

.300 

.109 

.409 

.951 

.196 

1.147 

1.595 

.100 

1.495 

February.. 

.297 

.085 

.382 

.909 

.190 

1.099 

1.519 

.063 

1.456 

March 

.243 

.047 

.290 

.844 

.151 

.995 

1.311 

.088 

1.223 

April  

.242 

.071 

.313 

.822 

.137 

.959 

1.303 

.075 

1.228 

May 

.251 

.100 

.351 

.852 

.166 

1.018 

1.397 

.103 

1.294 

June 

.300 

.079 

.379 

.500 

.203 

.703 

1.576 

.103 

1.473 

July 

.240 

.063 

.303 

.487 

.162 

.649 

1.485 

.084 

1.401 

August  .... 

.248 

.095 

.343 

.709 

.182 

.891 

1.579 

.085 

1.494 

September 

.278 

.096 

.374 

.682 

.158 

.840 

1.588 

.054 

1.534 

October.... 

.228 

.093 

.321 

.721 

.129 

.850 

1.580 

.072 

1.508 

N ovember 

.247 

.093 

.340 

.806 

.210  ' 

1.016 

1.846 

.091 

1.755 

December. 

.290 

.061 

.351 

.833 

.220 

1.053 

1.883 

.090 

1.793 

Year  

.271 

.092 

.363 

1.109 

.162 

1.271 

1.634 

.088 

1.546 

324 


COSTS  OF  MINING  ANTHRACITE, 


Cost  per  Ton  of  Supplies  Used  Inside. 


Distribution.  j 

Jan. 

Feb. 

Mar. 

Apr.j 

May. 

i 

Jun. 

Jul. 

Oils 

.010 

.011 

.007 

.010 

.007 

.009 

.006 

Powder 

.036 

.030 

.031 

.026 

.030 

.032 

.029 

Lumber - 

.007  I 

.025 

.011 

.004 

.002 

.008 

.007 

Props 

.040 

.027 

.021 

.015 

.022 

.027 

.019 

Feed  

.039 

.018 

.019 

.017 

.023 

.022 

.022 

Mules  killed,  etc 

.010 

.005 

.014 

.019 

.013 

.009 

.015 

T rails,  frogs,  etc 

.005 

.012 

.007 

.009 

.018 

.010 

.010 

Wire  ropes  

.018 

.016 

.025 

.013 

General  supplies  

.019 

.021 

.014 

.009 

.018 

.021 

.013 

Total  general  supplies 

.166 

.167  i 

t .140 

1 .109 

.133 

.163 

.134 

Pumping  machiuerv  

Hoisting  machinery  

.009 

1 

.005 

.004 

.012 

.016 

.023 

.004 

Ventilating  machinery 

Boilers  

1 

Mine  cars 

Engines 

.018 

.007 

, .016 

.017 

.017 

.024 

Total  repairs  

.030 

.023 

.011 

; .028 

.033 

.040 

.028 

Total  cost  inside  

.196 

! .190 

! .151 

.137 

.166 

1 .203 

.162 

Credits  

.100 

1 .063 

1 .088 

1 .075 

.103 

1 .103 

.084 

Net  cost  inside 

.096 

.127 

1 .063 

i 

: .062 

1 

.063 

: .100 

[ 

.078 

Cost  per  Ton  of  Supplies  Used  Outside. 


Distribution. 

Jan. 

Feb. 

Mar.' 

: 1 

Apr.  May.  Jun.  Jul. 

Oils 

.010 

.008 

.007 

.006 

.009 

.009 

.008 

Lumber - 

.022 

.0-25 

.003 

.016 

.015 

.005 

.012 

Feed  

.008 

.004 

.005 

.004 

.005 

.005 

.006 

Mules  killed,  etc 

T rails,  frogs,  etc 

.001 

.003 

.004 

.005 

.002 

Wire  ropes  

General  supplies  

.020 

.021 

.015 

.008 

.040 

.016 

.019 

Total  general  supplies 

.060 

[ .058 

.031 

.037 

.073 

.040 

.047 

Pumping  machiners^  

.001 

Hoisting  machinery 

.008 

.002 

.001 

.001 

.003 

.008 

.001 

Ventilating  machinerv 

.003 

Breaker  machinery....* 

.028 

.012 

.008 

.014 

.017 

.011 

.008 

Boilers  

.006 

.005 

.002 

.013 

.001 

.011 

.005 

Breaker 

.006 

.008 

.005 

.006 

.005 

.006 

.002 

Tracks  and  sidings  

.001 

Miscellaneous 

Total  repairs  

.049 

.027 

.016 

.034 

.027 

.039 

.016 

Total  cost  outside 

.109 

.085 

.047 

.071 

.100 

.079 

.063 

Credits  

Net  cost  outside 

.109 

.085 

.047 

.071 

.100 

.079 

.063 

In  the  two  tables  above  and  the  one  following,  the  fibres  were  available 
for  seven  months  of  the  year  only,  but  an  average  for  these  months  gives  a 
fair  average  for  the  year. 


WYOMING  REGION. 


325 


Itemized  Cost  of  Outside  Labor. 


Occupations. 

Jan. 

Feb. 

March. 

April- 

May. 

June. 

July. 

Foreman  and  assistants 

.013 

.012 

.007 

.006 

.006 

.006 

.003 

Clerks,  shipper  and  supply 

.004 

.004 

.003 

.003 

.002 

.002 

.002 

Hoisting  engineers 

.009 

.022 

.018 

.021 

.019 

.026 

.021 

Pump  and  fan  engineers 

.003 

.003 

.003 

.002 

.003 

J)03 

Locomotive  engineers  and  helpers 

.014 

.014 

.011 

.009 

.011 

.013 

.011 

Firemen  and  ashmen 

.078 

.071 

.056 

.060 

.063 

.069 

.057 

Stablemen 

.005 

.005 

.003 

.003 

.004 

.005 

.003 

Watchmen 

.007 

.006 

.004 

.005 

.006 

.006 

.004 

Total  miscellaneous 

.133 

.137 

.105 

.109 

.114 

.130 

.101 

Topmen  and  footmen 

.004 

.004 

.002 

.003 

.003 

.004 

.003 

Top  drivers  and  oilers 

.007 

.007 

.006 

.006 

.007 

.008 

.007 

Dumpmen 

.002 

.003 

.002 

.002 

.002 

.003 

.002 

Platform  and  docking  boss 

.014 

.013 

.013 

.012 

.012 

.012 

.012 

Chute  bosses 

.006 

.006 

.005 

.006 

.005 

.004 

.006 

Slate  pickers 

.059 

.063 

.058 

.053 

.048 

.056 

.057 

Car  loaders 

.007 

.007 

.007 

.006 

.006 

.008 

.008 

Breaker  engineer 

.003 

.003 

.002 

.002 

.002 

.001 

.002 

Dirt  and  plane  engineer 

.007 

.001 

.001 

.001 

.001 

.001 

* .001 

Rock  and  dirt  men 

.007 

.009 

.009 

.006 

.004 

.005 

.005 

General  laborers 

.012 

.013 

.009 

.011 

.020 

.022 

.012 

Total  breaker 

.128 

.129 

.114 

.108 

.110 

.124 

.115 

Pumping  machinery 

.001 

.001 

Hoisting  machinery 

.010 

.005 

.005 

.005 

.006 

.009 

.005 

Ventilating  machinery 

.003 

Breaker  machinery 

.005 

.004 

.004 

.006 

.003 

.002 

.002 

Boilers 

.004 

.004 

.001 

.005 

.002 

Breakers 

.007 

.009 

.007 

.005 

.011 

.019 

.006 

Tracks  and  sidings 

.008 

.007 

.007 

.009 

.007 

.008 

.007 

Miscellaneous 

.004 

.001 

.002 

Total  repairs 

.039 

.031 

.024 

.025 

.027 

.046 

.024 

Total  cost  outside  labor 

.300 

.297 

.243 

.242 

.251 

.300 

.240 

WYOMING  REGION  (PENNA.). 

The  following  tables  of  costs  for  the  Wyoming  region  give  mean  results 
from  a number  of  different  collieries  which  are  quite  widely  separated 
in  location  and  at  which  the  conditions  of  working  are  so  different  that 
the  mean  results  given  are  thought  to  represent  average  results  for  the 
entire  region.  They  also  apply,  approximately,  to  the  Lackawanna  Valley, 
where  the  general  conditions  are  the  same,  although  the  seams  are  much 
nearer  the  surface  than  in  the  Wyoming  region,  and  the  amount  of  gas 
present  in  the  coal  is  much  less.  These  same  figures  are  probably  also  fairly 
representative  of  the  Schuylkill  and  Shamokin  fields. 

The  collieries  for  which  the  following  figures  are  averages  are  all  operated 
through  shafts,  varying  in  depth  from  350  to  1,100  ft.,  and  many  of  the  mines 
are  extremely  gaseous.  The  number  includes  several  entirely  new  and 
modern  surface  and  underground  plants,  and  the  others,  though  not  new, 
have  been  overhauled  and  modernized  as  much  as  possible.  At  these 
collieries  10,000  men  were  employed  during  the  year  1895,  for  which  the 
data  are  given,  and  during  the  same  year  the  output  was  1,862,144  tons, 
distributed  during  the  year  as  follows: 


Month. 

Ton- 

nage. 

Days 

Worked. 

Month. 

Ton- 

nage. 

Days 

Worked. 

Month. 

Ton- 

nage. 

Days 

Worked. 

January. 

107,952 

7.94 

May 

179,752 

12.84 

September 

161,213 

11.52 

February 

98,109 

7.37 

June 

164,062 

11.92 

October.... 

198,161 

13.90 

March.... 

141,991 

9.95 

July 

145,445 

10.59 

November 

228,433 

17.15 

April 

136,375 

9.69 

August .. 

177,241 

12.96 

December 

123,406 

8.87 

326 


COSTS  OF  MINING  ANTHRACITE, 


Percentages  of  Different  Sizes. 


Month. 

Lump. 

Steamer. 

Broken. 

Egg. 

Stove. 

Chestnut. 

Pea. 

January  

8.21 

.02 

17.53 

20.31 

21.46 

18.04 

14.43 

February 

8.29 

.12 

17.75 

20.41 

20.85 

17.44 

15.14 

March  

6.20 

.55 

17.64 

20.04 

20.65 

18.00 

16.92 

April 

7.01 

.38 

16.76 

20.17 

20.92 

18.12 

16.64 

May  

4.79 

.27 

18.63 

20.33 

21.42 

18.23 

16.33 

June  

3.29 

.21 

22.43 

19.72 

20.21 

18.57 

15.57 

July  

7.84 

.42 

19.42 

19.54 

19.46 

18.58 

14.74 

August 

5.05 

.57 

19.84 

20.69 

18.92 

18.62 

16.31 

September  

4.25 

.27 

18.81 

21.98 

19.98 

19.32 

15.39 

October 

4.72 

.01 

16.77 

22.00 

21.27 

19.88 

15.35 

November  

2.69 

.16 

15.56 

22.42 

22.66 

20.71 

15.80 

December 

4.40 

.57 

14.03 

22.62  • 

21.27 

21.41 

15.70 

Year  

5.23 

.29 

17.96 

20.95 

20.80 

19.03 

15.74 

Costs  of  Mining  and  Preparation  per  Ton. 


Months. 

Outside. 

Inside. 

Total  Cost. 

Credits. 

Net  Cost. 

Labor. 

Supplies. 

Repairs. 

Total. 

Labor. 

Supplies. 

Repairs. 

Total. 

January  

.363 

.042 

.014 

.419 

.934 

.249 

.028 

1.211 

1.630 

.120 

1.510 

February 

.376 

.042 

.014 

.432 

.947 

.273 

.030 

1.250 

1.682 

.104 

1.578 

March  

.297 

.031 

.010 

.338 

.872 

.182 

.022 

1.076 

1.414 

.096 

1.318 

April 

.305 

.034 

.023 

.362 

.870 

.203 

.020 

1.093 

1.455 

.103 

1.352 

May  

.270 

.022 

.011 

.303 

.839 

.164 

.015 

1.018 

1.321 

.101 

1.220 

June 

.290 

.032 

.011 

.333 

.874 

.206 

.018 

1.098 

1.431 

.105 

1.326 

July  

.309 

.046 

.019 

.374 

.879 

.266 

.033 

1.178 

1.552 

.098 

1.454 

August 

.286 

.030 

.017 

.333 

.873 

.194 

.026 

1.093 

1.426 

.102 

1.324 

September  ... 

.284 

.039 

.012 

.335 

.890 

.201 

.024 

1.115 

1.450 

.105 

1.345 

October  

.267 

.036 

.013 

.316 

.856 

.188 

.020 

1.064 

1.380 

.100 

1.280 

November .... 

.262 

.029 

.010 

.301 

.860 

.214 

.018 

1.092 

1.393 

.104 

1.289 

December  ... 

.344 

.045 

.018 

.407 

.954 

.307 

.028 

1.289 

-1.696 

.120 

1.576 

Year 

.297 

.034 

.014 

.345 

.881 

.214 

.023 

1.118 

1.463 

.104 

1.359 

Coal  Production  of  United  States. 


Year. 

Bituminous. 

Anthracite. 

Tons  of  2,000  Lb. 

Value. 

Tons  of  2,240  Lb. 

Value. 

1890 

1895 

1897 

1898 

1899 

111,302,322 

135,118,193 

147,609,985 

166,592,023 

193,321,987 

$110,420,801 

115,779,771 

119,567,224 

132,586,313 

167,935,304 

46,468,641 

57,999,937 

52,611,680 

53,382,644 

53,944,647 

$66,383,772 

82,019,272 

79,301,954 

75,414,537 

88,142,130 

PRICES  OF  COAL. 

The  table  on  page  327,  given  by  the  U.  S.  Geological  Survey,  will  be  of  interest 
as  showing  the  fluctuations  in  the  average  prices  ruling  in  each  State  since  1886. 
Prior  to  that  year,  the  statistics  were  not  collected  with  sufficient  accuracy  to 
make  a statement  of  average  prices  of  any  practical  value.  These  averages  are 
obtained  by  dividing  the  total  value  by  the  total  product,  except  for  the  years 
1886, 1887,  and  1888,  when  the  item  of  colliery  consumption  was  not  considered. 


Average  Prices  per  Short  Ton  for  Coal  at  the  Mines  Since  1886. 


PRICES  OF  COAL. 


327 


pm  mmmm 


r-^ 


r^(N 


i 


^ ,0  o 


pm  mmmm  mwmw-i 


pm  mmmmmwmw-% 


pm^-  mmmm 


^232^  ^§222^^223  !22^i^3ll^2^2 


Pi22  ^^2^!-^S2S  2^2^1^213-5^2 


pi22  ^2223^^225  2 2- 


PSIS  22l2§§^^25i  i i^i-2i5§i2i 


Pii2  232222^221  I 2^1^211^1^! 


,-1  >.>. 
I e e 


l2ii2  232232-221  I 2-1-22521^= 


oa» 
rH  r-5 
Q g 


|i 

II 


a Exclusive  of  colliery  consumption,  h Includes  Alaska,  c Includes  Nebraska. 


328 


COST  OF  COKING  COAL, 


COST  OF  COKING  COAL. 

The  cost  for  labor  alone  of  coking  coal  has  been  given  by  a number  of 
companies  in  the  Connellsville  district  as  61  cents  per  ton  of  coke  produced, 
or  401  cents  per  ton  of  coal  coked,  exclusive  of  royalties,  taxes,  rents,  and 
such  fixed  charges. 

In  the  “American  Manufacturer”  for  July  27,  1899,  Mr.  F.  C.  Keighley 
gave  the  following  as  the  proportional  costs  of  the  several  items  of  mining 
and  coking  Connellsville  coal; 


Coke  Yard. 

Per 

Cent. 

Coke  Yard. 

Per 

Cent. 

Drawing 

70.01 

Shifting  c.ars 

1.28 

Leveling 

8.96 

Yard  bosses  

1.12 

Charging 

3.48 

Masons  on  repairs 

6.12 

Carters 

2.48 

Forking 

1.60 

Bookkeeper  and  superin- 

Individual cars  

.52 

tendent,  i of  total  for 

Sundry  

.51 

mine  and  yard 

2.04 

Yard  pumps 

.76 

Cleaning  tracks 

1.20 

Total  

100.08 

Mine. 

Per 

Cent. 

Mine. 

Per 

Cent. 

Room  coal  

52.15 

Machinist  

.49 

Drivers 

8.07 

Bookkeeping,  i of  total  for 

Heading  coal 

11.15 

mine  and  yard 

.49 

Rope  haulage  

2.81 

Outside  labor  

2.03 

Roads  

3.03 

Stable  boss 

.96 

Mine  bosses  

1.31 

Teams 

.65 

Fire  boss  

1.44 

Blacksmith  

.98 

Timber 

2.83 

Carpenters 

1.01 

Trappers 

.43 

Lamp  cleaners 

.82 

Superintendence,  i of  total 

Inside  pumps  

.59 

for  mine  and  yard 

.49 

Steam  pumps  

.55 

Cagers  

.66 

Surveys  

.41 

Runners  and  oilers  

.80 

Extra  men 

.51 

Engineers  

1.01 

Supplies 

.92 

Firemen  

1.13 

Betterments  

1.05 

Dumpers 

1.25 

Total 

100.02 

The  mine  labor  is  67.20^  of  the  total  labor  cost,  and  the  coke-yard  labor  is 
32.80^  of  the  total  labor  cost. 

Tne  cost  of  equipping  a coke  plant  and  opening  a mine  to  furnish  the 
coal  in  the  Connellsville  region  is  from  S500  to  |l,000  per  oven,  dependent  on 
the  kind  of  opening  for  the  mine  and  local  considerations.  ^00  per  oven  is 
a fair  price  for  a plant  when  the  conditions  are  favorable  and  the  mine  is  a 
drift  mine,  and  $1,000  is  a fair  price  for  a shaft  mine  about  300  ft.  deep, 
under  rather  unfavorable  conditions. 

Fulton  gives  the  cost  of  the  various  types  of  coke  ovens  as  follows; 

Not  saving  by-products:  Beehive,  $300;  Thomas,  $800;  McLanahan,  $800; 
Belgian,  $1,000;  Copp6e,  $1,000;  Bernard,  $1,000. 

Saving  by-products:  Simon  Carves,  $1,300;  Semet-Solvay,  $1,600;  Huessner, 
$1,400;  G.  Seibel,  $1,300;  Otto-Hoffman,  $1,600;  Festner-Hoffinan,  $1,500. 

The  usual  quantity  of  coal  required  to  make  1 ton  of  coke  is  1.4  to  1.6  tons. 

The  loss  in  loading  coke  at  the  ovens  and  again  unloading  it  at  the 
furnaces  or  steel  works  is  2^  to  3^.  During  the  winter  and  in  wet  seasons 
coke  takes  on  2^  to  Zf  of  moisture  in  transit  between  the  ovens  and  the 
furp^ces, 


EXPLOSIVES 


329 


EXPLOSIVES. 

The  characteristics  of  a good  blasting  explosive  are:  (1)  sufficient  stability 
and  strength;  (2)  difficulty  of  detonating  by  mechanical  shock;  (3)  handy 
form;  (4)  absence  of  injurious  effects  on  the  user. 

Explosives  are  divided  into  two  general  classes:  (1)  low  explosives  or 
direct-exploding  materials;  (2)  high  explosives  or  indirect-exploding  mate- 
rials that  require  a detonator. 

Low  Explosives.— Gunpowder  or  black  powder  is  the  type  of  this  group. 
I ts  composition  varies,  depending  on  the  purpose  for  which  it  is  to  be  used, 
but  the  ingredients  commonly  used  in  its  manufacture  are  saltpeter,  sulphur, 
and  charcoal. 

The  following  table  gives  the  composition  of  blasting  powder  in  different 
countries: 

Composition  of  Blasting  Powder  {Guttmann), 


Ingredients. 

Great 

Britain. 

Germany. 

Austria- 

Hungary. 

France. 

Russia. 

Italy. 

United 

Siaies. 

Saltpeter  

75 

66.0 

64 

62 

66.6 

70 

64 

Sulphur 

10 

12.5 

16 

20 

16.7 

18 

16 

Charcoal  

15 

21.5 

20 

18 

16.7 

12 

20 

High  Explosives.— These  are  a mixture  of  nitroglycerine  with  an  absorbing 
dope,  the  composition  of  which  is  such  that,  in  addition  to  thoroughly  and 
permanently  absorbing  the  nitroglycerine,  it  is  itself  a gas-producing  com- 
pound. Nitroglycerine  at  60°  F.  has  a specific  gravity  of  1.6.  It  is  odorless, 
nearly  or  quite  colorless,  has  a sweetish  burny  taste,  is  poisonous  even  in 
very  small  quantities,  and  is  insoluble  in  water.  All  nitroglycerine  com- 
pounds freeze  at  42°  F.,  and  explode  when  confined  at  360°  F.  It  takes  fire 
at  306°  F.,  and,  if  unconfined,  burns  harmlessly  unless  in  large  quantities,  so 
that  a part  of  it,  before  coming  in  contact  with  the  air,  becomes  heated  to 
-the  exploding  point. 

Thawing  Dynamite.- All  frozen  cartridges  should  be  thawed,  as,  when 
frozen,  cartridges  are  very  hard  to  explode,  and  even  if  they  do  explode, 
the  results  are  not  nearly  as  satisfactory  as  when  properly  thawed.  When 
cartridges  are  frozen,  do  not  expose  to  a direct  heat,  but  thaw  by  one  of 
the  following  methods:  First,  place  the  number  of  cartridges  needed  for 
a day’s  work,  on  shelves  in  a room  heated  by  steam  pipes  (not  live  steam) 
or  a stove.  Where  regular  blasting  is  done,  a small  house  can  be  built  for 
this  purpose,  fitted  with  a small  steam  radiator.  Exhaust  steam  through 
these  pipes  gives  all  heat  necessary.  Bank  your  house  around  with  earth, 
or,  preferably,  fresh  manure.  Second,  use  two  water-tight  kettles,  one 
smaller  than  the  other,  put  cartridges  to  be  thawed  in  smaller  kettle,  and 
place  it  in  larger  kettle,  filling  space  between  the  kettles  with  hot  water  at, 
say,  130°  to  140°  F.,  or  so  that  it  can  be  borne  by  the  hand.  To  keep  water 
warm,  do  not  try  to  heat  it  in  the  kettle,  but  add  fresh  warm  water.  Cover 
kettles  to  retain  heat.  In  thawing  do  not  allow  the  temperature  to  get 
above  212°  F.  Third,  where  the  number  of  cartridges  to  be  thawed  is  small, 
they  may  be  placed  about  the  person  of  the  blaster  until  ready  for  use,  the 
heat  of  the  body  thawing  the  cartridges.  Keep  cartridges  away  from  all 
fires— this  applies  to  all  explosives.  Do  not  be  in  a hurry,  but  thaw  slowly. 
Do  not  thaAV  before  an  open  fire.  Do  not  put  cartridges  in  an  oven,  on  a hot 
stove,  against  hot  iron  plates,  or  against  brick  casing  of  a boiler.  Do  not  put 
cartridges  in  hot  water,  or  expose  them  to  live  steam.  And  do  not  take  any 
kind  of  powder,  fuse,  or  caps  near  a blacksmith  shop. 

A large  number  of  high  explosives  are  made  that  vary  but  little  in  their 
composition,  the  main  difference  being  in  the  character  of  the  dope  and  in 
the  percentage  of  nitroglycerine.  The  trade  name  is  usually  determined  by 
the  percentage  of  nitroglycerine,  thus  lOj^  dynamite  means  that  the  dyna- 
mite contains  10^  of  nitroglycerine,  etc. 

Safety  explosives,  or,  as  they  are  called  in  England,  pemfffed  explosives,  are 
compounds  intended  for  use  in  gaseous  mines,  and  they  are  so  constituted 


830 


EXPLOSIVES. 


that  they  \v*ill  ignite  without  producing  the  extremely  high  temperature 
given  by  ordinary  explosives.  The  term  flameless  explosives  was  formerly 
used,  but  it  has  been  replaced  by  safety  explosives,  as  the'  absence  of  a flame 
is  not  now  necessary  to  a permitted  explosive. 

Common  Blasting  Explosives. 


Atlas. 


Brands  Equivalent  in  Strength  to  Atlas. 


Brand. 

Per  Cent. 

Nitroglycerine.  | 

1 Repauno  Gelatine. 

Hercules  Powder. 

i 

Hercules  Gelatine. 

Giant  Powder. 

Giant  Gelatine. 

Hecla  Powder. 

(V 

73 

O 

PL 

a 

A 

75 

A 

No.  1 XX 

No.  1 XX 

Old  No.  1 

No.l  A 

No.  1 XX 

B + 

60 

B + 

No.  1 

No.  1 

No.  1 A 

No.l 

No.  1 XS 

No.l 

B 

50 

B 

No.  2 SS 

No.  2 SS 

New  No.  1 

No.  2 

No.  1 X 

No.  2 XX 

C-f 

45 

c + 

No.  2 S 

N0.2S 

No.  2 Extra 

N0.2X 

c 

40 

c 

No.  2 

No.  2 

No.  2 

N0.3C 

No.l 

No.  2 

D + 

33 

No.  2C 

No.  2C 

N0.2X 

No.  3 A 

D 

30 

No.  3 

No.  3 

No.  2 

No.  3 

E + 

27 

N0.3B 

XXX 

N0.3X 

N0.3B 

E 

20 

No.  4B 

xxxx 

No.  3 

No.  4 

Drilling.— Adapt  the  size  and  depth  of  the  hole  to  the  work  to  be  accom- 
plished. As  a rule,  for  ordinary  rock  blasting,  the  distance  between  the  holes 
should  be  equal  to  from  one-half  to  the  total  depth  of  the  holes,  the  holes 
set  back  from  the  face  twice  as  far  for  dynamite  as  for  common  black 
powder,  say  a distance  equal  to  the  depths  of  the  holes  or  slightly  less,  and 
load  one-third  the  length  of  the  hole.  These  directions  are  only  general, 
and  do  not  apply  to  very  deep  holes.  Much  depends  on  character  and  hard- 
ness of  the  rock,  also  on  size  of  drill  holes.  In  all  cases,  the  experience 
and  judgment  of  the  blaster  must  be  his  guide. 

Diameter  of  Hoies.— In  driving  headings  or  sinking  shafts,  experience  shows 
that  holes  having  a diameter  varying  from  ^ to  H in.  at  the  bottom  are 
most  economical  in  hard  rock,  if  charged  with  the  strongest  high  explosive. 
On  the  contrary,  holes  of  large  diameter,  say  1^  to  2 in.  in  diameter,  and 
charged  with  strong,  low,  and  cheap  explosive,  are  the  best  when  operating 
in  weak  rock.  All  the  holes  in  the  heading  or  shaft  should  have  the  same 
diameter,  and  the  best  arrangement  is  to  give  an  equal  resistance  of  rock  to 
each,  and  to  so  place  each  hole  that  it  will  receive  the  greatest  benefit  from 
the  free  faces  formed  by  firing  the  previous  holes. 

Relation  of  Diameter  of  Hole  to  Length  of  Charge. — By  experiment,  it  has  been 
proved  that,  as  a rule,  the  length  of  the  charge  of  explosive  for  single  holes 
should  not  exceed  from  8 to  12  times  the  diameter  of  the  hole;  that  is,  a 
1"  hole  should  never  have  a charge  of  more  than  12  in.  of  explosive  placed 
in  it.  Where  several  holes  are  fired  together,  this  rule  is  sometimes  slightly 
deviated  from.  It  is  usually  best  to  employ  a length  of  charge  between  these 
two  limits,  as,  for  instance,  about  10  times  the  diameter  of  the  hole. 

Chambering  or  squibbing  is  the  blasting  out  of  a cavity  at  the  bottom  of  a 
drill  hole  to  allow  of  a larger  charge  of  explosive  being  used. 

Bulling  a drill  hole  is  the  working  of  clay  into  any  cracks  opening  into 
a drill  hole,  to  prevent  the  power  of  the  blast  being  scattered  through 
these  cracks. 

Charging.— The  charge  must  fit  and  fill  the  bottom  of  bore  and  be  packed 
solid.  If  holes  are  comparatively  dry,  slit  the  paper  of  the  cartridges  length- 
wise with  a knife,  and  as  each  *is  dropped  into  the  hole,  strike  a wooden 


BLASTING. 


331 


rammer  on  it  with  sufiBicient  force  to  make  the  powder  completely  fill  the 
bottom  and  diameter  of  the  bore.  Where  water  is  not  present,  a more  per- 
fect loading  is  made  by  taking  powder  out  of  cartridge  and  dropping  it  in 
loosely,  ram  each  6 or  8 in.  of  the  charge,  using  the  paper  of  each  cartridge 
as  a wad,  to  take  down  any  powder  that  may  have  stuck  to  the  sides  of  the 
hole.  If  water  is  standing  in  the  hole,  do  not  break  the  paper  of  the  car- 
tridges and  avoid  ramming  more  than  enough  to  settle  the  charge  on  the 
bottom, using  cartridges  of  as  large  diameter  as  will  readily  run  into  the  bore. 

When  cartridges  are  used,  the  last  cartridge  placed  in  the  hole  should 
contain  an  electric  exploder,  or  cap  with  fuse  attached.  When  loose  powder 
is  used,  a piece  of  cartridge  2 or  3 in.  in  length,  with  exploder  or  cap  attached, 
should  be  pressed  firmly  on  top  of  charge.  Some  blasters  put  an  exploder  or 
cap  in  the  first  cartridge  put  in  the  hole,  placing  remainder  of  charge  on  top. 
The  charge  should  be  placed  in  a solid  part  of  the  material  to  be  broken.  If 
possible,  the  face  should  be  undercut  and  then  the  overhanging  material 
shot  down.  Best  results  are  obtained  when  the  bore  holes  cross  the  faces  or 
layers  of  the  material  at  right  angles.  The  charges  should  be  placed  so  as  to 
disturb  the  sides  and  roof  of  a tunnel  through  material  of  medium  hardness 
as  little  as  possible.  The  charge  at  the  bottom  of  the  tunnel  should  be 
placed  from  6 to  12  in.  below  the  permanent  level. 

Amount  of  Charge.— No  invariable  rule  can  be  laid  down  as  to  the  diameter 
and  length  of  cartridges  to  be  used  under  any  and  all  circumstances,  nor  the 
amount  or  grade  of  powder  required  for  all  kinds  of  work.  Much  depends 
on  the  good  sense  and  judgment  of  the  persons  using  the  explosive. 
Guttmann,  in  his  well-known  handbook  on  blasting,  says:  “There  is  no  lack  of 
theories  for  the  determination  of  blasting  charges,  but  their  application 
depends  on  empirical  facts  determined  by  practical  work.  I therefore 
advise  that  the  calculation  of  charges  under  ordinary  conditions  be  neg- 
lected, and  recommend  watching  actual  operations  for  some  weeks,  asking 
for  explanation  from  the  most  expert  miners.  In  this  way  experience  will 
be  gotten  in  a short  time  that  will  enable  one  to  estimate  with  some  precision 
the  proper  charge  to  use  after  inspecting  the  spot  to  be  blasted." 

A good  rule  by  which  to  determine  the  weight  of  black  powder  to  use  in 
any  given  hole  in  bituminous  workings  is  the  following:  Find  the  distance 
in  feet  from  the  charge  out  in  the  line  of  least  resistance.  Multiply  the 
fourth  power  of  this  distance  by  the  diameter  of  the  hole  in  inches,  and 
divide  this  product  by  the  thickness  of  the  seam  in  inches.  The  result  will 
be  the  weight  of  the  charge  in  pounds.  Thus,  for  a 2i"  hole  in  a seam  of 
bituminous  coal  6 fit.  thick,  where  the  charge  is  placed  4^  ft.  deep  from  the 
face  of  the  coal,  or  cutting,  we  have  for  the  weight  of  charge  to  be  used, 


2 X ^ X 2 X 2 X 6 X 12 


Tamping.— In  deep  holes,  water  makes  a good  tamping,  but  fine  sand, 
clay,  etc.  are  generally  used.  Fill  in  for  the  first  5 or  6 in.  carefully,  so  as 
not  to  displace  cap  and  primer;  then  with  a hardwood  rammer  pack  bal- 
ance of  material  as  solid  as  possible,  ramming  with  the  hand  alone,  and  not 
using  any  form  of  hammer.  Never  use  a metal  tamping  rod. 

Firing.— If  the  work  is  wet,  or  the  charge  used  under  water,  use  water- 
proof fuse,  and  protect  the  end  of  the  fuse  by  applying  bar  soap,  pitch,  or 
tallow  around  the  edge  of  the  cap.  Water  must  not  be  allowed  to  reach  the 
powder  in  the  fuse  or  the  fulminate  in  the  cap.  Exploding  by  electricity  is 
best  under  water  at  great  depth,  as  the  pressure  of  water  is  so  great  on  the 
fuse  that  it  is  forced  through  and  dampens  it  so  as  to  prevent  firing. 

Seam  Blasting.— If  a seam  is  found  in  the  rock,  remove  the  powder  from 
the  cartridges  and  push  it  into  the  seam  and  fire  a cap  beside  it.  This  will 
open  the  seam  so  that  a larger  quantity  of  explosive  can  be  used,  and  the 
rock  broken  without  drilling.  In  blasting  coal,  slate,  marble,  granite,  free- 
stone, or  any  other  material  that  it  is  desirable  to  obtain  in  large  blocks, 
cartridges  of  small  diameter  should  be  used  in  wide  bore  holes,  the  charge 
being  rolled  in  several  folds  of  paper,  to  prevent  its  touching  the  sides  of  the 
bore  holes.  The  intensity  of  action  and  the  crushing  effect  of  the  explosive 
are  thus  lessened. 

Firing  by  Detonation.— Nitroglycerine  explosives  always  require  detonation 
by  a cap  or  exploder  in  order  to  develop  their  full  force.  Fig.  1 illustrates 
the  method  of  attaching  such  an  exploder  to  the  end  of  a fuse  and  the  pla- 
cing ofit  in  the  cartridge.  The  exploders  are  loaded  with  fulminate  of  mer- 
cury and  are  slipped  over  the  end  of  the  fuse,  after  which  the  upper  end  is 


332 


EXPLOSIVES. 


crimped  tightly  against  the  end  of  the  fuse,  as  shown.  (Miners  sometimes 
bite  the  caps  on  to  the  fuse  with  their  teeth.  This  is  a very  dangerous  pro- 
ceeding and  should  never  be  allowed,  as,  with  strong  caps,  one  of  them 
exploding  in  a man’s  mouth  would  prove  fatal.)  In  placing  the  cap  or 


Fig.  2.  Fig.  3. 


exploder  into  the  dynamite  or  giant-powder  cartridge,  care  should  be  taken 
that  only  about  two-thirds  of  the  cap  be  embedded  in  the  material  of  the 
cartridge,  for  if  the  fuse  had  to  pass  through  a portion  of  the  material  before 
reaching  the  cap,  there  would  be  danger  of  its  igniting  the  material,  thus 
causing  deflagration  of  the  cartridge  in  place  of  detonation.  The  fumes 
given  oif  by  high  explosives  are  much  worse  m the  case  of  deflagrating  a 
cartridge. 

The  electric  exploder.  Fig.  2,  has  wires  A and  B,  which  carry  the  current  to 
the  exploder.  />  is  a cement  (usually  sulphur)  that  protects  the  explosive 
compound  C (usually  mercury  fulminate)  and  the  whole  is  contained  in  a 
copper  shell.  A small  platinum  wire  E is  heated  by  the  passage  of  a current 

and  ignites  the  explosive.  Fig.  3 
shows  the  method  of  placing  a cap 
or  an  electric  exploder  in  a cartridge 
of  powder. 

When  a number  of  holes  are  ex- 
ploded at  one  time,  the  electric 
exploders  are  connected  in  series,  as 
shown  in  Fig.  4,  for  a small  number 
of  holes,  and  as  in  Fig.  5 for  a larger 
number. 

The  battery  for  furnishing  the 
current  of  electricity  is  a magneto 
machine  that  is  worked  by  either  pulling  up  or  by  depressing  a handle  or 
rack  bar,  or  else  by  turning  a crank. 

Directions  for  Blasting  by  Eiectricity.— Drill  the  number  of  holes  desired  to  be 


Fig.  4. 


fired  at  one  time;  depth  and  spacing  of  holes  depending  on  character  of 
rock,  size  of  drill  holes,  etc.,  the  blaster,  of  course,  using  his  judgment  in  this 
matter.  Load  the  hole  in  the  usual  manner,  fitting  one  cartridge  with  a fuse 


ARRANGEMENT  OF  DRILL  HOLES. 


333 


(electric  exploder)  instead  of  cap  and  fuse.  The  fuse  head  is  fitted  into 
the  bottom  end  of  the  cartridge,  or  into  the  middle  of  one  side  of  the 
cartridge,  where  a hole  has  been  punched  with  a pencil  or  small  sharp  stick 
to  receive  it;  push  the  powder  close  around  the  fuse  head.  The  fuse  can  then 
be  held  in  position  by  tying  a string  around  the  cartridge  and  the  fuse  wires, 
binding  the  wires  to  the  cartridge,  as  shown  in  Fig.  3.  A shows  head  of  fuse,  B 
the  two  fuse  wires,  C string  used  to  tie  wires  to  cartridge.  Avoid  taking 
hitches  in  fuse  wires,  as  by  this  very  common  practice,  the  insulation  of 
the  wires  may  be  injured  and  the  current  of  electricity  may  pass  from  one 
wire  to  the  other,  without  passing  through  the  cap,  hazarding  a misfire. 

The  cartridge  containing  the  fuse  is  put  in  on  top  of  the  charge  by  some 
blasters;  by  others,  at  bottom  of  the  charge.  The  best  place  for  it  is  in  the 
center  of  the  charge,  having  part  of  the  charge  above  and  part  below  it. 
In  tamping  the  hole,  great  care  must  be  taken  not  to  cut  the  wires,  or  injure  the 
cotton  covering  of  fuse  wires,  or  to  pull  the  fuse  out  of  the  cartridge.  Allow 
at  least  8 in.  of  the  fuse  wire  to  project  above  the  hole,  to  make  connections. 

When  all  the  holes  to  be  fired  at  one  time  are  tamped,  separate  the  ends 
of  the  two  wires  in  each  hole,  and,  by  the  use  of  connecting  wire,  join  one 
wire  of  the  first  hole  with  one  of  the  second,  the  other  or  free  wire  of  the 
second  with  one  of  the  third,  and  so  on  to  the  last  hole,  leaving  a free  wire 
at  each  end  hole. 

All  connections  of  wires  should  be  made  by  twisting  together  the  bare 
and  clean  ends;  it  is  best  to  have  the  joined  parts  bright.  Scrape  off  the  cotton 


covering  at  the  ends  of  the  wires  to  be  connected,  say  for  2 in.,  then  rub  the 
wire  with  a small  hard  stone.  This  makes  a bright  fresh  wire.  Be  sure  that 
all  connections  are  clean,  bright,  and  well  twisted.  Do  not  hook  or  loop  wires 
in  making  connections.  Bare  joints  in  wire  should  neyer  be  allowed  to  touch 
the  ground,  particularly  so  if  the  ground  is.  wet.  This  can  be  prevented  by 
putting  dry  stones  under  the  joints.  The  charges  having  all  been  connected, 
as  directed  above,  the  free  wire  of  the  first  hole  should  be  joined  to  one  of  the 
leading  wires,  and  the  free  wire  of  the  last  hole  to  the  other  of  the  two 
leading  wires.  The  leading  wires  should  be  long  enough  to  reach  a point  at 
a safe  distance  from  the  blast,  say  250  ft.  at  least.  All  being  ready,  and  not 
till  the  men  are  at  a safe  distance,  connect  the  leading  wires,  one  to  each  m 
the  projecting  screws  on  the  front  side  or  top  of  the  battery,  through  each 
of  which  a hole  is  bored  for  the  purpose,  and  bring  the  nuts  down  firmly  on 
the  wires.  Now,  to  fire,  take  hold  of  the  handle  for  the  purpose,  lift  the 
rack  bar  (or  square  rod,  toothed  on  one  side)  to  its  full  length,  and  press  it 
down,  for  the  first  inch  of  its  stroke  with  moderate  speed,  but  finishing  the 
stroke  with  all  force,  bringing  rack  bar  to  the  bottom  of  the  box  with  a solid 
thud,  and  the  blast  will  be  made.  Do  not  churn  rack  bar  up  and  down.  It 


334 


EXPLOSIVES. 


is  unnecessary  and  harmful  to  the  machine.  One  quick  stroke  of  the  rack 
bar  is  sufficient  to  make  the  blast.  Never  use  fuses  (exploders)  made  by 
different  manufacturers  in  the  same  blast.  Connecting  wire  should  be  of 


Fig.  8. 


Fig.  9. 


same  size  as  the  fuse  wire;  leading  wire  should  be  at  least  twice  as  large. 
Covering  on  wire  should  not  “ strip  ” or  come  off  easily. 

The  power  of  an  explosive  cannot  be  exactly  calculated  from  the  quantity 
and  temperature  of  the  gas  resulting  from  its  detonation,  as  it  is  impossible 
to  determine  the  exact  composition  of  gas  at  the  moment  of  explosion  and 
during  the  subsequent  cooling  period.  Tables  that  give  the  relative  strength 


Fig.  10. 


Fig.  11. 


of  explosives  are  apt  to  be  misleading,  as  so  much  depends  on  the  compo- 
sition of  the  explosive,  and  since  there  are  so  many  explosives  of  varying 
compositions  that  are  sold  under  the  same  name. 

Pressures  Developed  by  Explosives.— According  to  experiments  conducted 


ARRANGEMENT  OF  DRILL  HOLES. 


335 


by  Sarrau,  Vielle,  Noule,  and  Abel,  tlie  following  approximate  maximum 
l)ressures,  in  tons  per  square  inch,  developed  by  various  explosives,  have 
been  arrived  at;  Mercury  fulminate,  193;  nitroglycerine,  86;  guncotton,  71; 
blasting  powder,  43. 

Values  of  Explosives.— Taking  gunpowder  (containing  61^  saltpeter)  as  a 
standard,  and  calling  its  value  1,  the  following  are  the  comparative  values 


of  the  other  explosives:  Dynamite,  containing  75^  nitroglycerine,  2.2;  blasting 
gelatine,  containing  92^  nitroglycerine,  3.2;  nitroglycerine,  3.3. 

The  arrangement  of  drill  holes  for  driving  and  sinking  should  be  such  as  to 

Eermit  the  easy  handling  of  the  drills  and  also  to  minimize  the  number  of 
oles  and  the  weight  of  explosive.  Two  distinct  systems  are  in  use:  (1)  the 
center  cut,  by  which  a center  core  or  key  is  first  removed,  and  after  that 
concentric  layers  about  this  core;  (2)  the  square  cut,  in  which  the  lines  of 


336 


MACHINE  MINING. 


holes  are  parallel  to  the  sides  of  the  excavation,  the  rock  being  removed  in 
wedges  instead  of  in  concentric  circles. 

The  center-cut  method  is  shown  in  Figs.  6,  7,  8,  and  9,  Fig.  6 showing  the 
face  of  a heading,  Fig.  7 an  elevation  or  vertical  section,  and  Figs.  8 and  9 

glans.  The  numbers  of  the  holes  correspond  in  the  several  views.  The 
oles  are  supposed  to  be  drilled  by  rock  drills,  and  they  are  so  placed  that 
all  except  the  breaking-in  holes  have  an  equal  line  of  resistance.  The  num- 
ber of  holes  given  is  supposed  to  take  out  a clean  cut  of  the  whole  section 
abed  to  the  extent  of  3 ft.  6 in.  The  order  of  firing  the  holes  is:  (1)  break- 
ing-in shots  1,  2,  3,  and  4 simultaneously;  (2)  5,  6,  7,  8;  (3)  9,  10,  11,  12) 
(4)  13,  lU,  15,  16)  (5)  17,  18,  19,  20. 

The  square-cut  arrangement  is  shown  in  Figs.  12  (face),  10,  11  (plans), 
and  13  (vertical  elevation) . The  entering  wedge,  Fig.  11,  is  best  removed  in 
two  stages:  First,  the  part  egh  by  the  shots  1,  2,  3,  and  4;  and  second,  part 
efh  by  shots  5,  6,  7,  and  8.  The  other  shots  are  then  fired:  (1)  9, 10, 11, 12: 
(2)  13,  U,  15, 16)  (3)  17, 18, 19, 20,  each  volley  being  fired  either  simultaneously 
or  consecutively.  Where  there  is  a natural  parting  in  the  heading,  advan- 
tage is,  of  course,  taken  of  this  in  the  location  of  the  shots. 

Figs.  14  and  15  show  two  arrangements  of  drill  holes  used  in  sinking  the 
Parker  shaft  at  Franklin  Furnace,  N.  J.  The  size  of  the  shaft  was  10  ft.  X 
20  ft.  in  the  rock.  At  first,  only  6'  cuts  were  put  in,  but  these  were  gradually 
increased  until  11/  and  12'  cuts  were  pulled.  The  best  average  obtained  was 
66  ft.  of  shaft  from  6 consecutive  cuts. 


MACHINE  MINING. 


The  number  of  coal-mining  machines  in  use  has  increased  rapidly  within 
a very  short  time.  In  1896  there  were  1,446  in  use  in  the  United  States. 
During  1897  there  was  an  increase  of  542,  or  37.59^,  while  the  average  yearly 
gain  from  1891  to  1896  was  only  about  22/o.  The  total  tonnage  won  by 
machines  in  20  States  in  1897  was  22,649,220  short  tons,  or  16.17/«  of  the  total 
product  of  these  States,  and  15.3^  of  the  total  bituminous  product  of  the 
United  States.  A universal  mining  machine  has  not  yet  been  brought  out, 
and  one  of  the  principal  reasons  for  the  failure  of  mining  machines  in  a 
number  of  instances  has  been  the  attempt  to  use  a machine  under  condi- 
tions to  which  it  was  not  adapted.  When  a mining  machine  is  designed  and 
built  to  suit  the  conditions  under  which  it  is  to  be  operated,  it  is  safe  to  say 
that  there  are  but  few  mines  in  which  they  cannot  be  successfully  utilized. 
They  are  of  particular  advantage  where  there  is  a long  working  face  and 
where  the  coal  is  over  3 ft.  in  thickness.  Low  seams  require  more  under- 
cutting for  the  given  output  than  high  seams.  As  a rule  it  has  not  been 
found  economical  to  use  machines  in  seams  pitching  over  12°  to  15°,  though 
pick  machines  have  been  used  in  mines  having  an  inclination  of  23°,  the 
difficulty  being  not  so  much  in  the  cutting  as  in  moving  the  machine  from 
place  to  place. 

There  are  four  general  types  of  mining  machines  in  use;  pick  machines, 
chain-cutter  machines,  cutter-bar  machines,  and  longwall  machines.  The 
first  two  are  the  types  almost  universally  used  in  America.  Cutter-bar 
machines  have  almost  entirely  disappeared  from  use  excepting  one -type 
which  is  at  present  used  in  Iowa.  Longwall  mining  machines  have  not 
been  very  generally  adopted  in  America,  as  the  longwall  method  of  mining 
is  not  extensively  used. 

Both  compressed  air  and  electricity  are  used  for  operating  mining 
machines.  Pick  machines  driven  by  compressed  air  are  made  by  three 
separate  concerns.  Four  companies  make  electric  chain  machines  and  one  of 
these  four  is  also  making  a compressed-air  chain  machine.  One  makes  a 
longwall  machine,  and  one  has  brought  out  a pick  machine  for  electric 
power. 

Pick  machines  work  very  similarly  to  a rock  drill.  They  can  be  used 
wherever  mining  machines  are  applicable,  and  their  particular  advantage  is 
that  they  are  more  perfectly  under  the  control  of  the  operator,  who  can  cut 
around  pyrites  and  similar  obstructions  without  cutting  them  with  the 
machine. ' This  renders  such  a machine  particularly  applicable  for  seams  of 


VENTILATION  OF  MINES. 


337 


coal  having  rolls  in  the  bottom  and  containing  pyrites  or  other  hard  impuri- 
ties. They  are  also  applicable  for  working  pillars  on  which  there  is  a 
squeeze,  as  they  are  light  and  can  be  easily  handled  and  readily  removed. 

Chain-cutter  machines  consist  of  a low  metal  bed  frame  upon  which  is 
mounted  a motor  that  rotates  a chain  to  which  suitable  cutting  teeth  are 
attached.  To  operate  chain  machines  to  the  best  advantage,  the  coal  should 
be  comparatively  free  from  pyrites.  They  also  require  more  room  than  pick 
machines,  and  a space  from  12  to  15  ft.  in  width  is  necessary  along  the  face 
to  work  them  to  advantage.  These  machines  have  proved  failures  in  some 
mines  on  account  of  the  incessant  jarring  of  the  roof  by  the  rear  jack. 
Chain-cutter  machines  cannot  be  used  to  undercut  coal  when  a squeeze  is 
upon  it.  Coal  seams  that  are  comparatively  level  and  free  from  pyrites  and 
have  a comparatively  good  roof  can  undoubtedly  be  more  satisfactorily  and 
economically  cut  with  chain-cutter  machines  than  with  any  other  type. 

The  average  height  of  cut  is  4^  to  5 in.,  and  at  this  height,  the  chain- 
cutter  machines  makes  only  about  60^  as  much  small  coal  as  a pick  machine. 
This  is  not  always  an  advantage,  as  it  does  not  always  allow  sufficient  height 
for  the  coal  to  fall  down  after  the  cut  is  made.  In  a 3i'  seam,  3 men  are 
required  to  handle  the  machine  to  advantage. 

Shearing.— All  the  pick  machines  can  be  converted  into  shearing  machines 
and  can  be  used  for  longwall  work  by  using  a longer  striking  arm  and  a 
longer  supply  hose.  The  chain  machines  are  used  to  do  shearing  work  by 
having  the  cutting  parts  turned  vertically. 

Capacity.— The  average  producing  capacity  of  each  mining  machine  used 
in  the  United  States  was  11,398  tons  in  1891, 11,373  tons  in  1896,  and  11,393 
tons  in  1897.  So  much  depends  on  the  local  conditions  that  it  is  almost 
impossible  to  give  specific  data  of  rates  of  working  and  costs,  but  the 
following  are  fair  working  approximations. 

A good  pick  machine  will  undercut  450  sq.  ft.  in  10  hours,  while  an  ordi- 
nary miner  will  undercut  120  sq.  ft.  in  the  same  time.  In  a seam  varying  from 
to  6 ft.  in  thickness,  the  machine  will  undercut  from  50  to  100  tons  of  coal 
i 11 10  hours.  The  cost  of  undercutting  under  these  conditions  has  been  given 
MS  approximately  10  cents  per  ton.  Extraordinary  records  show  1,400  sq.  ft. 
to  have  been  cut  in  9 hours  in  Western  Pennsylvania,  and  in  an  8'  seam, 
210  tons  have  been  undercut  in  a shift  of  10  hours. 

A good  chain  cutter  will  make  from  30  to  45  cuts,  44  in.  wide  and  6 ft. 
deep,  in  10  hours  under  moderately  fair  conditions,  while  in  high  seams 
» wo  men  handling  the  same  machine  under  ordinary  conditions  can  make 
()0  cuts  pel  shift,  and  under  particularly  favorable  conditions,  80  to  120  cuts 
per  shift. 


VENTILATION  OF  MINES. 


This  subject  is  divided  naturally  into  (a)  gases  occurring  in  workings, 
explosive  conditions,  quantity  of  air,  distribution  of  air,  and  (5)  ventilating 
methods  and  machinery.  


THE  ATMOSPHERE. 

Composition.— Air  consists  chiefiy  of  oxygen  and  nitrogen,  with  small  and 
varying  amounts  of  carbonic-acid  gas,  ammonia  ^as,  and  aqueous  vapor. 
These  gases  are  not  chemically  combined,  but  exist  in  a free  state  in  uniform 
proportion,  as  follows: 

By  Volume.  By  Weight. 


Nitrogen 79.3  77.0 

Oxygen  20.7  23.0 


100.0  100.0 

Wherever  air  is  found,  its  composition  is  practically  the  same. 

Weight  .—The  weight  of  1 cu.  ft.  of  air  at  32°  F.  and  under  a barometric 
pressure  of  30  in.  is  .080975  lb.  Air  decreases  in  weight  per  cubic  foot  as  we 
ascend  in  the  atmosphere,  and  increases  as  we  descend  below  the  surface 
of  the  earth. 


338 


VENTILATION  OF  MINES. 


The  weight  of  1 cu.  ft.  of  dry  air  at  any  temperature  and  barometric 
pressure  is  found  by  means  of  the  formula 

1.3253  X B 
^ “ 459  + i ’ 

in  which  w = weight  of  1 cu.  ft.  of  dry  air;  B = barometric  pressure 
(inches  of  mercury);  t = temperature  (degrees  F.). 

The  constant  1.3253  is  the  weight  in  pounds  avoirdupois  of  1 cu.  ft.  of  dry 
air  at  an  absolute  temperature  of  1°  F.  and  1 in.  barometric  pressure. 

Example.— Find  the  weight  of  1 cu.  ft.  of  dry  air  at  a temperature  of 
60°  F.  and  a barometric  pressure  of  30  in. 


w 


1.3253  X 30 
459  + 60 


= .07661b. 


Table  of  Weight  of  Dry  Air. 


Weight  of  1 cu.  ft.  of  dry  air  at  different  temperatures  and  barometric 
pressures,  as  calculated  by  the  formula  w = — 


Temperature. 
Degrees  F. 
t 

Weight  of  1 Cu.  Ft.  of  Dry  Air  (Lb.  Avoirdupois'). 

Barometer  (In.). 

B = 27. 

Barometer  (In.). 

B = 28. 

Barometer  (In.). 

B = 29. 

Barometer  (In.). 

B = 30. 

0 

.07796 

.08085 

.08373 

.08662 

5 

.07718 

.08002 

.08285 

.08569 

10 

.07631 

.07914 

.08196 

.08478 

15 

.07550 

.07830 

.08109 

.08388 

20 

.07470 

.07747 

.08023 

.08300 

25 

.07393 

.07667 

.07941 

.08215 

30 

.07318 

.07589 

.07860 

.08131 

32 

.07288 

.07558 

.07828 

.08098 

35 

- .07244 

.07512 

.07780 

.08048 

40 

.07171 

.07435 

.07701 

.07967 

45 

.07099 

.07362 

.07625 

.07888 

50 

.07031 

.07291 

.07551 

.07811 

55 

.06961 

.07219 

.07477 

.07735 

60 

.06895 

.07150 

.07405 

.07660 

65 

.06828 

.07081 

.07324 

.07587 

70 

.06766 

.07016 

.07266 

.07516 

75 

.06701 

.06949 

.07197 

.07445 

80 

.06648 

.06884 

.07130 

.07376 

85 

.06576 

.06820 

.07064 

.07308 

90 

.06519 

.06760 

.07001 

.07242 

95 

.06490 

.06699 

.06938 

.07177 

100 

.06401 

.06638 

.06875 

.07112 

110 

.06288 

.065*21 

.06754 

.06987 

120 

.06180 

.06409 

.06638 

.06867 

130 

.06075 

.06300 

.06525 

.06750 

140 

.05974 

.06195 

.06416 

.06637 

150 

.05874 

.06092 

.06310 

.06528 

160 

.05781 

.05995 

.06209 

.06423 

170 

.05688 

.05899 

.06110 

.06321 

180 

.05601 

.05808 

.06015 

.06222 

190 

.05514 

.05718 

.05922 

.06126 

200 

.05430 

.05631 

.05832 

.06033 

220 

.05271 

.05466 

.05661 

.05856 

240 

.05119 

.05309 

.05498 

.05688 

260 

.04978 

.05162 

.05346 

.05530 

280 

.04840 

.05020 

.05200 

.05380 

300 

.04714 

.04888 

.05063 

.05238 

350 

.01423 

.04587 

.04751 

.04915 

400 

.04166 

.04321 

.04475 

.04629 

THE  BAROMETER. 


339 


Atmospheric  Pressure. — ThQ  ieim  barometric  pressure  pressure  caused 

by  the  weight  of  the  atmosphere  above  a given  point.  It  is  measured  by  the 
barometer,  and  this  gives  rise  to  the  synonymous  term  barometric  pressure. 
Atmospheric  pressure  is  usually  stated  in  pounds  per  square  inch,  while 
barometric  pressure  is  stated  in  inches  of  mercury.  Thus,  at  sea  level,  the 
atmospheric  pressure  under  normal  conditions  of  the  atmosphere  is  14.7  lb. 
per  sq.  in.,  while  the  barometric  pressure  at  the  same  level  is  30  in.  of 
mercury  column,  or  simply  30  in. 

BarometriaVariations.— The  pressure  of  the  atmosphere  is  not  constant,  but 
is  subject  to  fluctuations  depending  on  the  condition  of  the  atmosphere. 
Besides  these,  there  are  fluctuations  that  are  more  or  less  regular  and  are 
called  barometric  variations.  There  is  both  a yearly  and  a diurnal,  or  daily, 
variation.  Of  these  two,  the  more  important  and  the  more  regular  is  the 
daily  variation,  in  which  the  barometer  attains  a maximum  height  from  9 to 
10  o’clock  A.  M.,  and  a minimum  about  4 o’clock  p.  m.  Other  maximum  and 
minimum  readings  are  obtained  at  10  p.  m.  and  3 A.  M.,  respectively;  but 
these  are  not  as  pronounced  as  those  occurring  in  the  daytime.  The  daily 
barometric  variations  range  from  .01  to  .08  in. 

Mercurial  Barometer. — This  barometer  is  often  called  the  cistern  barometer; 
or,  when  the  lower  end  of  the  tube  is  bent  upwards  instead  of  the  mouth  of 
the  tube  being  submerged  in  a basin,  it  is  known  as  the  siphon  barometer. 
The  instrument  is  constructed  by  Ailing  a glass  tube  3 ft.  long,  and  having  a 
bore  of  i in.  diameter,  with  mercury,  which  is  boiled  to  drive  off  the  air. 
The  thumb  is  now  placed  tightly  over  the  open  end,  the  tube  inverted,  and 
its  mouth  submerged  in  a basin  of  mercury.  When  the  thumb  is  withdrawn, 
the  mercury  sinks  in  the  tube,  flowing  out  into  the  basin,  until  the  top  of 
the  mercury  column  is  about  30  in.  above  the  surface  of  the  mercury  in  the 
basin,  and  after  a few  oscillations  above  and  below  this  point,  comes  to  rest. 
The  vacuum  thus  left  in  the  tube  above  the  mercury  column  is  as  perfect 
a vacuum  as  it  is  possible  to  form,  and  is  called  a Torricelli  vacuum,  after  its 
discoverer.  There  being  evidently  no  pressure  in  the  tube  above  the 
mercury  column,  and  as  the  weight  of  this  column  standing  above  the  sur- 
face of  the  mercury  in  the  basin  is  suppbrted  by  the  pressure  of  the  atmos- 
phere, it  is  the  exact  measure  of  the  pressure  of  the  atmosphere  on  the 
surface  of  the  mercury  in  the  basin.  If  the  experiment  is  performed  at  sea 
level,  the  height  of  the  mercury  will  be  found  to  average  about  30  in.,  at 
higher  elevations  it  is  less,  while  if  we  descend  deep  shafts  below  this  level, 
it  's  greater.  Roughly  speaking,  an  allowance  of  1 in.  of  barometric  height 
is  made  for  each  900  ft.  of  ascent  or  descent  from  sea  level  (see  calculation  of 
barometric  elevations).  A thermometer  is  attached  to  each  mercurial 
barometer  to  note  the  temperature  of  the  reading,  as  it  is  customary  in  all 
accurate  work  with  this  instrument  to  reduce  each  reading  to  an  equivalent 
reading  at  32°  F., which  is  the  standard  temperature  for  barometric  readings. 
A scale  is  provided  at  the  top  of  the  mercury  column  with  its  inches  so 
marked  upon  it  as  to  make  due  allowance  for  what  is  called  the  error  of 
capacity.  In  other  words,  the  inches  of  the  scale  are  longer  than  real 
inches,  since  the  level  of  the  mercury  in  the  basin  rises  as  it  sinks  in  the  tube, 
and  vice  versa.  The*  top  of  the  mercury  column  is  always  oval,  convex 
upwards,  owing  to  capillary  attraction,  and  the  scale  is  read  where  it  is 
tangent  to  this  convex  surface. 

Aneroid  Barometer. — This  is  a more  portable  form  than  the  mercurial 
barometer.  It  consists  of  a brass  box  resembling  a steam-pressure  gauge, 
having  a similar  dial  and  pointer,  the  dial,  however,  being  graduated  to 
read  inches,  corresponding  to  inches  of  mercury  column,  instead  of  reading 
pounds,  as  in  a pressure  gauge.  Within  the  outer  case  is  a delicate  brass 
box  having  its  upper  and  lower  sides  corrugated,  which  causes  it  to  act  as  a 
bellows,  moving  in  and  out  as  the  atmospheric  pressure  on  it  changes.  The 
air  within  the  box  has  been  partially  exhausted,  to  render  it  sensitive  to 
atmospheric  changes.  The  movement  of  the  upper  surface  of  the  box  is 
communicated  to  the  pointer  by  a series  of  levers,  and  the  dial  is  graduated 
to  correspond  with  the  mercurial  barometer. 

Calculation  of  Atmospheric  Pressure.— The  weight  of  the  mercury  column 
of  the  barometer  is  the  exact  measure  of  the  pressure  of  the  atmosphere, 
since  it  is  the  downward  pressure  of  the  atmosphere  that  supports  the 
mercury  column,  area  for  area;  that  is  to  say,  the  pressure  of  the  atmosphere 
on  1 sq.  in.  supports  a column  of  mercury  whose  area  is  1 sq.  in.,  and  whose 
height  is  such  that  the  weight  of  the  mercury  column  is  equal  to  the  weight 
of  the  atmospheric  column.  Hence,  since  1 cu.  in.  of  mercury  weighs  .49  lb., 


340 


VENTILATION  OF  MINES. 


the  atmospheric  pressure  that  supports  30  in.  of  mercury  column  is  .49  X 30 
= 14.7  lb.  per  sq.  in.  In  like  manner,  the  atmospheric  pressure  correspond- 
ing to  any  height  of  mercury  column  may  be  calculated.  It  will  be  observed 
that  the  sectional  size  of  the  mercury  column  is  not  important,  since  it  is 
supported  by  the  atmospheric  pressure  on  an  equal  area,  but  the  calculation 
of  pressure  is  based  on  1 sq.  in. 

Water  Column  Corresponding  to  Any  Mercury  Column.— The  density  of  mercury 
referred  to  water  is  practically  13.6;  hence,  the  height  of  a water  column 
corresponding  to  a given  mercury  column  is  13.6  times  the  height  of  the 
mercury  column.  For  example,  at  sea  level,  where  the  average  barometric 
pressure  is  30  in.  of  mercury,  the  height  of  water  column  that  the  atmos- 
pheric pressure  will  support  is  13.6  X f§  = ^4  ft.  This  is  the  theoretical 
height  to  which  it  is  possible  to  raise  water  by  means  of  a suction  pump,  but 
the  length  of  the  suction  pipe  should  not  exceed  75^  or  80^  of  the  theoretical 
water  column. 

Calculation  of  Barometric  Elevations. — Such  elevations,  although  approxi- 
mate, are  useful  for  many  purposes.  The  barometric  readings  are  reduced 
to  equivalent  readings  at  the  standard  temperature  of  32°  F.,  and  for  deter- 
mining differences  in  elevation,  the  readings  of  two  barometers  should  be 
taken,  if  possible,  at  the  same  time.  It  must  not  be  supposed,  however,  that 
the  barometer  always  reads  the  same  for  the  same  elevation  at  this  tempera- 
ture. The  temperature  of  the  atmosphere  has  indeed  verj^  little  effect  on 
the  atmospheric  pressure,  which  is  due  to  the  weight  of  air  above  the  point 
of  observation,  aerial  currents,  and  other  phenomena. 

In  the  more  accurate  determinations  of  vertical  height  or  elevation  by 
means  of  the  barometer,  the  following  formula  is  usually  employed: 

E = reading  of  barometer  (inches)  at  lower  station; 
r = reading  of  barometer  (inches)  at  higher  station; 

T = temperature  (F.)  at  lower  station; 
t = temperature  (F.)  at  higher  station; 

H = difierence  of  level  in  feet  between  the  two  stations. 


= 56.300(logiJ-log  r)(l  + ^-*). 


More  simply: 


log  = 


R 


- + logr. 


H = 49,000 


mb 

300  (900  + I 
000  (900  + T + 0 — 900.HJ  ‘ 


°00  )• 


^ r49,000  (900  A T At)  A 900  J71 

^ “ ^149,0 ‘ 


Correction  for  Temperature.— Mercury  expands  about  .0001  of  its  volume 
for  each  degree  Fahrenheit.  To  reduce,  therefore,  a reading  at  any  tem- 
perature to  the  corresponding  reading  at  the  standard  temperature  of  32°  F., 
subtract  Tuioir  of  the  observed  height  for  each  degree  above  32°;  or,  if  the 
temperature  is  below  32°,  add  for  each  degree. 

Thus,  30.667  in.  at  62°  F.  is  equivalent  to  a reading  of  30.555  in.  at  32°  F., 
ao QO 

since  30.667-  (30.667)  = 30.667 -.092  = 30.555  in. 

Depth  of  Shafts.— The  barometer  is  often  employed  to  determine  the 
depth  of  a shaft  or  the  depth  of  any  point  in  a mine  below  a corresponding 
point  on  the  surface.  The  aneroid  is  employed  for  this  work,  being  more 
portable.  Allowance  must  always  be  made  in  such  cases  for  the  venti- 
lating pressure  of  the  mine.  A simple  formula  often  used  for  such  calcu- 
lations is  the  following: 

II  = 55,000(l--y/^), 


in  which  the  letters  stand  for  the  same  factors  as  designated  above. 

The  most  important  use  of  the  barometer  in  mining  imictice,  however  is 
found  in  the  warning  that  it  gives  of  the  decrease  of  atmospheric  pressure, 
and  the  expansion  of  mine  gases  that  always  follows. 


CHEMISTRY  OF  GASES. 


341 


CHEMISTRY  OF  GASES. 

All  matter  exists  in  one  of  three  forms,  solid,  liquid,  ov  gaseous,  according  to 
the  predominance  of  the  attractive  or  the  repulsive  forces  existing  between  the 
molecules.  For  example,  water  exists  as  ice,  or  in  a solid  form,  when  the 
attractive  force  exceeds  the  repulsive  force  between  its  molecules.  As 
ihe  temperature  is  raised  or  heat  is  applied,  the  ice  assumes  the  liquid  form 
due  to  the  more  rapid  vibration  of  the  molecules  of  which  it  is  composed. 
Ill  other  words,  the  repulsive  force  existing  between  the  molecules  is 
increased,  and  the  result  is  a liquid.  If  we  still  further  raise  the  tempera 
ture  by  applying  more  heat,  the  vibration  of  the  molecules  becomes  yet 
more  rapid,  the  repulsive  force  is  increased  between  the  molecules,  and  a 
gas  or  vapor  called  steam  is  formed. 

An  atom  is  the  smallest  conceivable  division  of  matter. 

A molecule  is  a collection  of  two  or  more  atoms,  united  by  affinity. 

The  atom  cannot  consist  of  more  than  one  element.  The  molecule  may 
be  either  simple  or  compound.  If  compound,  it  is  a chemical  compound, 
its  atoms  being  chemically  united. 

Chemical  Compounds.— A chemical  compound  is  one  formed  by  the  union 
of  two  or  more  atoms  chemically,  such  atoms  uniting  always  in  fixed  or 
definite  proportions.  The  properties  of  a chemical  compound  are  always 
the  same. 

Mechanical  Mixture.— A mechanical  mixture  is  composed  of  different  sub- 
stances that  are  not  chemically  united,  and  which  are  mixed  in  no  fixed 
proportion.  The  properties  of  a mechanical  mixture  present  a regular 
gradation  from  a maximum  to  a minimum  state.  Thus,  a solution  of 
common  salt  NaCl  in  water  is  not  a chemical  compound  of  salt  and  water, 
but  simply  a mechanical  mixture  of  the  salt  in  the  water.  If  more  salt  is 
added  to  the  water,  the  strength  of  the  mixture  or  the  brine  is  inereased; 
and  when  less  salt  is  present,  the  strength  is  less.  On  the  other  hand, 
salt  itself  is  a chemical  compound  formed  by  the  union  of  1 atom  of  sodium 
with  1 atom  of  chlorine,  the  two  atoms  being  bound  together  by  chemical 
affinity,  and  always  uniting  in  the  same  proportion,  1 atom  of  each,  to  form 
salt. 

The  air  that  we  breathe  is  a mechanical  mixture  of  nitrogen  and  oxygen 
gases,  with  small  amounts  of  other  ingredients.  The  nitrogen  and  oxygen 
gases  are  in  a free  state;  that  is  to  say,  they  are  not  combined  as  in  a chem- 
ical compound.  This  is  true,  although  the  proportion  of  these  two  gases, 
oxygen  and  nitrogen,  in  the  atmosphere,  is  uniformly  in  the  ratio  of,  say, 
1 volume  of  oxygen  to  4 of  nitrogen.  Firedamp  is  another  example  of  true 
mechanical  mixture,  consisting  chiefly  of  a mixture  of  marsh  gas  CH^  and 
air,  with  small  amounts  of  other  hydrocarbons  and  a varying  amount  of 
carbonic-acid  gas,  which  is  always  present  in  firedamp.  These  gases  are  not 
combined  chemically,  but  are  mixed  in  varying  proportions. 

Atomic  volume,  or  specific  volume,  means  simply  relative  volume.  These 
terms  refer  to  the  relative  volume  of  gases  resulting  from  any  particular 
reaction.  By  means  of  the  laws  of  atomic  volume,  we  can  ascertain  the 
volurnes  of  the  different  gases  resulting  from  any  particular  reaction.  The 
chemical  reaction  that  takes  place  between  the  elements  constituting 
the  different  gases  is  expressed  by  means  of  a chemical  equation.  When 
we  have  expressed  such  reaction  by  a chemical  equation,  we  can  then 
calculate  the  volumes  of  the  gases  formed,  with  respect  to  the  original 
volumes  of  the  gases  entering  into  the  reaction.  It  must  be  observed,  how- 
ever, that  the  atomic  volumes  express  merely  the  relative  volumes  of  gases; 
or,  in  other  words,  the  ratio  of  the  volumes  of  gases  before  and  after  the 
reaction  takes  place. 

Laws  of  Volume.— The  following  laws  of  volume  refer  to  gases  only,  and 
never  to  solids  or  liquids: 

First. — Equal  volumes  of  all  gases,  under  the  same  conditions  of  tempera- 
ture and  pressure,  contain  the  same  number  of  molecules.  Hence,  the 
molecules  of  all  simple  gases  are  of  the  same  size. 

Second. — The  molecules  of  compound  gases,  under  like  conditions  of  tem- 
perature and  pressure,  occupy  twice  the  volume  of  an  atom  of  hydrogen  gas. 

There  are  very  few  exceptions  to  these  two  laws  of  gaseous  volume,  and 
the  exceptions  are  unimportant  so  far  as  mining  practice  is  concerned. 

An  element  is  a form  of  matter  that  is  composed  wholly  of  like  atoms. 
Thus,  hydrogen,  oxygen,  iron,  copper,  gold,  and  silver  are  elements. 

Qhemlpal  Symbols  and  Equations.- To  facilitate  the  writing  of  chemical 


3i2 


VENTILATION  OF  MINES, 


equations  expressing  the  reaction  that  takes  place  between  elements  under 
certain  conditions,  it  is  usual  to  express  the  elements  by  letters  called 
symbols.  These  symbols  stand  for  the  elements  that  they  represent,  and  are 
written  as  capital  letters,  except  where  two  letters  are  used  to  express  a 
symbol,  in  which  case  the  tirst  letter  only  is  a capital.  Thus,  C is  the 
symbol  for  the  element  carbon,  but  Cu  is  the  symbol  for  copper  (cuprum) 
and  Co  is  the  symbol  for  cobalt.  It  is  important  that  these  symbols  be 
written  exactly  in  this  manner;  otherwise  they  are  liable  to  be  frequently 
misconstrued.  For  example,  Co  stands  for  cobalt,  while  the  symbol  CO 

Table  of  Elements. 


Element. 

Symbol. 

Atomic 

Weight. 

Element. 

1 Symbol. 

Atomic 

Weight. 

Aluminum  

Al 

27.5 

Manganese 

Mn 

55.0 

Antimony  (stibium) 

Sb 

120.0 

Molybdenum 

Mo 

96.0 

Argon(?)  

A 

Neodymium(?) 

Nd 

Arsenic  

As 

75.0 

Nickel  

Ni 

58.8 

Barium  

Ba 

137.0 

Niobium  

Nb 

94.0 

Beryllium 

Be 

9.4 

Nitrogen 

N 

14.0 

Bismuth 

Bi 

208.0 

Osmium  

Os 

191.0 

Boron 

B 

11.0 

Oxygen 

0 

16.0 

Bromine 

Br 

80.0 

Palladium  

Pd 

106.5 

Cadmium 

Cd 

112.0 

Phosphorus 

P 

31.0 

Caesium 

Cs 

133.0 

Platinum 

Pt 

197.0 

Calcium 

Ca 

40.0 

Potassium  (kalium) 

K 

39.0 

Carbon  

C 

12.0 

Praseodymium  (?)  

Pr 

Cerium  

Ce 

138.0 

Rhodium 

Rh 

104.0 

Chlorine 

Cl 

35.5 

Rubidium  

Rb 

85.0 

Chromium 

Cr 

52.5 

Ruthenium 

Ru 

104.0 

Cobalt 

Co 

59.0 

Samarium(?) 

Sa 

Columbium 

Cb 

93.7 

Scandium  

Sc 

Copper  (cuprum) 

Cu 

63.0 

Selenium 

Se 

79.0 

Didymium  

D 

147.0 

Silicon 

Si 

28.0 

Erbium(?) 

Er 

169.0 

Silyer  (argentum) ...... 

^9 

108.0 

Fluorine  

F 

19.0 

Sodium  (natrium)  

Na 

23.0 

Gallium 

Gcl 

69.0 

Strontium  

Sr 

87.5 

rioTTn  Q n 1 n tn 

Ge 

Sulphur  

S 

32.0 

VJTt/l  lildill  CilU. 

Gold  (aurum) 

An 

196.7 

Tantalum  

Ta 

182.0 

Helium(?) 

He 

Tellurium  

Te 

127.0 

Hydrogen 

H 

1.0 

Thallium 

Tl 

205.0 

Indium 

In 

113.4 

Thorium 

Th 

231.5 

Iodine 

I 

127.0 

Tin  (stannum) 

Sn 

108.0 

Ttt  ^iiTm 

Ir 

193.0 

Titanium 

Ti 

48.0 

Xli-AlltlllJ.  

Iron  (ferrum)  

Fe 

56.0 

Tungsten  (wolfram) ... 

W 

184.0 

Lanthanum 

La 

139.0 

Uranium 

U 

240.0 

Lead  (plumbum) 

Pb 

207.0 

Vanadium  

V 

51.2 

Lithium 

Li 

7.0 

Ytterbium 

Yb 

Magnesium 

Mg 

24.0 

Yttrium 

Y 

89.0 

Mercury  ( hydrargy- 

Zinc   

Zn 

65.0 

rum)  

Hg 

200.0 

Zirconium  

Zr 

90.0 

sianus  lur  r r 

two  elements,  carbon  and  oxygen.  v.  i ^ i + * 

A molecule  is  expressed  by  writing  the  symbols  of  its  elementary  atoms. 

, 1 o+/^TY^  rkf  Q cnhctflnpp  nr  plp.mpnt  entprs  into  ihp  compo- 


sition of  a molecule,  tne  numoer  Ol  aiums  U1  sucii  eiemuut  is  u\  a, 

small  subscript  letter  written  immediately  after  the  symbol  of  the  element. 
Thus  carbonic-acid  gas  is  composed  of  1 atom  of  carbon  chemically  united 
with ’2  atoms  of  oxygen,  and  is  expressed  by  the  symbol  CO^.  Where  the 
symbol  is  written  without  such  subscript  figure,  1 atom  only  is  meant. 
Thus  carbonic-oxide  gas  being  composed  of  1 atom  of  carbon  chemically 
united  to  l atom  of  oxygen,  is  expressed  by  the  symbol  CO. 


CHEMISTRY  OF  GASES. 


343 


A large  figure  written  before  the  symbols  expressing  the  molecule  indi- 
cates the  number  of  molecules  entering  into  the  reaction.  A large  figure  is 
sometimes  used  before  the  symbol  of  a single  element  to  indicate  the  number 
of  atoms  of  that  element  that  enter  the  reaction.  In  any  reaction  occurring 
between  atoms  of  matter,  no  matter  is  destroyed.  In  any  reaction,  there 
are  always  the  same  number  of  atoms  after  the  reaction  as  before  the 
reaction  took  place.  A chemical  equation  is  therefore  an  expression  of 
equality  between  the  atoms  before  and  after  a reaction  takes  place.  The 
first  member  of  the  equation  contains  the  substances  that  act  upon  each 
other,  while  the  second  member  of  the  equation  contains  the  substances 
that  are  formed  by  the  reaction.  The  number  of  atoms  is  the  same  in  each 
member  of  the  equation. 

Example. — To  express  the  reaction  that  takes  place  when  carbonic- 
oxide  gas  burns  in  the  air  to  produce  carbonic-acid  gas,  we  write 
CO  + 0 + 4iV  = CC2  + 4:N 

In  this  equation,  each  molecule  of  carbonic-oxide  gas  CO  takes  up  1 atom 
of  the  free  oxygen  of  the  atmosphere  to  form  carbonic-acid  gas  CO2.  The 
nitrogen  in  the  atmosphere  being  4 times  the  volume  of  oxygen,  is  expressed 
as  4 atoms  in  the  equation.  This  nitrogen,  however,  remains  inactive,  and 
takes  no  part  in  the  reaction.  It  is  written  on  both  sides  of  the  equation  for 
the  purpose  of  determining  the  atomic  volumes  of  the  gases  before  and  after 
the  reaction,  as  explained  below. 

The  reaction  for  an  explosion  of  firedamp  is 

CH^  + 40  4-  leN  = CO2  -h  2H.2O  4-  UN 

In  this  equation,  each  molecule  of  marsh  gas  CH^  is  dissociated;  that  is 
to  say,  its  atoms  are  separated.  The  atom  of  carbon  in  the  molecule  unites 
with  2 atoms  of  the  oxygen  of  the  air  to  form  carbonic-acid  gas  CO2.  The 
4 atoms  of  hydrogen,  in  like  manner,  combine  with  two  atoms  of  oxygen  in 
the  air  to  form  2 molecules  of  water  or  steam  2 (MO),  or  2H2O.  The  nitro- 
gen in  this  equation  is  equal  to  4 times  the  volume  of  the  oxygen  consumed, 
and  is  therefore  written  as  UN,  since  a total  of  4 atoms  of  oxygen  have 
been  used.  The  nitrogen  is  however  inert,  and  plays  no  part  in  the  reac- 
tion itself,  but  is  written  here  on  both  sides  of  the  equation,  as  in  the 
previous  equation,  in  order  to  properly  represent  the  atomic  volumes  of 
the  gases  or  their  relative  volumes  before  and  after  the  reaction  takes  place. 

Calculation  of  the  Relative  Volumes  of  Gases.— To  calculate  the  relative 
volumes  of  the  gases  before  and  after  the  reactions  expressed  in  each  of  the 
equations  given  in  the  preceding  paragraphs,  write  beneath  the  symbol 
of  each  molecule  or  atom  its  atomic  volume.  In  the  chemical  equation 
expressing  the  reaction  that  takes  place  when  carbonic-oxide  gas  CO  burns 
to  carbonic-acid  gas  CO2,  we  have  as  follows: 

CO  4-  0 4-  4iV  = (7024-  4Ar 

Atomic  volumes,  2+14-4=  2 + 4 
or,  in  this  reaction,  7 volumes  have  been  reduced  to  6 volumes.  Such  a 
change  of  volume  often  takes  place  in  chemical  reactions.  All  attempts  to 
explain  the  cause  of  this  change  of  volume,  however,  have  thus  far  failed; 
but  that  the  change  of  volume  does  take  place  has  been  demonstrated  by  a 
large  number  of  experiments. 

To  calculate  the  volume  of  air  consumed  in  the  complete  explosion  of 
100  cu.  ft.  of  carbonic-oxide  gas  CO,  we  write  the  ratio  of  the  relative  volumes 
of  carbonic-oxide  gas  and  air,  which  is  2 : (1  + 4),  or  2 : 5;  and  to  obtain  the 
actual  volume  of  air  consumed  in  the  explosion  of  100  cu.  ft.  of  carbonic- 

5 X 100 

oxide  gas,  we  write  the  proportion  2 : 5 : : 100  : or  x = — — = 250  cu.  ft. 

To  find  the  volume  of  carbonic-acid  gas  CO2  produced  in  the  complete 
explosion  of  100  cu.  ft.  of  carbonic-oxide  gas  CO,  write  the  ratio  of  the  atomic 
volumes  of  these  two  gases  2 : 2,  which  shows  no  change  of  volume,  and, 
therefore,  the  volume  of  carbonic-acid  gas  CO2  produced  will  be  the  same  as 
the  volume  of  carbonic-oxide  gas  CO  burned. 

To  find  the  volume  of  air  consumed  in  the  complete  explosion  of  100 
cu.  ft.  of  marsh  gas  CH^,  write  the  equation  expressing  the  reaction  that 
takes  place  in  this  explosion  as  given  above, 

^4  + 40  + 16iVr  = CO2  + 2H2O  + 16A^ 

Atomic  volumes,  2 + 4-1-  16  = 2 -|-  4 4-  16 

There  is  no  change  of  volume  caused  by  the  explosion,  since  22  volumes 
on  one  side  of  the  equation  produce,  likewise,  22  volumes  on  the  other  side; 
or  22  volumes  before  the  explosion  produce  22  volumes  after  the  explosion. 


344 


VENTILATION  OF  MINES. 


To  find  the  volume  of  air  consumed,  we  write  the  ratio  of  the  atomic 
volumes  of  marsh  gas  and  air  2 : (4  + 16),  or  2 : 20,  or  1 : 10;  that  is  to 
say,  roughly  speaking,  the  amount  of  air  consumed  in  the  complete  explo- 
sion of  marsh  gas  is  10  times  the  volume  of  the  marsh  gas.  This  is  not  exact, 
however,  as  the  volume  of  nitrogen  in  the  air  is  3.83  times  the  volume  of 
oxygen.  Making  this  correction,  the  volume  of  air  consumed  in  the  complete 
explosion  of  marsh  gas  is  9.66  times  the  volume  of  the  gas. 

To  determine  the  percentage  of  pure  marsh  gas  in  the  above  firedamp 
mixture  (marsh  gas  and  air),  we  write  the  ratio  of  the  atomic  volumes  of 

these  two,  2 ; (2  + 4 + 15.32),  or  1 ; 10.66;  and  X 100  = 9.38/o  of  CH^. 

lU.DD 

The  volume  of  carbonic-acid  gas  formed  in  this  reaction  is  equal  to  the 
volume  of  marsh  gas  consumed,  and  the  volume  of  watery  vapor  is  double 
the  volume  of  marsh  gas  consumed;  the  total  volume  of  gas  and  vapor 
formed  by  the  reaction  is  the  same  as  the  original  volume  of  marsh  gas  and 
air,  or  firedamp  mixture,  since  the  sum  of  the  atomic  volumes  on  each  side 
of  the  equation  is  the  same. 

Atomic  weight  is  the  relative  weight  of  an  atom  of  an  element  compared 
with  an  atom  of  hydrogen.  Atomic  weight  is,  then,  not  an  absolute  weight 
to  be  expressed  in  pounds,  ounces,  or  any  other  denomination,  but  is  simply 
relative  weight.  The  atomic  weight  of  each  of  the  elements  is  given  in  the 
table  on  page  342. 

Molecular  weight  is  the  sum  of  the  atomic  weights  of  the  elements  forming 
the  molecule,  taking  the  atomic  weight  of  each  element  as  many  times  as 
there  are  atoms  of  that  element  in  the  molecule.  A molecule  of  water  is 
composed  of  2 atoms  of  hydrogen  and  1 atom  of  oxygen,  and  as  the  atomic 
weight  of  hydrogen  is  1 and  that  of  oxygen  16,  the  molecular  weight  of 
water  is  (2  X 1)  + 16  = 18.  In  the  same  manner,  since  a molecule  of  marsh 
gas  CHu  is  composed  of  4 atoms  of  hydrogen  and  1 of  carbon,  and  the  atomic 
weight  of  hydrogen  is  1 and  that  of  carbon  12,  the  molecular  weight  of  marsh 
gas  is  (4  X 1)  + 12  = 16. 

The  density  of  a gas  is  the  weight  of  any  volume  compared  with  the 
weight  of  the  same  volume  of  hydrogen  or  some  other  standard.  The 
density  of  a gas  is  constant  at  all  temperatures  and  pressures,  the  change 
of  temperature  and  pressure  affecting  the  gas  in  question  and  the  standard 
alike.  The  density  of  air  referred  to  hydrogen  is  14.38. 

(a)  The  density  of  any  simple  gas,  referred  to  hydrogen  as  unity,  is  equal  to 
its  atomic  weight,  (b)  The  density  of  any  compound  gas,  referred  to  hydrogen 
as  unity,  is  one-half  of  its  molecular  weight. 

Specific  Gravity  of  Gases.— The  specific  gravity  of  a gas  is  the  weight  of 
that  gas  referred  to  the  weight  of  a like  volume  of  air  as  a standard.  It  is, 
in  other  words,  the  ratio  between  the  weight  of  like  volumes  of  any  gas  and 
air,  both  the  air  and  gas  being  subject  to  the  same  temperature  and  pressure. 
Thus,  since  the  weight  of  1 cu.  ft.  of  air  at  a temperature  of  60°  F.  and  30  in. 
barometric  pressure  is  .0766  lb.,  and  the  weight  of  1 cu.  ft.  of  carbonic-acid 
gas  CO2  is  .11712  lb.  at  the  same  temperature  and  pressure,  the  specific 
11712 

gravity  of  carbonic-acid  gas  is  ‘ = 1.529. 

.07od 

Weight  of  Gases.— The  weight  of  1 cu.  ft.  of  any  gas  at  any  given  tempera- 
ture and  pressure  is  found  by  first  calculating  the  weight  of  1 cu.  ft.  of  dry 
air  at  the  same  temperature  and  pressure  by  means  of  the  formula  given  on 
page  338  for  air,  and  then  multiplying  this  weight  by  the  specific  gravity  of 
the  gas  referred  to  air  as  a standard. 

Example.- To  determine  the  weight  of  1 cu.  ft.  of  carbonic-acid  gas  at  a 
temperature  of  60°  F.,  and  30  in.  barometric  pressure,  we  multiply  the 
weight  of  1 cu.  ft.  of  dry  air,  at  this  temperature  and  pressure,  as  found 
above  (.0766  lb.),  by  the  specific  gravity  of  carbonic-acid  gas  (1.529).  Thus, 
.0766  X 1.529  = .117121b. 

The  table  on  page  349  gives  the  specific  gravity  of  the  gases  common  in 
mining  practice,  referred  to  air  as  a standard. 

Expansion  of  Air  and  Gases.— All  air  and  gases  expand  uniformly  at  the 
same  rate.  The  expansion  and  contraction  of  air  and  gases  follow  two 
simple  laws  that  we  will  consider  under  the  heads  (a)  Ratio  of  volume  and 
absolute  temperature  and  (5)  Ratio  of  volume  and  absolute  pressure. 

Absolute  temperature  means  the  temperature  as  reckoned  from  absolute 
zero,  which  is  the  point  on  the  temperature  scale  below  which  it  is  assumed 
that  no  substance  can  exist  in  a gaseous  state.  The  absolute  zero  of  the 


PEESSUEE. 


345 


Fahrenheit  scale  is  assumed  in  mining  practice  as  459°  below  zero.  Hence, 
the  absolute  temperature  corresponding  to  any  common  temperature  is 
found  by  adding  459°  to  the  common  temperature.  Thus,  the  absolute 
temperature  corresponding  to  60°  F.  is  459  + 60  = 519°. 

Absolute  Pressure.— The  term  absolute  pressure  refers  to  the  total  pressure 
supported  by  air  or  gas;  i.  e.,  the  pressure  above  a vacuum.  Gauge  pressure 
is  the  pressure  above  the  atmosphere.  Absolute  pressure  is  always  the 
atmospheric  pressure  plus  the  gauge  pressure.  If  a gauge  pressure  on  a 
boiler  indicates  60  lb.  per  sq.  in.,  the  absolute  pressure  supported  by  the 
steam  in  the  boiler  will  be  60  + 14.7  = 74.7  lb.  per  sq.  in.  Or,  if  the  ventila- 
ting pressure  in  a mine  is  equal  to  13  lb.  per  sq.  ft.,  the  absolute  pressure 
supported  by  the  air  in  the  airways  will  be  13  + (14.7  X 144)  = 2,129.8  lb. 
per  sq.  ft. 

Relation  of  Volume  and  Absolute  Temperature  {Charles'  or  Gay  Lussac' slaw). 
The  volume  of  any  air  or  gas  varies  directly  as  its  absolute  temperature. 

Relation  of  Volume  and  Absolute  Pressure  {Boyle's  or  Mariotte's  law). — The 
volume  of  any  air  or  gas  varies  inversely  as  the  absolute  pressure  it  supports. 
For  example,  if  we  double  the  absolute  pressure  supported  by  air  or  gas, 
the  volume  of  the  air  or  gas  will  be  reduced  to  one-half  its  original  volume; 
if  we  multiply  the  absolute  pressure  3 times,  we  reduce  the  volume  to  one- 
third  the  original  volume;  etc. 

Example.— The  intake  current  of  a mine  is  50,000  cu.  ft.  of  air  per  minute; 
the  ventilating  pressure  is  13  lb.  per  sq.  ft.  The  temperature  of  the  intake  is 
20°  F.;  the  temperature  of  the  return  air  is  70°  F.  Calculate  the  volume  of 
the  return  air-current  per  minute,  according  to  the  rules  of  expansion  of  air, 
due  to  the  increase  of  temperature  and  decrease  of  pressure,  in  the  return 
current. 

The  increased  volume  of  the  return  air,  due  to  the  decrease  of  pressure 
and  increase  of  temperature,  is  found  by  writing  a compound  proportion, 
the  first  member  of  which  consists  of  two  ratios,  viz.,  the  direct  ratio  of  the 
absolute  temperatures,  and  the  inverse  ratio  of  the  absolute  pressures,  accord- 
ing to  the  two  laws  stated  above.  That  is,  we  write 


Or, 


(459  + 20)  ; (459  + 70) ) . 
2,116.8  : 2,129.8  j ' 


: 50,000  : x. 


529  X 2,129.8  X 50,000 
479  X 2,116.8 


55,558  cu.  ft. 


Example.— In  a compressed-air  plant,  the  gauge  shows  a pressure  of  80  lb. 
per  sq.  in.;  the  area  of  the  piston  is  20  sq.  in.,  and  its  stroke  10  in.  The  pump 
makes  100  strokes  per  minute.  Assuming  there  is  no  leakage  of  air  past  the 
piston,  what  will  be  the  volume  of  air  discharged  from  the  pump  into  the 
mine  per  minute? 

The  volume  of  air  discharged  from  the  pump  cylinder  per  minute 

20  X 10  X 100 

= — = 11-57  cu.  ft.  (cylinder  pressure).  The  absolute  pressure 

1 j 7 

on  the  air  in  the  cylinder  is  80  + 14.7  = 94.7  lb.  The  absolute  pressure  on 
the  discharged  air  is  simply  the  atmospheric  pressure  (14.7  lb.).  Hence,  we 

94  7 ' 

write  the  proportion  14.7  : 94.7  : : 11.57  : x;  or,  x = X 11-57  = 74.54  cu.  ft. 
per  minute,  nearly. 

In  calculating  the  expanded  volume  of  air  or  gas,  it  will  be  observed  that 
the  ratio  of  the  original  volume  to  the  expanded  volume  is  always  equal  to 
the  product  of  the  direct  ratio  of  the  absolute  temperatures  and  the  inverse 
ratio  of  the  absolute  pressures,  which  gives  a compound  proportion,  the  first 
member  of  which  consists  of  two  ratios,  the  one  a direct  ratio  and  the  other 
an  inverse  ratio. 

Weight  Produces  Pressure.— In  the  study  of  the  barometer  as  a means  of 
measuring  atmospheric  pressure,  we  observe  that  the  weight  of  the  atmos- 
phere produced  the  atmospheric  pressure.  In  like  manner,  the  weight  of  all 
fluids  produces  pressure,  and  this  pressure  acts  equally  in  all  directions. 
This  is  an  important  consideration  in  the  study  of  mine  ventilation,  since  it 
has  given  rise  to  the.  measurement  of  pressure  by  air  or  motive  columns. 

Calculation  of  Pressure.— An  air  column,  or  motive  column,  in  ventilation, 
is  a column  of  air  having  a base  of  1 sq.  ft.,  and  of  such  height  that  its  weight 
shall  be  equal  to  any  given  pressure.  To  calculate  the  height  of  air  column 
corresponding  to  any  given  pressure,  divide  the  pressure  in  pounds  per 
square  foot  by  the  weight  of  1 cu.  ft.  of  the  air.  Mine  pressure  is  also 


346 


VENTILATION  OF  MINES. 


measured  by  the  water  column  that  it  will  support,  as  in  the  water  gauge,  or  by 
the  mercury  column,  as  in  the  barometer.  In  the  measurement  of  pressure 
by  means  of  the  water  column,  the  weight  of  the  water  column  must  be 
equal  to  the  pressure,  area  for  area. 

Since  the  weights  of  these  columns  are  proportional  to  their  sectional  areas, 
it  makes  no  difference  what  this  area  may  be,  the  weight  of  the  column 
calculated  for  a sectional  area  of  1 sq.  in.  will 
equal  the  pressure  per  square  inch  that  supports 
the  same. 

Hence,  since  1 cu.  in.  of  mercury  weighs  .49  lb., 
.49  X 30  = 14.7  lb.  is  the  atmospheric  pressure 
corresponding  to  a height  of  30  in.  of  mercury,  or, 
as  we  say,  30  in.  of  barometer.  If  we  consider  a 
cubical  box,  as  shown  in  the  accompanying 
figure,  holding  exactly  1 cu.  ft.  of  water,  and 
assume  the  weight  of  the  water  to  be  62.5  lb., 
as  is  usual  in  practice,  and  divide  the  bottom  of 
the  box  into  144  sq.  in.,  as  shown  in  Fig.  1,  we 
observe: 

(a)  The  pressure  of  the  water  on  the  bottom 
of  the  box  is  equal  to  the  weight  of  the  water, 

62.5  lb.;  that  is  to  say,  the  pressure  per  square  foot  due  to  1ft.  of  water  column 
is  62.5  lb. 

(b)  The  pressure  on  the  bottom  of  the  box,  when  the  water  is  only 
1 in.  deep,  is  equal  to  the  weight  of  a layer  of  water  1 in.  thick,  or 
62  5 

= 5.2  lb.;  or,  the  pressure  per  square  foot  due  to  1 in.  of  water  column 
is  5.2  lb. 

(c)  The  pressure  per  square  inch  on  the  bottom  of  the  box  is  equal  to 
the  weight  of  a prism  of  water  1 ft.  high,  and  having  a base  of  1 sq.  in. 

= .434;  or,  the  pressure  per  square  inch  due  to  1 ft.  of  water  column  is  .kSk  lb. 

These  principles  relating  to  the  pressure  of  fluids  are  important  to  the 
student  of  mining,  of  which  the  following  are  examples: 

1.  In  a mountainous  country,  several  thousand  feet  above  sea  level, 
where  the  barometer  registers,  say,  only  21  in.,  it  is  desired  to  know  the 
theoretical  height  a pump  will  draw.  .49  X 21  = 10.29  lb.  atmospheric 

pressure,  and  = 24  ft.,  nearly.  The  theoretical  suction,  in  this  instance, 

is  24  ft.,  nearly,  but  the  actual  draft  or  suction  would  vary  from  | to  ^ of 
this,  according  to  the  perfection  of  the  pump. 

2.  The  water-gauge  reading  between  the  intake  and  return  airways  of  a 
certain  mine  is  2.5  in.;  to  determine  the  pressure  per  square  foot,  we  have, 

2.5  X 5.2  = 13  lb.  per  sq.  ft. 

3.  To  determine  the  pressure  per  square  foot  on  a mine  dam,  due  to  a 
vertical  head  of  200  ft.,  62.5  X 200  = 12,500  lb. 

4.  To  express  in  air  column  or  motive  column,  a mine  pressure  equivalent 
to  a water-gauge  reading  of  3 in.,  assuming  the  temperature  of  the  air  to  be 
60°  F.  and  the  barometric  pressure  30  in.,  we  have  for  the  weight  of  1 cu.  ft. 

1 3253  X 30 

of  air  at  this  temperature  and  pressure  w = = .0766  lb.  The 

459  -|-  oO 

pressure  per  square  foot  due  to  3 in.  of  water  gauge  is  3 X 5.2  = 15.6.  Then, 

we  have  for  motive  column,  m = = 204  ft. 

.0/66 

Diffusion  and  Transpiration  of  Gases.— Diffusion  of  gases  means  the  mixing 
of  the  gaseous  volumes.  Graham  took  several  glass  tubes,  and  inserting  in 
one  end  of  each  a plug  of  plaster  of  Paris  that  was  porous,  he  filled  each 
tube  with  a different  gas;  as  for  example,  oxygen,  hydrogen,  nitrogen,  etc. 
He  then  placed  the  open  end  of  each  inverted  tube  in  a basin  of  mercury, 
supporting  the  tubes  in  an  erect  position.  The  gas  in  each  tube  immedi- 
ately began  to  diffuse  through  the  porous  plaster 'plug  into  the  atmosphere, 
and  it  was  observed  that  the  mercury  rose  in  each  tube  to  take  the  place  of 
the  gas  that  passed  into  the  atmosphere.  The  mercury  rose  in  the  hydrogen 
tube  4 times  as  fast  as  in  the  oxygen  tube,  and  in  the  other  tubes  the  mer- 
cury rose  at  different  rates. 

Rate  of  Diffusion  (Graham’s  Law).— The  rate  of  diffusion  of  gases  into  air  is 


DIFFUSION  OF  GASES. 


847 


in  the  inverse  ratio  of  the  square  roots  of  their  densities.  The  density  of 
oxygen  being  16  and  hydrogen  1,  the  rate  of  diffusion  of  oxygen  as  compared 
with  hydrogen  is  1 to  4;  that  is  to  say,  the  rate  of  diffusion  of  oxygen  is  only 
one-fourth  that  of  hydrogen. 


Table  Showing  the  Cokresponding  Mercury  and  Air  Columns,  and 
Pressure  per  Square  Foot  for  Each  Inch  of  Water  Column. 


Water  Gauge. 
Inches. 

Mercury  Column. 
Inches. 

o 

am 

o 

<D 

1 

Pressure. 

Lb.  per  Sq.  Ft. 

Water  Gauge. 

Inches. 

1 

Mercury  Column. 

Inches. 

Air  Column. 

Feet  (T.  60°,  B.  30"). 

Pressure. 

Lb.  per  Sq.  Ft. 

1 

.0735 

68 

5.2 

6 

.4412 

407 

31.2 

2 

.1471 

136 

10.4 

7 

.5147 

475 

36.4 

3 

.2206 

204 

15.6 

8 

.5882 

543 

41.6 

4 

.2941 

272 

20.8 

9 

.6618 

611 

46.8 

5 

.3676 

340 

26.0 

10 

.7353 

679 

52.0 

Table  Showing  the  Corresponding  Water  Column,  and  Pressure  per 
Square  Foot  for  Each  Inch  of  Mercury  Column. 


Barometer. 

Inches. 

Water  Column. 
Feet. 

^ Pressure. 

Lb.  per  Sq.  In. 

Barometer. 

Inches. 

Water  Column. 
Feet. 

Pressure. 

Lb.  per  Sq.  In. 

1 

1.13 

.49 

16 

18.13 

7.84 

2 

2.27 

.98 

17 

19.27 

8.33 

3 

3.40 

1.47 

18 

20.40 

8.82 

4 

4.54 

1.96 

19 

21.53 

9.31 

5 

5,67 

2.45 

20 

22.67 

9.80 

6 

6.80 

2.94 

21 

23.80 

10.29 

7 

7.93 

3.43 

22 

24.93 

10.78 

8 

9.06 

3.92 

23 

26.07 

11.27 

9 

10.20 

4.41 

24 

27.20 

11.76 

10 

11.33 

4.90 

25 

28.33 

12.25 

11 

12.46 

5.39 

26 

29.47 

12.74 

12 

13.60 

5.88 

27 

30.60 

13.23 

13 

14.73 

6.37 

28 

31.73 

13.72 

14 

15.87 

6.86 

29 

32.87 

14.21 

15 

17.00 

7.35 

30 

34.00 

14.70 

Note.— One  foot  of  water  column  is  equivalent  to  a pressure  of  .434  lb.  per 
sq.  in.  The  weight  of  air  at  60°  F.,  barometer  30  in.,  is  the  weight  of 
water;  but  the  ratio  of  air  to  water  is  often  assumed  as  1.2 : 1,000,  for  quick 
calculation.  The  specific  gravity  of  mercury  at  32°  F.  (standard  tempera- 
ture for  barometric  reading^  is  13.62;  and  a cubic  foot  of  mercury  at  this 
temperature  weighs  849  lb.  For  ordinary  calculation,  the  weight  of  1 cu.  ft. 
of  water  is  taken  as  62.5  lb.  The  exact  weight  of  1 cu.  ft.  of  pure  water,  at  a 
temperature  of  32°  F.,  is,  however,  62.418  lb. 

The  diffusion  of  marsh  gas  (Sp.  Gr.  .559)  is  much  more  rapid  than  that  of 
carbonic-acid  gas  (Sp.  Gr.  1.529).  The  diffusion  of  gases,  however,  is  greatly 
assisted  by  the  movement  of  the  air-current;  or  by  the  movement  of  the  gas 
as  it  tends  to  rise  or  fall,  according  to  its  relative  density  and  position  in  the 
airway.  For  example,  suppose  a gas  feeder  to  be  located  in  the  floor  of  an 
airway.  The  marsh  gas  given  off  from  the  feeder,  being  lighter  than  air, 


348 


VENTILATION  OE  MINES, 


tends  to  rise  toward  the  roof.  The  action  of  rising  helps  a diffusion  of  this 
gas  very  much.  On  the  other  hand,  a feeder  located  in  the  roof  gives  off  the 
same  gas,  which  tends  to  accumulate  along  the  roof,  and  if  the  air-current 
is  at  all  sluggish  at  this  point,  the  diffusion  of  the  marsh  gas  will  be  compar- 
atively slow.  It  often  happens  that  a feeder  in  the  roof  or  other  high  point 
of  the  workings  gives  off  gas  more  quickly  than  diffusion  can  take  place, 
where  the  air-current  is  sluggish.  This  results  in  the  accumulation  of  a 
body  of  pure  marsh  gas  at  this  point.  In  like  manner,  we  often  have  an 
accumulation  of  a large  body  of  carbonic-.acid  gas,  or  blackdamp,  near  the 
floor  or  other  low  place  in*  the  mine  workings,  where  the  air-current  is 
sluggish  and  where  the  blackdamp  is  formed  quicker  than  diffusion  takes 
place. 

Limit  of  Diffusion.— The  diffusion  of  gases  continues  to  take  place  until  the 
mixture  of  the  gases  is  uniform.  It  is  a curious  fact  that  this  takes  place 
earlier  or  quicker  in  the  case  of  gases  whose  densities  differ  widely,  than  where 
the  densities  of  the  two  gases  are  nearly  alike.  Thus,  saturation  will  take 
place  more  quickly  in  the  diffusion  of  carbonic-acid  gas  into  air  than  in  the 
diffusion  of  firedamp  into  air,  although  the  rate  of  diffusion  of  the  latter  is 
greater  than  of  the  former,  firedamp  being  lighter  than  carbonic-acid  gas. 

The  property  of  diffusion  is  of  the  greatest  importance  in  the  ventilation 
of  mines,  since  it  is  owing  to  this  that  the  air-current  is  enabled  to  sweep 
away  these  gases  from  their  lurking  places  in  the  workings  more  rapidly 
and  effectually  than  it  otherwise  could. 

Transpiration  of  gases  is  the  exuding  of  the  gases  from  the  pores  of  the  coal 
in  which  they  are  contained.  It  is  a well-known  fact  that  transpiration 
takes  place  more  rapidly  from  a newly  exposed  face  of  coal.  This  is  owing 
to  the  fact  that  the  gas  pent  up  in  the  coal,  or  occluded  in  the  seam,  tends 
to  escape  at  the  first  opportunity,  when  the  seam  is  exposed  to  the  atmos- 
phere. The  gas  is  under  a certain  pressure,  as  we  have  previously  observed, 
and,  as  the  mine  workings  penetrate  the  coal  seam,  the  gases  are  forced 
outward  from  the  coal  by  their  own  pressure,  thus  expanding  into  the  air  ol 
the  mine. 

The  transpiration  of  gas  from  coal  seams  differs  very  widely,  in  some 
seams  it  being  so  rapid  and  violent  as  to  splinter  and  break  the  coal  in  its 
effort  to  escape.  It  frequently  causes  a crackling  sound  peculiar  to  a very 
gaseous  seam,  and  in  some  cases,  causes  fine  coal  to  be  thrown  into  the  face 
of  the  miner. 


GASES  FOUND  IN  MINES. 

Oxygen  0 is  a colorless,  odorless,  tasteless,  non-poisonous  gas.  It  is  heavier 
than  air,  having  a specific  gravity  of  1.1056.  It  is  the  great  supporter  of  life 
and  combustion.  Oxidation,  or  the  union  of  any  of  the  elements  with 
oxygen,  is  simply  another  term  for  combustion  in  its  broadest  sense.  Most 
forms  of  matter  containing  carbon  are  easily  decomposed  at  certain  teinper- 
atures,  through  carbon  seeking  to  combine  with  the  oxygen  of  the  air  to 
form  carbonic-acid  gas  CO2.  This  union  of  the  oxygen  with  other  elements, 
or  oxidation,  takes  place  at  all  temperatures.  It  is  less  active  when  the 
temperature  is  low,  and  is  then  known  as  slow  combustion.  An  example  of 
this  is  found  in  the  gob  fires  that  occur  so  frequently  in  mine  workings. 
The  fine  coal  that  is  so  often  thrown  back  into  the  gob  is  acted  on  first  by 
moisture,  and  as  its  temperature  rises,  carbonic-oxide  gas  is  formed  in  small 
quantities  by  the  union  of  the  carbon  of  the  coal  with  the  oxygen  of  the  air; 
as  the  temperature  rises,  more  gas  is  formed.  Heat  is  caused  by  the  chemical 
action  due  to  the  interchange  of  the  atoms,  this  heat  being  often  sufficient  to 
ignite  the  gas  formed,  spontaneous  or  active  combustion  resulting.  Oxygen 
is  the  element  in  the  atmosphere  on  which  all  life  depends. 

Nitrogen  iV  is  a colorless,  odorless,  and  tasteless  gas;  it  is  neither  combus- 
tible nor  a supporter  of  combustion;  it  is  not  poisonous,  and  is  lighter  than 
air,  having  a specific  gravity  of  .9713.  Nitrogen  is  a particularly  inert  gas;  it 
takes  no  active  part  in  any  combustion,  in  the  sense  of  causing  such  com- 
bustion. Its  province  is  to  dilute  oxygen  of  the  atmosphere,  on  which 
life  depends.  Were  it  not  for  this  dilution,  oxidation  would  be  too  rapid, 
and  not  as  completely  under  control  as  at  present.  The  effect  of  nitrogen 
on  human  life  would  be  to  suffocate,  if  breathed  pure,  inasmuch  as  it  would 
exclude  oxygen  from  the  lungs.  Nitrogen  itself  nas  no  life-giving  power. 

Marsh  gas  CH^,  often  called  light  carbureted  hydrogen,  or  methane,  is  a 
chemical  compound,  consisting  of  4 atoms  of  hydrogen  to  1 atom  of  carbon. 


GASJES  FOUND  IN  MINES. 


349 


It  is  one  of  the  chief  gases  occluded  in  coal  seams,  and  results  from  the 
metamorphism  of  the  carbonaceous  matter  from  which  coal  is  formed,  when 
such  metamorphism  has  taken  place  with  the  exclusion  of  air,  and  in  presence 
of  water.  Pure  marsh, gas  is  colorless,  odorless,  and  tasteless,  and  is  lighter 
than  air.  Its  specific  gravity  is  .559,  and  it  diffuses  rapidly  in  the  air,  forming 
a firedamp  mixture.  Marsh  gas  burns  with  a blue  flame,  but  it  will  not 
support  combustion,  and  a lamp  placed  in  it  is  immediately  extinguished. 
In  the  mine,  it  is  a difficult  matter  to  place  a lamp  in  a body  of  pure  marsh 
gas,  since  the  gas  diffuses  so  rapidly  that  a firedamp  mixture  always  sur- 
rounds a body  of  pure  gas,  which  may  exist  high  up  in  some  cavity  of  the 
roof,  or  at  the  face  of  a steep  pitch  where  the  circulation  is  slow  and  the 
feeder  at  the  face  is  giving  off  a large  amount  of  gas.  The  flaming  of 
the  lamp  in  passing  through  a firedamp  mixture  would  at  once  cause  the 
withdrawal  of  the  lamp  before  reaching  the  body  of  pure  marsh  gas.  But 
could  a lamp  be  placed  in  a body  of  pure  marsh  gas,  it  would  be  extinguished 
at  once.  Marsh  gas  is  not  poisonous,  and  when  mixed  with  air  in  sufficient 
proportion,  it  may  be  breathed  for  a considerable  time  with  impunity  (see 
Firedamp).  Pure  marsh  gas  does  not  support  life,  but  suffocates  by  exclu- 
ding oxygen  from  the  lungs. 

Other  Hydrocarbons.— All  gases  that  are  compounds  of  carbon  and  hydrogen 
are  called  hydrocarbons.  Of  these,  the  chief  member  is  marsh  gas,  or  light 
carbureted  hydrogen,  described  in  the  preceding  paragraph;  the  other 
hydrocarbons  are  called  heavy  hydrocarbons.  The  chief  of  these  are  olefiant 
gas  and  ethane  Coife-  Both  of  these  gases,  like  marsh  gas,  are  the 

result  of  the  metamorphism  of  carbonaceous  matter,  during  the  formation  of 
the  coal,  but  unlike  marsh  gas,  they  have  been  produced  in  the  absence  of 
water,  and  as  a result  they  contain  a larger  percentage  of  carbon  than 
marsh  gas.  They  always  exist  in  common  with  marsh  gas,  as  occluded  gases 
in  coal  seams,  but  to  a far  less  extent.  Each  of  these  gases  possesses  a higher 
illuminating  power,  burning  with  a brighter  flame  than  marsh  gas.  This  is 
due  to  the  larger  percentage  of  carbon  present  in  their  composition.  Their 
remaining  properties  are  very  similar  to  the  properties  given  for  marsh  gas; 
they,  however,  when  present  in  a firedamp  mixture,  lower  the  temperature 
of  Ignition,  and  render  the  mixture  more  dangerous  than  it  would  be 
otherwise. 

Constants  for  Mine  Gases.— The  following  table  shows  the  symbols,  specific 
gravities,  and  relative  velocities  of  diffusion  and  transpiration  of  the  principal 
mine  gases,  arranged  in  the  order  of  their  specific  gravities,  air  being  taken  asl. 
The  values  given  in  the  next  to  the  last  column  of  this  table  were 
obtained  by  experimenting  with  the  gases,  and  agree  quite  closely  with 
the  calculated  values  given  in  the  preceding  column.  From  this  column 
we  see  that  1,344  volumes  of  marsh  gas  will  diffuse  in  the  same  time  as  1,000 
volumes  of  air,  or  812  volumes  of  carbonic-acid  gas. 


Table  of  Mine  Gases. 


Name  of  Gas. 

Symbol. 

Specific 

Gravity. 

1 

Relative  Velocity 
of  Diffusion. 

(Air  « 1.) 

Relative  Velocity 
of  Transpiration. 
(Air  = 1.) 

l/sp.  Gr. 

Air  

- 1.00000 

1.0000 

1.000 

1.0000 

Carbonic  acid 

CO2 

1.529 

.8087 

.812 

1.2371 

Sulphureted  hy- 

drogen  

H^S 

1.1912 

.9162 

.95 

Oxygen  

0 

1.1056 

.0510 

.9487 

.903 

Olefiant  

C^H^ 

.978 

1.0112 

1.0191 

1.788 

Nitrogen 

N 

.9713 

1.0147 

1.0143 

1.0303 

Carbonic  oxide  ... 

CO 

.967 

1.0169 

1.0149 

1.034 

Steam 

H2O 

.6235 

1.2664 

Marsh  gas 

CH^ 

.559 

1.3375 

1.344 

1.639 

Hydrogen 

H 

.06926 

3.7794 

3.83 

2.066 

Carbonic-oxide  gas  CO,  often  called  whitedamp,  is  a chemical  compound 
consisting  of  1 atom  of  carbon  united  to  1 atom  of  oxygen.  To  a certain 


150 


VENTILATION  OF  MINES. 


extent  it  occurs  as  an  occluded  gas  in  coal.  It  is  chiefly  formed,  however, 
in  coal  mines,  by  the  slow  combustion  of  carbonaceous  matter  in  the  gobs  or 
waste  places  of  the  mine,  where  the  supply  of  air  is  limited.  It  is  always  the 
product  of  the  slow  combustion  of  carbon  in  a limited  supply  of  air.  It  is 
therefore  one  of  the  chief  products  of  gob  fires,  and  is  also  a product  of  the 
explosion  of  powder  in  blasting.  This  gas  often  fills  the  crevice  made 
behind  a standing  shot,  and  causes  the  fiash  that  takes  place  when  the 
miner  puts  his  lamp  behind  such  shot  to  examine  the  same.  This  gas  is 
formed  in  large  quantities  whenever  the  flame  of  a blast  or  explosion  is 
projected  into  an  atmosphere  in  which  coal  dust  is  suspended.  The  force  of 
a blast  often  blows  the  dust  into  the  air,  and  the  flame  acting  on  it  distils 
carbonic-oxide  gas. 

Carbonic-oxide  gas  is  lighter  than  air,  having  a specific  gravity  of  .967, 
and  it  thereicre  accumulates  near  the  roof  and  in  the  higher  working 
places.  It  is  colorless,  odorless,  and  tasteless.  It  is  combustible,  burning 
with  a light-blue  flame.  This  is  the  flame  often  seen  over  a freshly  fed 
anthracite  fire.  It  is  also  a supporter  of  combustion,  being  the  only  mine 
gas  that  burns  and  also  supports  combustion.  This  property  leads  to  very 
important  results  in  mines,  inasmuch  as  it  lengthens  the  flame  of  a lamp  or 
the  flame  of  a blast.  Any  flame  is  fed  by  this  gas,  and  is  thereby  transmitted 
through  the  mine  airways,  from  one  point  to  another.  The  same  property 
extends  very  widely  an  otherwise  local  explosion.  This  gas  has  the  widest 
explosive  range  of  any  gas  known  to  mining,  except  hydrogen.  The  effect 
of  its  presence  in  firedamp  mixtures  is  always  to  widen  the  explosive  range 
of  the  firedamp,  causing  it  to  become  explosive  in  larger  and  smaller 
proportions  than  it  otherwise  would.  Carbonic-oxide  gas  is  a very  poison- 
ous gas,  and  acts  on  the  human  system  as  a narcotic,  producing  drowsiness 
or  stupor,  followed  by  acute  pains  in  the  head,  back,  and  limbs,  and  after- 
ward by  delirium.  It  acts,  when  breathed  into  the  lungs,  to  absorb  the 
oxygen  from  the  blood,  or,  in  other  words,  poisons  the  blood. 

Carbonic-oxide  gas  is  detected  in  mine  workings  by  its  effect  on  the  flame 
of  a lamp,  which  burns  more  brightly  in  the  presence  of  the  gas,  and  reaches 
upwards  as  a slim,  quivering  taper,  having  often  a pale-blue  tip  that, 
however,  is  not  readily  observed. 

Carbonic-acid  gas  CO2,  often  called  blackdamp  or  chokedamp,  is  a chemical 
compound  consisting  of  1 atom  of  carbon  united  to  2 atoms  of  oxygen.  It  is 
heavier  than  air,  having  a specific  gravity  of  1.529.  It  therefore  accumulates 
near  the  floor  or  in  the  low  places  of  the  mine  workings.  It  is  always  the 
result  of  the  complete  combustion  of  carbon  in  a plentiful  supply  of  air,  and 
is  a product  of  the  breathing  of  men  and  animals,  burning  of  damps,  or  any 
other  complete  combustion.  It  is  always  present  in  occluded  gases. 

Carbonic-acid  gas  is  a colorless,  odorless  gas,  but  possesses  a peculiarly 
sweet  taste,  which  may  be  detected  in  the  mouth  when  it  is  inhaled  in  large 
quantities.  It  is  not  combustible,  nor  is  it  a supporter  of  combustion. 
Lamps  are  at  once  extinguished  by  it.  It  diffuses  slowly  into  the  atmosphere, 
and  is  a difficult  gas  to  remove  in  ventilating.  It  is  not  poisonous,  but  acts 
to  suffocate  by  excluding  oxygen  from  the  lungs.  Its  effect,  when  breathed 
for  any  length  of  time,  is  to  cause  headache  and  nausea,  followed  by  weak- 
ness and  pains  in  the  back  and  limbs;  when  present  in  larger  quantities,  it 
causes  death  by  suffocation.  This  gas,  when  present  in  firedamp  mixtures, 
has  the  opposite  effect  from  that  of  carbonic-oxide  gas,  inasmuch  as  it 
narrows  the  explosive  range  of  the  firedamp,  and  renders  such  mixtures 
inexplosive,  which  would  otherwise  be  explosive  (see  Firedamp). 

Carbonic-acid  gas  is  detected  in  the  mine  air  by  the  dimness  of  the  lamps 
and  by  their  extinguishment  w^hen  present  in  larger  quantities.  It  should 
always  be  looked  for  at  the  floor,  and  in  low  places  of  the  mine  workings. 

Sulphureted  hydrogen  II2S  occurs  at  times  as  an  occluded  gas  in  coal  seams, 
but  more  often  exudes  from  the  strata  immediately  underlying  or  over- 
lying  those  seams.  It  is  generally  supposed  to  be  formed  by  the  disintegra- 
tion of  pyrites  in  the  presence  of  moisture.  It  is  heavier  than  air,  having  a 
specific  gravity  of  1.1912.  It  is  a colorless  gas,  having  a very  disagreeable 
odor  resembling  that  of  rotten  eggs,  and  is  known  to  the  miners  as  stinkdamp. 
It  is  an  exceedingly  dangerous  gas  when  occurring  in  considerable  quan- 
tities. When  mixed  with  7 times  its  volume  of  air,  it  is  violently  explosive. 
It  is  extremely  poisonous,  acting  to  derange  the  system  when  breathed 
in  small  quantities,  and,  v/hen  inhaled  in  larger  (piantities,  it  produces 
unconsciousness  and  prostration.  Its  smell  serves  as  the  best  means  for  its 
detection. 


GASES  FOUND  IN  3IINES. 


351 


Firedamp.— The  general  term  firedamp  relates  to  any  explosive  mixture  of 
marsh  gas  and  air,  although  in  some  localities  this  term  is  understood  as 
referring  to  any  mixture  of  marsh  gas  and  air  whatever,  whether  explosive 
or  otherwise.  Many  persons  speak  of  pure  marsh  gas  as  firedamp.  The  first 
meaning  given  above,  however,  is  the  general  acceptation  of  the  term. 

Pure  marsh  gas  when  present  in  small  quantities  in  the  air  burns  in  the 
flame  of  the  lamp  without  explosion.  As  the  quantity  of  the  gas  is 
increased,  the  effect  on  the  flame  of  the  lamp  is  at  once  noticeable.  As  the 
proportion  of  gas  in  the  air  is  further  increased,  and  approaches  the  lower 
explosive  limit,  the  lamp  flame  enlarges,  snaps,  and  crackles.  When  the 
proportion  of  gas  to  air  is  1 to  13,  slight  explosions  occur  within  the  lamp, 
the  flame  of  the  lamp  jumping  violently.  As  the  proportion  of  gas  is 
increased,  the  violence  of  the  explosion  is  augmented  until  it  reaches  a 
maximum,  when  the  proportion  of  gas  to  air  is  1 to  (exactly,  1:9.38). 
This  is  the  proportion  of  gas  and  air  in  firedamp,  when  at  its  maximum 
explosive  violence.  From  this  point,  as  the  quantity  of  gas  is  still  further 
increased,  the  violence  of  the  explosion  decreases,  until  it  becomes  very 
feeble  when  the  proportion  of  gas  and  air  is  1 to  5i,  and  ceases  altogether 
beyond  this  point.  The  explosive  limits  of  marsh  gas,  or  the  limits  of  fire- 
damp mixtures,  are  then  as  follows:  Lower  limit,  1 volume  of  gas  to  13 
volumes  of  air;  higher  limit,  1 volume  of  gas  to  volumes  of  air.  These 
limits  refer  to  pure  firedamp,  or,  in  other  words,  a firedamp  mixture  con- 
sisting of  pure  marsh  gas  and  air. 

It  rarely  happens  that  firedamp,  as  found  in  mine  workings,  is  pure,  but 
contains  admixtures  of  other  gases,  such  as  carbonic-acid  gas  CO2,  carbonic- 
oxide  gas  CO,  and  heavy  hydrocarbons. 

Afterdamp.— The  term  afterdamp  relates  to  the  gaseous  mixture  that  exists 
in  mine  workings  after  an  explosion  of  gas.  The  composition  of  afterdamp 
is  exceedingly  variable,  and  admits  of  no  general  analysis  that  can  be 
applied  with  certainty  to  any  one  explosion.  The  conditions  that  obtain 
in  an  explosion  are  so  manifold,  and  control  so  completely  the  character  of 
the  gases  formed,  that  it  is  impossible  to  give  more  than  a general  analysis 
of  afterdamp. 

The  chief  products  of  the  complete  explosion  of  pure  firedamp  are  car- 
bonic-acid gas,  watery  vapor,  and  nitrogen  (see  page  343).  The  explosion  of 
firedamp  is  seldom,  however,  complete.  Where  a large  body  of  gas  has 
exploded,  the  air-current  in  the  mine  workings  does  not  furnish  sufficient 
air  for  the  complete  combustion  of  the  firedamp,  and  as  a result,  a large 
amount  of  carbonic-oxide  gas  is  formed,  and  is  present  in  the  afterdamp  of 
the  explosion.  The  presence  of  this  gas  (CO)  renders  the  afterdamp  far 
more  dangerous  than  it  would  otherwise  be,  for  two  reasons:  The  gas  itself 
is  very  poisonous,  and  its  presence  is  not  at  once  detected  by  the  zealous 
men  that  are  working  to  rescue  their  fellow  workmen.  The  lamps  burn 
very  brightly  in  this  gas,  and  the  rescuers  press  forward  unconscious  of  their 
real  danger  until  overcome  by  the  effects  of  the  gas.  The  presence  of  coal 
dust  in  suspension  in  the  mine  air  at  the  time  of  the  explosion,  or  thrown 
into  the  air  by  the  force  of  the  explosion,  results  at  once  in  the  production 
of  a large  amount  of  carbonic-oxide  gas.  It  is  a well-known  fact,  also,  that 
carbonic-acid  gas  CO2,  formed  as  a direct  product  of  the  explosion,  or  which 
may  be  present  in  the  mine  air  before  the  explosion,  coming  in  contact 
with  the  incandescent  carbon  of  the  coal  dust,  is  converted  by  it,  at  the  high 
temperature  of  the  flame,  into  carbonic-oxide  gas  CO,  We  observe,  there- 
fore, that  an  explosion,  in  all  its  effects,  tends  to  the  rapid  and  abundant 
production  of  this  most  dangerous  gas. 

The  other  products  of  an  explosion  are  numerous,  but  for  the  larger  part, 
unimportant,  except  as  they  do  not  support  life.  We  have  mentioned  and 
described  only  those  gases  forming  the  larger  portion  of  the  afterdamp,  or 
constituting  the  active  agents  in  an  explosion. 

Occurrence  of  Gases  in  Mines.— Most  of  the  gases  occurring  in  mines  are 
occluded  in  the  coal  or  the  strata  adjacent  to  the  coal  seam.  These  occluded 
gases  differ  widely  in  different  coals,  but  are  chiefly  marsh  gas  with  varying 
quantities  of  heavy  hydrocarbons  (olefiant  gas,  ethane,  etc.)  and  carbonic- 
acid  gas  to  a limited  extent.  In  some  coals,  a large  percentage  of  nitrogen 
gas  is  occluded,  which,  however,  transpires  very  slowly  into  the  atmosphere. 
Sulphureted  hydrogen,  when  present,  usually  exudes  from  the  underlying 
or  overlying  strata  of  the  coal  seam.  These  occluded  gases  are  the  result  of 
coal  formation,  according  to  the  best  authorities  and  evidence.  They  exist 
in  the  pores  of  the  coal  under  considerable  pressure  due  to  the  weight  of  the 


352 


VENTILATION  OF  MINES. 


superincumbent  strata.  When  the  strata  adjacent  to  the  coal  seam  are 
impervious  to  gases,  the  occluded  gases  remain  pent  up,  and  we  have  what 
is  called  a gaseous  seam.  The  tendency  of  the  gas  is  always  to  escape  to  the 
surface  or  into  the  mine  workings,  at  the  first  opportunity. 

These  gases  have  each  their  separate  effects,  and  their  combined  effect  is 
sometimes  very  complicated.  We  can  only  study  to  become  familiar  with 
the  separate  characteristics  of  each  of  these  gases,  and  judge  of  their  com- 
bined effect  when  present  in  firedamp  mixtures.  For  example,  one  effect  of 
all  these  gases  when  present  in  firedamp  mixtures  is  to  dilute  the  firedamp, 
and  to  that  extent  weaken  its  explosive  force.  Dilution  of  the  firedamp  by 
carbonic-acid  gas  CO2  decreases  very  rapidly  the  explosiveness  of  the  fire- 
damp. When  carbonic-acid  gas  is  present  in  firedamp  to  the  extent  of  one- 
seventh  its  volume,  explosion  ceases  altogether;  in  other  words,  the 
firedamp  is  rendered  inexplosive.  The  effect  of  smaller  quantities  of  this 
gas  is  to  contract  the  explosive  limits  of  the  firedamp  as  well  as  to  weaken 
the  explosion.  The  effect  of  carbonic-oxide  gas  CO  when  present  in  fire- 
damp mixtures  is  likewise  to  dilute  the  firedamp.  The  flame,  however,  is 
lengthened  by  this  gas,  and  the  explosive  limits  of  the  firedamp  mixture  are 
widened.  In  other  words,  mixtures  of  marsh  gas  and  air,  which  were  not 
explosive  mixtures,  are  rendered  explosive  by  the  presence  of  carbonic- 
oxide  gas. 

The  chief  source  of  the  other  mine  gases  lies  in  the  slow  combustion 
of  carbonaceous  matter  in  the  gob,  gob  fires,  burning  of  lamps,  breathing 
of  men  and  animals,  etc.  The  table  on  page  353  shows  the  percentage  of 
occluded  gases  in  a number  of  coals  and  their  volume  at  normal  temper- 
ature and  pressure. 

Gas  Feeders  (Pockets).— The  occluded  gas  of  a coal  seam  escapes  when- 
ever opportunity  is  offered,  and  accumulates  in  the  pockets  and  crevices 
of  the  adjoining  strata,  forming  what  are  called  gas  feeders.  These  consti- 
tute a very  dangerous  element  in  the  mining  of  gaseous  seams,  inasmuch  as 
when  such  a crevice  or  feeder  is  tapped  by  the  miner’s  drill,  the  gas,  which 
is  usually  under  heavy  pressure,  blows  out  in  a large  volume,  at  times  even 
blowing  the  drill  from  the  hole. 

Pressure  of  Occluded  Gases.— Occluded  gases  exist  under  a pressure  that  is 
proportionate  to  the  weight  of  the  overlying  strata.  Numerous  experiments 
in  England,  France,  and  Belgium  show  that  the  pressure  of  gases  occluded 
in  coal  seams  frequently  amounts  to  from  10  to  16  atmospheres,  and  in  some 
cases  has  reached  32  atmospheres.  These  high  pressures  of  occluded  gases 
manifest  themselves  frequently  in  the  boring  of  gas  wells,  where  the  tools 
are  at  times  blown  from  the  bore  hole. 


Pressure  of  Occluded  Gas. 


Name  of  Mine. 

Depth  of  Hole. 
Feet. 

Pressure. 

Pounds. 

Elmore  mine,  main  bed 

8.53 

4.36 

Hetton  mine,  Hutton  bed 

8.98 

6.96 

Eppleton  mine,  Hutton  bed... 

46.90 

36.14 

Balden  mine,  Bensham  bed... 

31.85 

71.41 

Harris  Navigation  mine 

32.80 

22.04 

Merthyr  Vale  mine  

49.20 

39.67 

Celynen  mine 

54.48 

68.32 

Hafton  mine  (1,214  ft.  deep) 

16.24 

196.30 

Harton  mine  

27.55 

230.44 

Harton  mine  

37.13 

294.45 

Amount  of  Gas.— Experiments  made  by  the  Prussian  Firedamp  Commission 
have  given  results  varying  from  357  to  2,400  cu.  ft.  of  gas  liberated  per  ton  of 
coal  mined.  Mr.  Chesneau  gives  1,377  cu.  ft.  at  the  Herin  mine,  Anzin. 
Experiments  at  the  Ronchamp  mines  give  883  cu.  ft. 

Outbursts  of  gas  are  frequent  occurrences  in  some  coal  seams.  They  are 
caused  by  the  occludeij  gas’  finding  its  way  to  a vertical  crevice  or  cleat  in  the 


GASES  FOUND  IN  MINES. 


853 


Gases  Enclosed  in  the  Pores  of  Coal  and  Evolved  in  Vacuo 
AT  212°  E.— {Thomas.) 


Name  of  Colliery. 

Quality. 

CO2 

0 

CH^ 

N 

Quar 

60 

08 

Cu.  Ft.  g 

per  ^ 

Short  Ton. 

Navigation 

Steam. 

13.21 

.49 

81.64 

4.66 

250.0 

80 

Dunraven  

Steam. 

5.46 

.44 

84.22 

9.88 

218.0 

70 

Cyfarthfa  

Steam. 

18.90 

1.02 

67.47 

12.61 

147.0 

47 

Bute 

Steam. 

9.25 

.34 

86.92 

3.49 

375.0 

120 

Bonville’s  Court 

Anthracite. 

2.62 

93.13 

4.25 

555.0 

178 

Watney’s 

Anthracite. 

14.72 

84.18 

1.10 

600.0 

192 

Plymouth  Iron  Works 

Bituminous. 

36.42 

.80 

62.78 

55.9 

18 

Cwm  Clydach 

Bituminous. 

5.44 

1.05 

63.76 

29.75 

55.1 

18 

Bettwys  

Bituminous. 

22.16 

6.09 

2.68 

69.07 

24.0 

8 

Gases  Enclosed  in  the  Pores  of  Coal  and  Evolved  in  Vacuo 
AT  212°  F.— ( IT.  Le  Chatellier. ) 


Locality. 

CH^ 

CO2 

N 

0 

Analyst. 

Dunraven  mine  (blowers) 

96.70 

.47 

2.79 

J.  W.  Thomas. 

Dunraven  mine  (bore  hole) 

96.50 

.44 

3.02 

J.  W.  Thomas. 

Garswood  mine 

84.16 

.86 

12.30 

2.65 

W.  Kellner. 

Gars  wood  mine  (blowers) 

88.86 

.41 

8.90 

1.83 

W.  Kellner. 

Glamorgan  mine  (blowers) 

93.01 

.27 

5.94 

.78 

W.  Kellner. 

Dombran  mine  (blowers) 

95.11 

.48 

4.07 

.34 

( Austrian  Firedamp 

Karwin  mine , 

94.59 

.18 

4.48 

.75 

X Commission. 

Karwin  mine  (blowers)  

99.10 

.20 

.70 

Hruschau  mine 

79.16 

.19 

17.04 

.61 

Hruschau  mine  (blowers) 

87.93 

.83 

10.25 

.99 

Peters wald  mine  (blowers) 

90.00 

.15 

9.25 

.60 

Segen  Gottes  mine  

83.51 

1.17 

15.02 

.30 

Sauer. 

Segen  Gottes  mine  ( bore  hole ) 

87.16 

1.11 

11.73 

Sauer. 

Liebe  Gottes  mine  (borehole) 

77.69 

3.77 

18.48 

.06 

Sauer. 

Gases  Enclosed  in  the  Pores  of  Coal  and  Evolved  in  Vacuo 
AT  212°  E.—{Schondorff.) 


Locality. 


Blowers. 

Bonifacius  mine  at  Kray  (Essen)  

Consolidation  mine  at  Schalk  (Westphalia) 
Konig  mine  at  Neunkirchen  (Saarbruck) 

Oberkirchen  mine  at  Schaumburg  

Cavities  in  the  roof,  Lothringen  mine  at 

Castrop  (Westphalia)  

New  Iserlohn  mine  at  Lawgendren  (West- 
phalia)   


CHi 

C2He 

H 

CO2 

N-j-0 

90.94 

1.40 

.30 

7.36 

89.88 

5.84 

.67 

3.61 

84.89 

1.62 

.65 

12.84 

f 60.46 

37.64 

2.11 

2.56 

193.66 

.88 

.63 

4.80 

27.95 

1.35 

.45 

70.25 

f 4.75 

.09 

1.34 

65.00 

1 4.00 

.06 

.40 

95.00 

354 


VENTILATION  OF  MINES. 


Fig.  2. 


coal  seam,  as  illustrated  in  Fig.  2,  and  the  pressure  of  the  gas  thus  becomes 
distributed  over  a large  area.  Thus,  a pressure  of  10  atmospheres  of  a gas 
feeder  becoming  distributed  over  an  area  of  200  sq.  ft.  results  in  a total  pres- 
sure of  upwards  of  2,000  tons,  upon  a comparatively  small  area  of  coal. 

As  mine  openings  approach  proximity 
to  such  a locality,  this  pressure  man- 
ifests itself  by  bursting  the  coal  from 
its  position  in  the  face,  and  throwing 
it  into  the  entries,  in  some  cases  com- 
pletely blocking  the  openings  or  pas- 
sageways. Such  an  occurrence  is 
termed  an  outburst.  It  is  frequently 
accompanied  by  thunderings  and 
poundings,  which  manifest  themselves 
for  several  days  previous  to  the  actual 
outburst  of  gas.  These  poundings  are 
taken  as  a warning  by  the  miners 
experienced  in  such  regions.  The 
poundings  are  probably  the  result  of 
the  gas  working  its  way  from  one 
crevice  to  another,  always  advancing 
closer  and  closer  to  the  mine  openings,  where  they  finally  burst  forth  with 
extreme  violence. 

Testing  for  Gas  by  Lamp  Flame.— Marsh  gas  and  firedamp  are  detected  in 
mine  workings  by  the  small  flame  cap  that  envelopes  and  surmounts  the 
flame  of  the  lamp  in  a firedamp  mixture.  This  flame  cap  is  caused  by  the 
gaseous  mixture,  which  burns  as  it  comes  in  contact  with  the  flame. 
The  proportion  of  gas  in  the  mixture  determines  the  height  of  the  flame  cap. 
When  testing  for  gas,  the  lamp  flame  is  first  reduced  to  a small,  uniform 
size,  and  although  this  is  not  a universal  practice,  it  has  the  advantage  of 
giving  uniform  results.  The  lamp  is  held  in  an  upright  position,  in  one 
hand,  while  the  eyes  are  carefully  screened  by  the  other  hand  from  the 
glare  of  the  light,  the  lamp  being  slowly  raised  toward  the  roof  where  gas  is 
suspected.  The  flame  is  carefully  watched  for  the  first  appearance  of  a cap, 
and  the  height  of  the  cap  is  carefully  noted.  Many  lamps  are  provided  with 
a graduated  scale  set  opposite  to  the  flame,  so  that  the  height  of  a cap  may 
be  estimated  with  accuracy.  After  the  observation,  the  lamp  is  quietly  and 
promptly  withdrawn  from*  the  gas.  Should  flaming  occur  within  the  lamp, 
as  sometimes  happens  when  it  is  raised  too  quickly,  or  when  the  gaseous 
mixture  is  strong,  the  lamp  should  be  withdrawn  carefully  and  not  with 
undue  haste,  as  there  is  danger  of  the  flame  of  the  gases  burning  within  the 
lamp  being  forced  through  the  gauze  by  a rapid  movement.  This  requires 
great  presence  of  mind  on  the  part  of  the  person  using  the  lamp. 

In  Fig.  3 the  heights  of  flame  cap  due  to  the  presence  of  different  proportions 
of  marsh  gas  are  shown.  These  heights,  as  given,  refer  to. the  experimental 
heights  of  flame  cap  ob- 
tained with  pure  marsh 
gas.  It  should  be  ob- 
served, however,  that  the 
presence  of  other  gases 
in  the  firedamp  will  vary 
its  explosive  character, 
and  this  fact  very  mate- 
rially modifies  the  explo- 
siveness of  certain  caps. 

For  example,  in  the  ex- 
periments on  pure  marsh 
gas,  a 2"  flame  cap  was 
found  to  be  inexplosive; 
while,  in  the  mine,  and 
with  the  variable  char- 
acter of  the  firedamp  mixtures  usually  found  there,  a flame  of  in.  is 
often  found  to  indicate  explosive  con*ditions.  Again,  flames  of  even  less 
height  than  this  often  indicate  dangerous  conditions,  especially  where 
the  coal  is  inflammable  and  there  is  much  fine  dust  present  in  the 
atmosphere.  These  conditions  account  readily  for  the  various  statements 
that  we  commonly  see  in  regard  to  the  explosiveness  of  certain  flames.  In 
fact,  each  fire  boss  learns,  after  years  of  experience,  to  depend  wholly  on  his 


SAFETY  LAMPS. 


355 


own  knowledge,  guided  by  the  conditions  that  exist  in  the  workings  and 
with  which  he  has  become  familiar. 


SAFETY  LAMPS. 

The  safety  lamp  is  designed  to  give  light  in  gaseous  workings  without  the 
danger  of  igniting  the  gases  present  in  the  atmosphere.  The  principle  of 
the  safety  lamp  depends  on  the  cooling  effect  that  an  iron-wire  gauze  exerts 
on  flame.  It  is  a well-known  fact  ‘that  all  gases  ignite  at  certain  fixed 
temperatures,  and  if  this  temperature  is  decreased  from  any  cause,  the  flame 
is  extinguished. 

Use  of  Safety  Lamps.— Safety  lamps  are  used  for  two  general  purposes  in 
the  mine,  and  may  be  classified  under  two  heads:  (a)  lamps  for  general  use; 
{h)  lamps  for  testing  for  gas. 

Safety  Lamps  for  General  Work. — The  essential  features  of  a lamp  designed 
for  general  mine  work  are:  (1)  safety  in  strong  currents;  (2)  good  illuminating 
power;  (3)  security  of  lock  fastening;  (4)  freedom  from  flaming;  (5)  security 
against  accident;  (6)  simplicity  of  construction.  The  conditions  under 
which  a lamp  is  placed  at  the  working  face  differ  from  those  that  attend 
the  testing  for  gas.  The  illuminating  power  of  the  lamp  must  be  good,  so 
that  the  workman  can  see  clearly  what  he  is  doing.  The  lamp  must  not 
be  too  sensitive  to  gas,  or  its  tendency  to  flame  will  necessitate  that  a care- 
ful watch  be  kept  of  it,  and  this  would  interfere  with  the  prosecution  of  the 
miner’s  work.  Again,  the  miner  is  too  often  careless  or  neglectful  of  his 
lamp,  and  would  fail  to  give  it  the  required  attention.  The  lamp  is  often 
upset,  and  is  apt  to  be  broken  by  flying  coal,  or  by  a fall,  unless  carefully 
protected.  The  lamp  should  be  so  securely  locked  as  not  to  permit  of  any 
tampering  on  the  part  of  the  miner  without  its  being  detected  in  the  lamp 
room.  In  order  that  the  lamp  may  be  thoroughly  and  rapidly  cleaned,  its 
construction  should  be  simple.  The  lamp  should  be  easily  taken  apart  and 
put  together  again  after  it  is  cleaned. 

Lamps  for  Testing. — The  essential  features  of  a lamp  for  testing  purposes 
are:  (1)  free  admission  of  air  below  the  flame;  (2)  no  reflecting  surface 
behind  the  flame;  (3)  ability  to  test  for  a thin  layer  of  ^as  at  the  roof. 
When  testing  for  gas,  it  is  important  to  have  a free  admission  of  the  air 
below  and  around  the  flame,  as  the  flame  cap  is  very  sensitive  and  is  inter- 
fered with  seriously  by  the  conflicting  ascending  and  descending  currents 
in  a lamp  in  which  the  air  enters  above  the  flame.  A more  uniform  cap  will 
be  given  where  the  currents  ascend  quietly  around  the  flame.  This  feature 
is  very  important  to  the  production  of  a good  flame  cap,  and  it  is  this  feature 
that  makes  the  Davy  lamp  such  a favorite  among  fire  bosses.  In  order  that 
a flame  cap  shall  be  readiljr  observed,  there  should  be  no  reflection  behind 
it,  as  the  eye  is  easily  deceived  under  these  conditions.  A scale  by  which 
the  height  of  the  flame  cap  may  be  accurately  measured,  is  a convenient 
feature  in  many  lamps  for  testing  purposes. 

In  the  use  of  the  common  Davy  lamp  in  testing  for  gases,  it  is  a common, 
although  dangerous,  practice  to  turn  the  lamp  on  its  side  and  place  it  close 
up  against  the  roof.  In  this  position,  the  flame  is  very  apt  to  pass  through  the 
gauze,  from  two  causes:  The  gauze  is  readily  heated,  because  the  flame  cap 
IS  close  against  it,  and  when  heated,  affords  no  protection  against  the 
passage  of  the  flame  and  the  ignition  of  the  gas  outside  the  lamp.  Again, 
in  this  position,  small  particles  from  the  roof  are  apt  to  fall  upon  the  gauze, 
and  this  may  often  assist  in  the  passage  of  the  flame  through  the  gauze.  A 
dirty  gauze  is  unsafe.  When  the  lamp  is  turned  sideways,  the  gauze  may 
become  smoked  by  contact  with  the  flame,  and  this  smoke,  or  deposit  of 
carbon,  assists  greatly  the  passage  of  flame  through  the  gauze.  Another 
common  and  dangerous  practice  on  the  part  of  the  fire  boss  is  to  brush  the 
gas  down  on  the  lamp  with  his  cap.  By  so  doing,  there  is  great  danger  of 
the  flame  being  blown  through  the  gauze  and  igniting  the  gas  that  may  be 
present.  On  these  accounts,  it  is  essential  that  a good  lamp  for  testing  pur- 
poses shall  be  able  to  draw  its  air  from  a point  close  to  the  roof,  in  cases 
where  it  is  necessary  to  do  so.  This  is  often  accomplished  by  an  extra  tube, 
which  is  supplied  with  the  lamp,  and  which  may  be  taken  off  the  lamp 
when  not  in  use.  This  tube  extends  up  the  outside  of  the  lamp  to  the  top. 

An  important  feature  of  a lamp  for  testing  purposes  is  the  uniformity  of 
its  flame.  A more  uniform  flame  is  obtained  in  the  use  of  alcohol  instead  of 
the  lard  oil  commonly  used  in  the  safety  lamp. 


356 


SAFETY  LAMPS, 


Detection  of  Small  Percentages  of  Gas. — The  Davy  lamp  in  the  hands  of  a 
careful  person  may  he  made  to  detect  the  presence  of  gas  in  quantities  as 
low  as  3^.  It  is  claimed  by  some  fire  bosses  that  2^  of  gas  may  be  detected 
with  a good  Davy.  For  the  detection  of  small  quantities  of  gas,  specially 
constructed  lamps  have  been  used.  These  lamps  are  designed  to  burn 
alcohol  or  hydrogen,  giving  a non-luminous  flame.  Among  these  may  be 
mentioned  the  Pieler  lamp,  burning  alcohol,  which  it  is  claimed  will  detect 
as  small  a quantity  of  gas  as  A device  known  as  the  Clowes  gas  tester 
has  been  invented,  and  may  be  attached  to  many  safety  lamps.  It  consists 
of  a hydrogen  tube  that  is  designed  to  furnish  a small  stream  of  hydrogen 
to  the  lamp  flame  when  testing  for  gas.  Surrounding  the  wick  of  the  lamp 
is  a closely  fitting  cone,  to  which  the  hydrogen  from  the  tube  is  supplied. 
AVhen  the  lamp  is  to  be  used  for  testing  for  gas,  the  wick  is  lowered, 
extinguishing  the  oil  flame  after  the  hydrogen  is  turned  on.  It  is  claimed 
that  gas  may  be  detected  in  as  small  quantities  as  by  this  apparatus 
attached  to  any  good  safety  lamp  admitting  its  air  below  the  flame. 

The  Shaw  gas  tester  is  useful  for  determining  the  percentage  of  marsh 
gas  in  the  mine  air,  but  it  cannot  be  applied  at  the  face,  and  samples  of  gas 
must  be  taken  to  the  surface  for  analysis. 

Oils  for  Safety  Lamps.— Most  safety  lamps  burn  vegetable  oils,  which  are 
considered  the  safest  for  mining  use,  and  so  reported  by  the  English  Mine 
Commission.  Such  oils  are  rape-seed  oil  and  colza  oil,  made  from  cabbage 
seed.  Seal  oil  is  also  largely  used,  and  was  regarded  as  a safe  oil  by  the 
English  Mine  Commission.  Seal  oil  affords  a better  light  than  vegetable  oils, 
and  in  its  use  there  is  less  charring  of  the  wick.  A mixture  of  1 part  of  coal 
oil  to  2 parts  of  rape  or  seal  oil  is  often  used,  and  improves  the  light,  but  the 
smoke  from  the  flame  is  increased.  The  Ashworth-Hepplewhite-Gray  lamp 
is  constructed  to  burn  coal  oil,  or  a mixture  of  coal  and  lard  oil.  The  Wolf 
lamp  is  especially  designed  for  burning  naphtha  or  benzine.  Special  tests 
have  been  made  to  prove  the  safety  of  using  such  a fluid  in  this  lamp,  and 
resulted  in  demonstrating  the  fact  that  the  lamp  was  safe  under  any  condi- 
tions that  might  aj’ise.  A thorough  test  was  made,  the  oil  vessel  of  the 
burning  lamp  being  heated  to  180°  F.,  at  which  point  the  lamp  was 
extinguished  without  manifesting  any  dangerous  results. 

Types  of  Safety  Lamps.— In  the  year  1815,  Sir  Humphrey  Davy  and  George 
Stevenson,  the  latter  a poor  miner,  discovered,  simultaneously,  that  flame 
would  not  pass  through  small  openings  in  a perforated  iron  plate.  This  led 
to  the  construction  of  what  are  known  as  the  Davy,  and  the  Stevenson  or 
“ Geordy,”  lamps.  The  Davy  lamp  is  still  a great  favorite  among  fire  bosses 
for  the  detection  of  gas  in  mine  air.  Inasmuch  as  all  safety  lamps,  of  which 
there  are  a large  number,  depend  on  the  same  principle,  we  will  only 
describe  such  lamps  as  possess  essential  features,  and  which  show  important 
improvements  and  the  gradual  developments  in  safety-lamp  construction. 

Davy  Lamp. — Fig.  4 (a)  shows  a wire  gauze  cylinder  about  5 in.  in  height 
and  in.  in  diameter,  surmounted  by  a gauze  cap  2 in.  in  depth.  The 
gauze,  which  has  28  wires  to  the  inch,  or  784  apertures  to  the  square  inch,  is 
fastened  to  a brass  standard,  which  secures  it  to  the  oil  cup  or  lamp  below. 
The  gauze  at  the  top  of  the  lamp  is  doubled  by  the  cap,  which  gives  greater 
security  at  this  point,  where  the  flame  tends  to  pass  through  the  gauze  more 
quickly,  and  where  the  gauze  is  more  readily  burned  out.  The  mixture  of 
gas  and  air  enters  the  lamp  in  the  lower  part  of  the  gauze,  and  burns  within 
the  lamp,  the  products  of  combustion  passing  out  through  the  upper  portion 
of  the  gauze  cylinder.  This  lamp  gives  a good  flame  cap,  on  account  of  the 
free  access  of  the  air  below  the  flame,  which  prevents  smoking  and  increases 
the  illuminating  power  of  the  lamp.  As  a lamp  for  general  use,  the  Davy 
lamp,  however,  is  unsafe,  on  account  of  its  liability  to  flame.  In  many 
mining  localities  the  use  of  this  lamp  is  prohibited  by  law,  except  for 
purposes  of  examining  for  gas,  when  it  must  be  used  solely  by  properly 
authorized  fire  bosses.  The  flame  of  the  lamp  is  also  unjDrotected  from  the 
force  of  rapid  air-currents,  and  is  not  safe  when  the  velocity  of  the  current 
exceeds  6 ft.  per  second.  The  illuminating  power  of  the  lamp  is  also  not 
sufficient  for  general  work, 

Clanny  Lamp.— The  unbonneted  Clanny  lamp,  Fig.  4 (6),  is  constructed 
according  to  the  same  principles  as  the  Davy  lamp,  differing  only  in  the 
fact  that  the  lower  part  of  the  wire  gauze  surrounding  the  flame  is  replaced 
by  a strong  glass  cylinder  or  chimney.  The  purpose  of  this  is  to  increase 
the  illuminating  power  of  the  lamp.  The  lamp,  when  clean,  gives  a good 
light,  but  the  entrance  of  the  air  at  a point  above  the  flame,  and  its  descent 


KINDS  OF  LAMPS. 


357 


(dJ 


(e)  (f) 

Fig.  4. 


358 


SAFETY  LAMPS. 


within  the  lamp  to  the  flame,  causes  the  lamp  to  smoke,  due  to  the  conflict 
of  the  ascending  and  descending  air-currents  within  the  lamp.  The  smoke 
becomes  deposited  on  the  glass  chimney,  which  interferes  greatly  with  the 
light.  This  lamp  is  not  a good  one  for  gas  testing,  and  in  fact  cannot  be 
used  for  that  purpose  to  any  advantage.  The  unbonneted  Clanny  is  not 
safe  in  an  air-current  having  a velocity  greater  than  8 ft.  per  second.  The 
bonneted  Clanny  obviates  this  difficulty  to  a large  extent,  but  increases  the 
tendency  of  the  lamp  to  smoke. 

Mueseler  Lamp.— This  lamp.  Fig.  4 (c),  in  all  respects  resembles  the  Clanny 
lamp  just  described,  except  that  the  tendency  in  the  Clanny  lamp  to  smoke 
is  overcome  in  the  Mueseler  by  increasing  the  draft  by  means  of  an  interior 
wrought-iron  chimney  or  tube,  supported  within  the  lamp,  and  reaching 
down  to  within  an  inch  of  the  base  of  the  flame.  The  air  enters  the  lamp 
as  in  the  Clanny,  above  the  flame,  but  is  deflected  downw’ards  by  the  central 
tube,  and  passes  under  the  edge  of  this  tube,  ascending  through  it  to  the  top 
of  the  lamp,  where  it  escapes.  The  Mueseler  lamp  is  a better  lamp  for 
illuminating  purposes  than  the  Clanny,  and  presents  more  security,  when 
bonneted,  against  explosions  within  the  lamp.  This  lamp  will  withstand  a 
current  of  very  much  higher  velocity  than  the  Clanny  lamp,  and  is 
reputed  to  be  safe  in  a current  having  a velocity  of  100  ft.  per  second.  The 
lamp  is  not  a good  lamp  for  the  detection  of  gas.  It  does  not  flame, 
however,  as  quickly  as  the  Clanny  lamp. 

Warsaut  Lamp.— This  lamp.  Fig.  4 (d),  is  built  after  the  Clanny  lamp  in 
every  respect,  but  is  supplied  with  multiple-gauze  chimneys,  one  within  the 
other,  the  effect  of  which  is  to  increase  the  security  against  explosion  of  gas 
within  the  lamp.  The  bonneted  Marsaut  lamp  is  a peculiarly  strong  lamp 
in  this  respect.  The  gauze  used  in  the  caps  of  this  lamp  has  934  apertures  to 
the  square  inch.  This  lamp  is  often  extinguished  in  an  explosive  mixture 
by  the  force  of  the  explosion  within  itself.  It  gives  a good  light  and  is  a good 
lamp  for  general  work;  it  is  not,  however,  a good  lamp  for  testing  for  gas. 

Ashworth-Heppiewhite-Gray  Lamp  —This  lamp.  Fig.  4 (e),  combines  a number 
of  characteristic  features.  It  is  designed  for  general  work,  as  well  as  for 
testing  for  gas.  It  often  happens  that  gas  accumulates  in  a thin  layer  along 
the  roof  of  an  entry  or  working  place,  and  is  not  detected  by  the  use  of  the 
Davy  lamp  or  any  ordinary  lamp.  The  Gray  lamp  is  so  arranged  that  it 
can  be  made  to  draw  its  air  from  the  top  of  the  lamp,  by  means  of  openings 
in  the  top  of  the  four  standards  of  the  lamp,  the  air  passing  down 
through  the  standards,  and  into  the  lamp,  below  the  flame.  When  not 
in  use  for  testing,  openings  can  be  made  in  the  lower  part  of  the  stand- 
ards by  moving  a slide,  and  air  enters  at  these  openings.  The  lamp  is  essen- 
tially a bonneted  Clanny.  The  glass  chimney,  however,  as  well  as  the  gauze 
that  surmounts  it,  is  made  in  a conical  form,  the  purpose  of  this  being  to 
diffuse  the  light  upward  for  examination  of  the  roof  of  the  mine.  The 
conical  form  given  to  the  gauze  also  strengthens  the  lamp  against  explo- 
sions of  gas  within.  This  lamp  is  a very  good  all-around  lamp,  and  possesses 
good  illuminating  power. 

Wolf  Lamp.— The  Wolf  lamp.  Fig.  4 (/),  is  rapidly  growing  in  popularity 
having  been  already  introduced  in  a large  number  of  mines  in  America  and 
England,  and  on  the  Continent.  This  lamp  is  essentially  a Clanny  lamp 
with  a free  admission  of  air.  It  is  compact  and  efficient,  and  has  good 
illuminating  power,  and  is  also  constructed  in  different  forms,  combining, 
as  desired,  any  or  all  of  the  features  of  previous  lamps.  Two  of  its  charac- 
teristic features,  however,  consist  in  a self-lighting  arrangement  accom- 
plished by  means  of  a percussive  device,  which  ignites  a wax  taper  within 
the  lamp,  and  a locking  device,  which  can  be  opened  only  with  a powerful 
magnet.  This  relighting  device  is  an  important  feature  in  any  safety  lamp 
for  general  use,  inasmuch  as  the  most  dangerous  conditions  exist  immedi- 
ately after  an  explosion,  and  the  miners  are  abvays  left  to  grope  their  way 
in  the  dark.  A large  number  of  lives  are  lost,  owing  to  the  confusion  that 
ensues,  the  men  becoming  bewildered  and  losing  their  w^ay,  when  they  are 
shortly  overcome  by  the  afterdamp  of  the  explosion.  This  lamp  permits  of 
immediate  relighting  with  safety  to  the  men. 

LocktRg  Lamps.— The  ordinary  lock  consists  of  a lead  plug,  which,  when 
inserted  in  the  lamp,  will  show  the  least  tampering  on  the  part  of  the 
miner.  Other  locks  consist  of  an  ordinary  turnbolt  operated  by  a peculiar 
key.  Magnetic  locks  allow  of  the  opening  of  the  lamp  only  by  means  of  a 
strong  magnet  kept  in  the  lamp  room. 

Cleaning  Safety  Lamps.— Safety  lamps  should  be  thoroughly  and  regularly 


CARE  OF  SAFETY  LAMPS. 


359 


cleaned  and  filled  between  each  shift.  Each  lamp  should  then  be  lighted 
and  inspected  by  a competent  person  before  being  given  to  the  miner.  A 
careful  inspection  of  the  gauze  of  the  lamp  is  necessary,  as  well  as  of  all  the 
joints  by  which  air  may  enter  the  lamp.  It  should  be  known  to  a certainty 
that  each  lamp  is  securely  locked  before  leaving  the  lamp  room. 

Relighting  Stations.— These  stations  are  located  at  certain  places  in  gaseous 
mines  where  they  can  be  supplied  with  a current  of  fresh  air,  and  where 
there  is  no  danger  from  the  gases  of  the  mine.  The  lamp  is  apt  to  be 
overturned,  or, to  fall,  and  is  often  extinguished  thereby;  and  if  these 
stations  were  not  provided,  the  man  would  have  to  return  with  his  lamp  to 
the  surface  in  order  to  have  it  relighted.  Such  a station  is  always  located  at 
the  entrance  of  the  gaseous  portion  of  a mine,  in  cases  where  the  entire 
mine  does  not  liberate  gas. 

Illuminating  Power  of  Safety  Lamps. — The  following  table  gives  the  illumi- 
nating power  or  candlepower  of  some  of  the  principal  lamps.  The  light  of  a 
sperm  candle  is  taken  as  1,  or  unity. 


Name  of  Lamp. 


Illuminating  Power 
of  Lamp. 


Davy 

Geordy  

Clanny 

Mueseler  

Evan  Thomas....; 

Marsaut,  3 gauzes 

Marsaut,  2 gauzes 

Marsaut,  with  How'at’s  deflector 

Ashworth-Hepplewhite-Gray 

Wolf  


.16 

.10 

.20 

.35 

.45 

.45 

.55 

.65 


.90 


EXPLOSIVE  CONDITIONS  IN  MINES. 

In  the  ventilation  of  gaseous  seams,  the  air-current  may  be  rendered 
explosive  by  the  sudden  occurrence  of  any  one  of  a number  of  circum- 
stances that  cannot  be  anticipated.  Among  these  are  the  following:  (1) 
Derangement  of  the  ventilating  current.  (2)  Sudden  increase  of  gas  due  to 
outburts,  falls  of  roof,  feeders,  fall  of  barometric  pressure,  etc.  (3)  Presence 
of  coal  dust  thrown  into  suspension  in  the  air,  in  the  ordinary  working  of 
the  mine,  or  by  the  force  of  blasting  at  the  working  face,  or  by  a blown-out, 
or  windy,  shot.  (4)  Pressure  due  to  a heavy  blast,  or  any  concussion  of  the 
air  caused  by  closing  of  doors,  etc.  (5)  Rapid  succession  of  shots  in  close 
workings.  (6)  Accidental  discharges  of  an  explosive  in  a dirty  atmosphere. 
Any  or  all  of  these  causes  may  precipitate  an  explosion  at  any  moment. 
Hence,  the  condition  of  the  air-current  should  be  maintained  far  within  the 
explosive  limit.  The  explosive  conditions  vary  considerably  -in  different 
coal  seams.  The  nature  of  the  coal  and  its  enclosing  strata,  its  friability 
and  inflammability,  together  with  the  character  of  its  occluded  gases,  deter- 
mine, to  a large  extent,  the  explosive  conditions  in  the  seam.  Experience 
in  any  particular  seam  or  district  must  always  be  the  best  guide,  and  furnish 
the  best  standard  for  determining  the  explosiveness  of  any  given  lamp 
flame.  For  example,  a 2"  flame  may  be  comparatively  safe  in  a small  mine 
where  the  coal  is  hard  and  not  particularly  flammable,  while  a 1^"  flame 
cap  would  be  considered  unsafe  in  mines  where  the  conditions  are  more 
favorable  to  the  generation  of  gas  and  formation  of  coal  dust.  The  daily 
output  of  the  mine  and  the  general  care  that  is  enforced  upon  the  miners 
at  the  working  face  are  factors  that  should  always  be  considered  and  taken 
into  serious  account  in  determining  explosive  conditions  (see  Testing  for 
Gas  by  Lamp  Flame). 

Derangement  of  Ventilating  Current.— The  flow  of  the  air-current  must  be 
uniform  and  continuous.  Doors  must  be  kept  closed,  since  the  mere  setting 
open  of  a door,  for  a short  period  of  time,  is  sufficient  to  precipitate  a serious 
explosion.  Any  contemplated  change  in  the  current,  by  the  erection  of 
brattices,  air  bridges,  stoppings,  etc.,  should  be  carefully  considered  before 
the  work  is  begun,  and  every  precaution  adopted  to  secure  the  safety  of  the 


360 


VENTILATION  OF  MINES, 


men.  Derangement  of  the  current  may  occur  through  a fall  of  roof  upon 
the  main  airway,  by  which  the  area  of  the  airway  is  reduced,  which  results 
in  the  reduction  of  the  quantity  of  air  passing  in  the  mine.  If  this  fall  is 
not  noticed  at  once,  serious  results  may  happen.  The  utmost  vigilance  is 
therefore  required  on  the  part  of  tire  bosses  and  all  connected  with  mine 
workings.  The  failure  of  the  ventilating  apparatus  is  another  source  that 
gives  rise  to  the  derangement  of  the  current.  As  a rule,  furnaces  are  not 
now  employed  for  the  ventilation  of  gaseous  seams.  There  are,  however, 
some  furnaces  in  use  in  such  seams,  and  these  require  constant  attention 
lest  the  fire  should  burn  low.  Upon  any  accident  occurring  to  the  ventila- 
ting machinery,  notice  should  at  once  be  given  to  the  inside  foreman,  and 
the  men  withdrawn  as  rapidly  as  possible. 

A sudden  increase  of  gas  may  occur  at  any  time  in  a gaseous  seam,  owing 
to  an  outburst,  which  suddenly  yields  a large  volume  of  gas  and  may 
render  the  mine  air  in  that  section  extremely  explosive.  The  men  working 
on  the  return  of  such  a current  must  be  hastily  withdrawn,  and  all  lights 
extinguished.  A heavy  fall  of  coal  in  the  mine  workings  or  in  the  airways, 
or  the  tapping  of  a large  gas  feeder,  produces  the  same  effect  in  a less  degree. 
The  nearer  the  fall  of  roof  takes  place  to  the  face  of  the  workings,  the  more 
liable  it  is  to  be  followed  with  a large  flow  of  gas,  inasmuch  as  the  gas  near 
the  face  has  not  had  time  to  drain  off,  as  in  the  case  of  old  workings.  This 
fact  is  always  true  in  reference  to  new  workings  in  a gaseous  seam.  The  gas 
continues  to  flow  freely  for  a considerable  period,  when  its  flow  gradually 
decreases  until  it  about  ceases.  When  a large  feeder  has  been  tapped,  it 
may  be  plugged  for  a time,  if  necessary,  but  the  better  practice  is  to  allow  it 
to  flow  freely  and  diffuse  into  the  air-current,  which  should  be  sufficiently 
increased  to  dilute  the  quantity  of  gas  given  off  and  to  render  it  inexplosive. 
The  men  upon  the  return  air  should  be  notified.  It  is  dangerous  practice  to 
light  these  feeders. 

When  there  is  a large  area  of  abandoned  workings  in  the  mine,  any 
considerable  fall  of  barometric  pressure  is  usually  followed  by  a large 
outflow  of  gas  from  the  gobs  or  waste  places  of  the  mine.  A fall  of  1 in.  in 
5 hours  represents  a very  rapid  decrease  of  barometric  pressure.  At  all  large 
collieries  there  is,  or  should  be,  a good  standard  barometer  located  upon  the 
surface  near  the  shaft.  In  many  cases,  these  barometers  are  self-recording, 
and  are  often  provided  with  an  automatic  alarm  that  gives  warning  when- 
ever a fall  of  barometric  pressure  occurs.  This  warning  should  at  once  be 
conveyed  to  the  men  in  the  workings,  and  every  precaution  adopted  to 
avoid  evil  results.  The  fact  is  fairly  well  established  that  a fall  of  atmos- 
pheric pressure  is  not  followed  by  an  outflow  of  gas  from  the  mine  workings 
for  the  space  of,  say,  3 hours  after  such  fall  occurs.  This  statement  must’  be 
regarded  with  caution,  however,  as  it  largely  depends  on  the  condition  and 
extent  of  the  abandoned  workings.  Where  these  are  full  of  gas,  its  expan- 
sion affects  the  condition  of  the  airways  much  more  quickly  than  in  cases 
where  these  working  places  are  partly  ventilated. 

Effect  of  Coal  Dust  in  Mine  Workings.— According  to  the  greater  or  less  flam- 
mability of  the  coal,  the  presence  of  fine  dust  in  the  airways  and  workings  of 
the  mine  becomes  a dangerous  factor.  Certain  coals  are  extremely  friable 
and  are  reduced  readily  to  fine  dust,  which  is  thrown  into  suspension  in  the 
air-current  by  the  ordinary  operations  of  the  miners  in  their  work,  as  well 
as  by  the  concussion  of  the  air  from  numerous  causes,  and  by  the  movement 
of  cars  and  the  traveling  of  men  and  animals  upon  the  various  haul- 
ways  and  passageways.  For  a long  time  it  was  questioned  whether  fhe 
presence  of  dust  was  a dangerous  factor,  except  where  there  was  also  a 
small  percentage  of  gas  in  the  air.  Evidence,  however,  has  well  established 
the  fact  that  coal  dust  of  itself  is  a dangerous  element,  and  may  often  be  the 
sole  cause  of  an  explosion,  when  acted  upon  by  a flame  of  sufficient  intensity 
and  magnitude.  The  action  of  the  flame  is  to  distil  carbonic-oxide  gas  CO 
from  the  fine  particles  of  dust  suspended  in  the  air.  The  explosion  of  the 
gas  thus  formed  causes  a further  disturbance  and  raises  a larger  supply  of 
dust,  which  likewise  contributes  to  the  liberation  of  fresh  quantities  of  gas, 
and  thus  an  explosion  is  generated  and  transmitted.  Small  quantities  of 
marsh  gas  greatly  increase  the  violence  of  this  action,  but  explosions  in 
flouring  mills  and  well-ventilated  coal  bins  establish  the  fact  that  such 
occurrences  are  not  dependent  on  the  presence  of  marsh  gas. 

Too  much  fliith  must  not  be  placed  in  the  use  of  water  by  sprinkling  for 
laying  the  dust.  This  has  a beneficial  effect  in  the  immediate  vicinity,  but 
^ large  amount  of  water  is  required  to  render  an  untidy  working  place  safe 


MINE  EXPLOSIONS. 


361 


at  firing  time.  Better  practice  is  to  allow  no  accumulations  of  dust  at  the 
face.  This  should  be  regularly  loaded  out  with  the  coal. 

Pressure  as  Affecting  Explosive  Conditions. — Gaseous  mixtures  that  are  not 
explosive  in  the  ordinary  condition  of  a mine,  often  become  explosive 
under  the  momentary  pressure  to  which  they  are  subjected  by  heav3’' 
blasting,  and,  in  some  instances,  this  may  occur  from  the  concussion 
of  the  air  caused  by  the  quick  shutting  of  a door.  In  the  latter  case,  how- 
ever, the  explosive  condition  of  the  air  would  necessarily  have  to  be  close  to 
the  limit,  in  order  for  such  a slight  occurrence  to  precipitate  an  explosion. 
The  factor  of  pressure  as  increasing  the  explosiveness  of  gaseous  mixtures 
should  be  considered  and  constantly  borne  in  mind. 

Rapid  Succession  of  Shots  in  Close  Workings. — It  constantly  happens  that 
two,  three,  or  more  shots  are  fired  by  means  of  fuse  or  touch  squibs  in  a 
single  chamber  or  heading,  where  the  circulation  of  air  is  not  al  ways  the 
best.  The  practical  effect  is  that  a considerable  quantity  of  carbonic-oxide 
gas  CO  is  produced  by  the  firing  of  the  first  shot,  and  this  gas  does  not  have 
time  to  diffuse  or  become  diluted  by  the  air-current  before  it  is  fired  by  the 
flame  of  the  following  shots.  An  explosion  may  often  be  precipitated  by  such 
an  occurrence,  if  the  workings  are  at  all  dusty.  Two  shots  at  the  most  are  all 
that  should  be  fired  at  one  time  in  a close  chamber  or  heading. 

Mine  Explosions. — The  explosion  of  gas  in  a mine  usually  arises  from  the 
ignition  of  an  explosive  mixture  of  gas  and  air  called  firedamp,  which  has 
accumulated  in  some  unused  chamber  or  cavity  of  the  roof,  or  in  the  waste 
places  of  the  mine,  and  has  been  ignited  by  a naked  light,  by  the  flame  of  a 
shot,  or  by  a mine  fire.  The  initial  force  of  an  explosion  is  generally 
expended  locally,  but  the  flame  continues  to  feed  upon  the  carbonic-oxide 
gas  generated  by.  the  incomplete  combustion  of  the  firedamp  mixture, 
and  distilled  also  from  the  coal  dust  thrown  into  the  air  by  the  agitation. 
Air  is  required  to  burn  this  carbonic-oxide  gas;  this  causes  the  flame  to 
travel  against  the  air-current,  or  in  the  direction  in  which  fresh  air  is  found. 
In  the  other  direction,  or  behind  the  explosion,  the  flame  is  soon  extin- 
guished in  its  own  trail  when  the  initial  force  of  the  explosion  is  expended. 
The  explosion  continues  to  travel  along  the  airways  against  the  current  as 
long  as  there  is  sufficient  gas  or  coal  dust  for  it  to  feed  upon,  or  until  its 
temperature  is  cooled  below  the  point  of  ignition,  by  some  cause  such  as,  for 
example,  the  rapid  expansion  of  the  area  of  the  workings.  We  observe  the 
chief  factor  in  transmitting  an  explosion  is  the  presence  of  carbonic-oxide 
gas,  which  lengthens  the  flame  and  extends  the  effect. 

The  recoil  of  an  explosion  is  the  return  of  the  flame  along  the  path  that  it 
has  just  traversed.  In  the  recoil,  the  flame  burns  more  quietly,  advances 
more  slowly,  and  travels  close  to  the  roof.  The  evidence  found  at  the  point 
where  a recoil  took  place,  or  an  explosion  turned  back,  has  been  sufficient 
to  establish  the  fact  that  the  recoil  is  caused  primarily  by  a cooling  of  the  tem- 
perature, probably  caused  very  largely  by  an  expansion  of  the  area  of  the 
airway.  Soot  is  often  deposited  at  this  point  in  considerable  quantity,  if  the 
action  of  the  flame  is  not  such  as  to  consume  it.  This  fact  alone  shows  the 
combustion  at  this  point  to  have  been  incomplete.  Immediately  in  the  rear 
of  the  flame  is  a mixture  of  carbonic-oxide  gas  CO,  which  bursts  into  flame 
at  the  sudden  stoppage  of  the  advancing  explosion.  This  is  rendered 
possible  by  the  flow  of  cold  air  from  the  adjacent  chambers  and  workings 
along  the  floor  of  the  airway.  The  flame  now  retreats,  burning  the  trail  of 
carbonic-oxide  gas  along  the  roof,  fed  by  the  cold  air  along  the  floor. 

To  Explore  Workings  After  a Serious  Explosion.— The  shafts  or  slopes  and  the 
ventilating  machinery  should  claim  the  first  attention  of  those  on  the 
surface,  and  an  effort  should  be  made  to  reach  the  bottom  as  expeditiously 
as  possible.  Assistance  from  neighboring  collieries,  both  in  the  way  of 
skilled  labor  and  advice,  should  also  be  requested.  Should  the  shaft  or  slope 
need  repairs  before  communication  between  top  and  bottom  is  restored,  the 
person  in  charge  on  the  surface  should,  in  the  meantime,  see  that  props  of 
the  lengths  in  ordinary  use,  brattice  boards,  brattice  cloth,  and  nails  are 
brought  to  a convenient  place  for  putting  on  the  cage  or  car,  and  he  ought 
also  to  collect  all  the  tools  likely  to  be  required,  such  as  axes,  saws,  ham- 
mers, etc.  It  is  also  important  that  rough  tracings  of  the  workings  be 
prepared  for  the  use  of  the  leader  of  each  squad  of  explorers.  Officials  will 
understand  how  useful  these  will  be  to  those  that  are  penetrating  into  work- 
ings about  which  every  man  of  his  squad  may  have  been  heretofore  ignorant. 

When  the  explorers  have  arrived  at  the  bottom  and  are  ready  to  proceed, 
there  should  be  for  each  section,  if  more  than  one  is  operated  upon,  two 


362 


VENTILATION  OF  MINES. 


managers,  each  having  his  own  squad  of  men,  and  his  own  particular  duty 
to  do.  One  may  take  charge  of  restoring  the  ventilation,  the  inspection  of 
the  workings,  and  the  clearing  of  the  roads;  the  other  may  appoint  and 
have  charge  of  the  bottom  man,  the  conveying  of  material,  and  the  detailing 
of  stretcher  companies  where  required.  They  can  consult  and  help  each 
other  in  every  difficulty,  but  system  is  necessary  if  the  work  is  to  be  done  in 
the  shortest  possible  time. 

The  manager  who  has  charge  of  the  men  in  front  should  appoint  two 
experienced  men  with  good  nerves  to  act  as  foremen,  instructing  them  to 
inspect  and  report  to  him  the  condition  of  the  workings  within  a short 
radius.  He  should  then  form  the  rest  of  his  men  into,  say,  three  squads  of 
three  each,  who  will  work  together  at  stoppings  or  falls  until  separated  by 
him,  or  until  the  end  of  the  shift.  Being  near  the  bottom,  it  will  probably 
be  found  that  all  is  clear  for  three  or  four  breast  or  stoop  lengths,  and  stop- 
pings are  required  to  be  put  up.  Material  will  be  required  for  this,  and 
when  the  cage  is  first  sent  to  the  top  for  it,  it  should  not  be  kept  there  to 
enable  the  top  man  to  put  on  a big  load,  but  it  should  be  sent  down  with  all 
despatch,  loaded  with  a half  dozen  each  of  props  and  brattice  boards,  with 
one  piece  of  cloth  and  nails.  This  will  allow  a start  to  be  made,  and  will 
prevent  the  anxious  men  from  worrying  over  what  to  them  is  an  unac- 
countable delay.  Larger  loads  can  be  sent  do^vn  in  subsequent  trips.  For 
convenience  in  carrying,  the  brattice  cloth  may  be  cut  in  lengths  to  suit  the 
gangways  or  headings  with  2 or  3 ft.  to  spare.  Squad  No.  1 should  be 
detailed  to  the  first  stopping.  This  may  be  put  up  with  boards  at  top  and 
bottom  and  cloth  between.  If  the  air-current  is  strong,  a few  of  the  follow- 
ing stoppings  may  be  put  up  by  squads  No.  2 and  No.  3,  with  cloth  only 
stretched  between  two  props.  These  can  be  very  rapidly  put  up  and  will 
drive  the  ventilation  forwards,  thus  allowing  the  firemen  to  extend  rapidly 
the  area  of  inspection.  These  stoppings  can  be  completed  by  No.  1 detail. 
In  a short  time  it  may  become  impossible  to  proceed  in  this  manner.  The 
foul  air  will  in  all  probability  become  more  difficult  to  dislodge,  and  eventu- 
ally one  detail  may  be  able  to  put  up  stoppings  as  quickly  as  the  firedamp  or 
chokedamp  can  be  carried  off.  Part  of  what  may  be  called  the  ventilating 
detail  can  now  be  transferred  to  the  bearer  detail,  the  duties  of  the  latter 
having  become  heavier  as  the  stoppings  advanced.  It  is  not  an  easy  task  to 
carry  props  long  distances  in  a stooping  posture,  and  wTien  to  that  is  added, 
it  may  be,  the  carrying  out  of  the  living  or  dead  bodies,  the  men  begin  to 
fag  very  soon.  But  the  person  in  charge  here  must  see  that  the  forward 
party  is  kept  in  material  for  stoppings  so  that  no  delay  may  occur  on  that 
account.  A system  of  staging  gives  relief  to  the  carrying  parties. 

To  conclude  with  a few  general  remarks:  Let  those  that  have  never  yet 
assisted  to  explore  a mine  after  an  explosion  be  assured  of  this,  that  the 
chief  requisites  in  a leader  are  a capacity  for  hard  work  and  the  ability  to 
organize  his  men  into  a system,  however  roughly,  whereby  work  will  be  best 
forwarded.  It  will  not  speed  the  work  to  say  to  a dozen  or  more  men, 
generally,  do  this  or  that,  neither  is  it  beneficial  to  allow  all  the  workmen 
to  discuss  matters  and  suggest  plans.  Those  in  charge  ought  to  arrange  what 
is  to  be  done.  Anything  else  results  in  noise  and  confusion.  And  let  men 
that  are  sent  from  other  collieries  take  with  them  their  own  tools  and  lamps. 
Those  in  charge  ought  to  take  note  of  the  position,  etc.  of  bodies  found,  and 
of  every  point  which  is  likely  to  throw  light  on  the  cause  or  origin  of  the 
explosion.  This  can  be  more  correctly  done  before  the  roads  are  disturbed 
by  dust  and  travel.  These  notes  might  not  only  be  the  means  of  ascertain- 
ing the  cause  of  explosion,  but  also  of  pointing  out  a way  of  prevention  in 
the  future. 

In  no  case  after  an  explosion  should  the  air-current  of  the  mine  be 
reversed  from  its  usual  course,  except  only  after  careful  consideration, 
because  of  the  reliance  placed  by  the  entombed  workmen  on  their  knowl- 
edge of  the  direction  in  which  the  air  should  be  mo\ung;  and  the  reversal 
of  the  current  may  drive  the  gases  of  the  explosion  upon  them  with  disas- 
trous results.  Conditions  must  be  allowed  to  remain  as  they  exist,  and  the 
rescuers  conform  themselves  to  such  conditions  in  the  best  manner  possible. 


QUANTITY  OF  AIR  REQUIRED  FOR  VENTILATION. 

The  quantity  of  air  required  for  the  adequate  ventilation  of  a mine  can- 
not be  stated  as  a rule  applicable  in  every  case.  Regulations  that  would 
supply  a proper  amount  of  air  for  the  ventilation  of  a thick  seam  would  be 


ELEMENTS  IN  VENTILATION. 


363 


found  to  cause  great  inconvenience  if  applied  without  modification  to  the 
workings  in  a thin  seam.  Likewise,  the  ventilation  of  an  old  mine  with 
extended  workings,  a large  area  of  which  has  been  abandoned,  and  in  many 
cases  not  properly  sealed  off,  will  require,  naturally,  a larger  quantity  of  air 
per  capita  than  a newly  opened  mine  or  shaft.  The  natural  conditions 
existing  in  rise  and  dip  workings,  with  respect  to  the  gases  that  may  be 
liberated  or  generated  in  those  workings,  call  for  the  modification  of  the 
quantity  of  air  required  in  each  case.  For  example,  dip  workings,  where 
much  blackdamp  is  generated,  will  require  a larger  quantity  of  air,  or 
higher  velocity  at  the  working  face,  to  carry  off  such  damps;  and  rise  work- 
ings, liberating  a large  amount  of  marsh  gas,  will  likewise  require  a higher 
velocity  at  the  working  face.  On  the  other  hand,  a reversal  of  these 
conditions,  such  as  a large  quantity  of  marsh  gas  being  liberated  in  dip 
workings,  or  a similar  amount  of  blackdamp  being  generated  in  rise  work- 
ings, will  require  a comparatively  low  velocity  of  the  air  at  each  respective 
working  place. 

Quantity  Required  by  State  Laws.— The  quantity  of  air  required  by  the 
laws  of  the  several  States  is  generally  specified  as  100  cu.  ft.  per  man 
per  minute,  and  in  many  cases  an  additional  amount  of  600  cu.  ft.  per 
animal  per  minute  is  stated.  This  quantity  is  in  no  case  stated  as  the 
actual  amount  of  air  required  for  the  use  of  each  man  or  animal,  but  is  only 
the  result  of  experience,  as  showing  the  quantity  of  air  required  for  the 
proper  ventilation  of  the  average  mine,  based  on  the  number  of  men  and 
animals  employed.  The  number  of  men  employed  in  a mine  is  an  indica- 
tion of  the  extent  of  the  working  face,  while  the  number  of  animals 
employed  is  an  indication  likewise  of  the  extent  of  the  haulage  roads,  or  the 
development  of  the  mine.  These  amounts  refer  particularly  to  non-gaseous 
seams. 

The  Bituminous  Mine  Law  of  Pennsylvania  specifies  that  there  shall  be 
not  less  than  100  cu.  ft.  per  minute  per  person  in  any  mine,  while  150  cu.  ft. 
are  required  in  a mine  where  firedamp  has  been  detected. 

The  Anthracite  Mine  Law  of  Pennsylvania  specifies  a minimum  quantity 
of  200  cu.  ft.  per  minute  per  person.  Each  of  these  laws  contains  modifying 
clauses,  which  specify  that  the  amount  of  air  in  circulation  shall  be  sufficient 
to  “dilute,  render  harmless,  and  sweep  away”  smoke  and  noxious  or 
dangerous  gases. 

Quantity  of  Air  Required  for  Dilution  of  Mine  Gases. — To  determine  this 
requires  a knowledge  of  the  quantity  of  gas  generated  or  liberated  in  the 
workings.  The  quantity  of  air  for  dilution  should  be  ample,  and  should  be 
such  as  not  to  permit  the  condition  of  the  current  to  approach  the  explosive 
point.  The  ventilation  should  be  ample  at  the  face. 

Quantity  of  Air  Required  to  Produce  the  Necessary  Velocity  of  Current  at  the 
Face. — This  consideration  modifies  considerably  the  quantity  of  air  required 
for  the  ventilation  of  thick  and  thin  seams.  The  velocity  of  the  current  is 
dependent  not  only  on  the  quantity  of  air  in  circulation,  but  on  the  area  of  the 
air  passage.  This  area  is  quite  small  in  thin  seams,  and  often  very  large  in 
thick  seams.  As  a result,  the  velocity  is  often  low  at  the  face  of  thick 
seams,  and  insufficient  for  the  proper  ventilation  of  the  face,  although  the 
quantity  of  air  passing  into  such  a mine  may  be  very  large.  A certain 
velocity  of  the  current  is  always  required  in  order  to  sweep  away  the  gases. 
This  velocity  depends  on  the  character  of  the  gases  and  the  position  of  the 
workings.  Heavy  damps  are  hard  to  move  from  dip  workings  where  they 
have  accumulated;  and,  likewise,  lighter  damps  accumulating  at  the  face 
of  steep  pitches  are  hard  to  brush  away,  and  the  velocity  of  the  current  in 
these  cases  must  be  equal  to  the  task  of  driving  out  these  gases. 


ELEMENTS  IN  VENTILATION. 

The  elements  in  any  circulation  of  air  are  (a)  horsepower,  or  power 
applied;  (6)  resistance  of  the  airways,  or  mine  resistance,  which  gives  rise 
to  the  total  pressure  in  the  airway;  (c)  velocity  generated  by  the  power 
applied  against  the  mine  resistance. 

Horsepower  or  Power  of  the  Current.— The  power  applied  is  often  spoken 
of  as  the  power  upon  the  air.  It  is  the  effective  power  of  the  ventilating 
motor,  whatever  this  may  be,  including  all  the  ventilating  agencies, 
whether  natural  or  otherwise.  The  power  upon  the  air  may  be  the  power 
exerted  by  a motive  column  due  to  natural  causes,  or  to  a furnace,  or  may 


364 


VENTILATION  OF  MINES. 


be  the  power  of  a mechanical  motor.  The  power  upon  the  air  is  always 
measured  in  foot-pounds  per  minute,  which  expresses  the  units  of  work 
accomplished  in  the  circulation. 

Mine  Resistance.— The  resistance  offered  by  a mine  to  the  passage  of  an 
air-current,  or  the  mine  resistance,  is  due  to  the  friction  of  the  air  rubbing 
along  the  sides,  top,  and  bottom  of  the  air  passages.  This  friction  causes  the 
total  'ventilating  pressure  in  the  airway,  and  is  equal  to  it.  Calling  the 
resistance  E,  the  unit  of  ventilating  pressure  (pressure  per  square  foot)  p, 
and  the  sectional  area  of  the  airway  a,  we  have,  E = pa;  that  is  to  say,  the 
total  pressure  is  equal  to  the  mine  resistance. 

Velocity  of  the  Air-Current.— Whenever  a given  power  is  applied  against  a 
given  resistance,  a certain  velocity  results.  For  example,  if  the  power  il 
( toot-pounds  per  minute)  is  applied  against  the  resistance  pa,  a,  velocity  v 
(feet  per  minute)  is  the  result;  and  since  the  total  pressure  pa  moves  at 
the  velocity  v,  the  work  performed  each  minute  by  the  power  applied  is  the 
I roduct  of  the  total  pressure  by  the  space  through  which  it  moves  per 
minute,  or  the  velocity.  Thus,  u = {pa)  v. 

Relation  of  Power,  Pressure,  and  Velocity. — The  relation  of  these  elements  of 
'\'entilation  is  not  a simple  relation.  For  example,  a given  power  applied  to 
move  air  through  an  airway  establishes  a certain  resistance  and  velocity  in 
the  airway.  The  resistance  of  the  airway  is  not  an  independent  factor;  that 
is  to  say,  it  does  not  exist  as  a factor  of  the  airway  independent  of  the 
velocity,  but  bears  a certain  relation  to  the  velocity.  Power  always  produces 
resistance  and  velocity,  and  these  two  factors  always  sustain  a fixed  relation. 

This  relation  is  expressed  as  follows:  The  total  pressure  or  resistance  varies 
as  the  square  of  the  velocity;  i.  e.,  if  the  power  is  sufficient  to  double  the 
velocity,  the  pressure  will  be  increased  4 times;  if  the  power  is  sufficient  to 
multiply  the  velocity  3 times,  the  pressure  will  be  increased  9 times.  Thus, 
we  observe  that  a change  of  power  applied  to  any  airway  means  both  a 
change  of  pressure  and  a change  of  velocity. 

Ag,ain,  since  the  power  is  expressed  by  the  equation  u = {p  a)  v,  and  since 
pa,  or  the  total  pressure,  varies  as  v-,  the  work  varies  as  vK  From  this  it 
follows  that,  if  the  velocity  is  multiplied  by  2,  and,  consequently,  the  total 
!>ressure  by  4,  the  work  performed  {pa)  v will  be  multiplied  by  2^  = 8.  We 
til  us  learn  that  the  power  applied  varies  as  the  cube  of  the  velocity. 


MEASUREMENT  OF  VENTILATING  CURRENTS. 

The  measurement  and  calculation  of  any  circulation  in  a mine  airway 
includes  the  measurement  of  (a)  the  velocity  of  the  air-current,  {h)  of  pres- 
sure, (c)  of  temperature,  {d)  calculation  of  pressure,  quantity,  and  horse- 
power of  the  circulation. 

These  measurements  should  be  made  at  a point  in  the  airway  where  the 
airway  has  a uniform  section  for  some  distance,  and  not  far  from  the  foot  of 
the  downcast  shaft  or  the  fan  drift. 

Measurement  of  Velocity.— For  the  purpose  of  mine  inspection,  the  velocity 
of  the  air-current  should  be  measured  at  the  foot  of  the  downcast,  at  the 
mouth  of  each  split  of  the  air-current,  and  at  each  inside  breakthrough,  in 
each  split.  These  measurements  are  necessary  in  order  to  show  that  all  the 
air  designed  for  each  split  passes  around  the  face  of  the  workings. 

The  measurement  of  the  velocity  of  a current  is  best  made  by  means  of 
the  anemometer.  This  instrument  consists  of  a vane  placed  in  a circular 
frame  and  having  its  blades  so  inclined  to  the  direction  of  its  motion  that 
I ft.  of  lineal  velocity  in  the  passing  air-current  will  produce  1 revolution  of 
the  vane.  These  revolutions  are  recorded  by  means  of  several  pointers, 
each  having  a separate  dial  upon  the  face  of  the  instrument,  the  motion 
being  communicated  by  a series  of  gear-wheels  arranged  decimally  to  each 
other.  Most  anemometers  are  provided  with  a large  central  pointer  that 
makes  1 revolution  for  each  100  revolutions  of  the  vane.  The  dial  for  this 
pointer  is  marked  by  100  divisions,  which  record  the  number  of  lineal  feet 
of  velocity.  In  very  accurate  work  with  the  anemometer,  certain  constants 
are  used  as  suggested  by  the  instrument  maker,  but  these  constants  are  of 
little  value  in  ordinary  practice  and  are  of  doubtful  value  even  in  more 
accurate  observations. ' 

The  measurement  of  the  velocity  of  an  air-current  must  necessarily 
represent  only  approximately  the  true  velocity  in  the  airway.  The  air 
travels  with  a greater  velocity  in  the  center  of  the  airway,  and  is  retarded  at 


ME  AS  VREMENT  OF  PRESS  VRE.  365 


the  sides,  top,  and  bottom  by  the  friction  of  these  surfaces.  Hence,  the 
air  to  a large  extent  rolls  upon  these  surfaces,  which  naturally  generates  an 
eddy  at  the  sides  of  airways.  When  measuring  the  air,  the  anemometer 
should  be  held  in  a position  exactly  perpendicular  to  the  direction  of  the 
current,  and  moved  to  occupy  different  positions  in  the  airway,  being 
held  an  equal  time  in  each  position,  or  it  may  be  moved  continuously 
around  the  margin  of  the  airway,  and  through  the  central  portion.  The 
person  taking  the  observation  should  observe  the  caution  of  not  obstruct- 
ing the  area  of.  the  airway  by  his  body,  as  the  area  is  thereby  reduced,  and 
the  velocity  of  the  current  increased.  The  area  of  the  airway  is  accurately 
measured  at  the  point  where  the  observations  are  taken. 

To  obtain  the  quantity  of  air  passing  (cubic  feet  per  minute),  multi pl^^ 
the  area  of  the  airway,  at  the  point  where  the  velocity  is  measured,  by  the 
velocity. 

Example. — The  anemometer  gives  a reading  of  1,320  ft.  in  2 minutes,  the 
height  of  the  airway  is  6 ft.  6 in.,  and  its  average  width  8 ft.  8 in.  What 
volume  of  air  is  passing  in  the  airway  per  minute? 

1 320 

X 8|  X 37,180  cu.  ft.  per  min. 

The  measurement  of  the  ventilating  pressure  is  made  by  means  of  a water 
column  in  the  form  of  a water  gauge. 

Water  Gauge.— The  water  gauge  is  simply  a glass  U tube  open  at  both  ends. 
Water  is  placed  in  the  bent  portion  of  the  tube,  and  stands  at  the  same 
height  in  both  arms  of  the  tube  when  each  end  of  the  tube  is  subjected  to 
the  same  pressure.  If, 
however,  one  end  of  the 
tube  is  subjected  to  a 
greater  pressure  than 
the  other  end,  the  water 
will  be  forced  down  in 
that  arm  of  the  tube, 
and  will  rise  a corre- 
sponding height  in  the 
other  arm,  the  differ- 
ence of  level  in  the  two 
arms  of  the  tube  repre- 
senting the  water  col- 
umn balanced  by  the 
excess  of  pressure  to 
which  the  water  in  the 
first  arm  is  subjected. 

An  adjustable  scale 
graduated  in  inches 
measures  the  height  of 
the  water  column.  The 
zero  of  the  scale  is  ad- 
justed to  the  lower 
Fig.  5.  water  level,  and  the 
upper  water  level  will 
then  give  the  reading  of  the  water  gauge.  One  end  of  the  glass  tube  is 
drawn  to  a narrow  opening  to  exclude  dust,  while  the  other  end  is  bent  to 
a right  angle,  and  passing  back  through  the  standard  to  which  the  tube  is 
attached,  is  cemented  into  the  brass  tube  that  passes  through  a hole  in  the 
partition  or  brattice,  when  the  water  gauge  is  in  use.  The  bend  of  the  tube 
is  contracted  to  reduce  the  tendency  to  oscillation  in  the  height  of  water 
column.  (See  Fig.  5.) 

When  in  use,  the  water  gauge  must  be  in  a perpendicular  position.  It  is 
placed  upon  a brattice  occupying  a position  between  two  airways,  as  shown 
at  A,  Fig.  6.  The  brass  tube  forming  one  end  of  the  water  gauge  is 
inserted  in  a cork,  and  passes  through  a hole  bored  in  the  brattice.  The 
water  gauge  must  not  be  subjected  to  the  direct  force  of  the  air-current,  as 
in  this  case  the  true  pressure  will  not  be  given.  Fig.  6 shows  the  instrument 
as  occupying  a position  in  the  breakthrough,  between  two  entries.  It  will 
be  observed  that  the  water  gauge  records  a difference  of  pressure,  each  end 
the  water  gauge  being  subject  to  atmospheric  pressure,  but  one  end  in 
addition  being  subject  to  the  ventilating  pressure,  which  is  the  difference  of 


Fig.  6. 


366 


VENTILATION  OF  MINES. 


pressure  between  the  two  entries.  The  water  gauge  thus  enables  us  to 
measure  the  resistance  of  the  mine  inhye  from  its  position  between  two 
airways.  If  placed  in  the  first  breakthrough,  at  the  foot  of  the  shaft,  it 
measures  the  entire  resistance  of  the  mine,  but  if  placed  at  the  mouth  of  a 
split,  it  measures  onlj^  the  resistance  of  that  split.  It  never  measures  the 
resistance  outhye  from  its  position  in  the  mine,  but  always  inbye  (see  Calcula- 
tion of  Pressure). 

Measurement  of  Temperature.— It  is  important  to  measure  the  temperature 
of  the  air-current  at  tne  point  where  the  velocity  is  measured,  as  the  tem- 
perature is  an  important  factor  of  the  volume  of  air  passing  (see  Expan- 
sion of  Air  and  Gases,  etc.). 

Thermometers.— Thermometers  measure  changes  in  the  temperature  of  the 
atmosphere  by  the  contraction  and  expansion  of  mercury  or  spirits;  or  they 
may  be  made  entirely  of  metal,  and  the  changes  of  temperature  are  then 
measured  by  the  expansion  and  contraction  of  the  sensitive  metallic 
portion.  These  latter  are  known  as  aneroid  thermometers.  The  Fahren- 
heit thermometer  is  the  one  most  commonly  used  in  America.  By  this 
scale,  the  freezing  point  of  water  at  the  sea  level  is  placed  at  32°  above  zero; 
the  boiling  point  of  water  at  sea  level  is  placed  at  212°  above  zero,  so  that  the 
space  between  these  two  points  is  divided  into  180°. 

Reaumur  and  Centigrade  thermometers  are  used  on  the  continent  of 
Europe.  Of  these  two,  the  first  is  generally  used  in  Germany,  and  the 
second  in  France,  but  the  latter  is  almost  exclusively  used  by  the  scientists 
of  all  nations. 

In  the  Reaumur  thermometer,  the  freezing  and  boiling  points  are  placed 
at  0°  and  80°,  respectively.  In  the  Centigrade,  the  freezing  and  boiling 
points  are  placed  at  0°  and  100°,  respectively. 

To  Convert  Fahrenheit  Into  Centigrade.— (1)  Subtract  32  and  divide  the 
remainder  by  1.8,  or  multiply  by  |. 

If  a Fahrenheit  thermometer  registers  167°,  what  will  be  the  register  by  a 
Centigrade  thermometer  ? 


— g — = 75°  Centigrade.  ^ = 75°  Centigrade. 


To  Convert  Centigrade  Into  Fahrenheit.— (1)  Multiply  by  1.8,  or  |,  and  add  32. 
If  the  Centigrade  thermometer  registers  75°,  what  will  be  the  register  by  a 
Fahrenheit  thermometer? 


75  X 1.8  + 32  = 167°  Fahrenheit. 


— ^ + 32  = 167°  Fahrenheit. 
5 


To  Convert  Fahrenheit  Into  Reaumur.— (1)  Subtract  32,  and  divide  by  2.25, 
or  multiply  by  f. 

If  the  Fahrenheit  thermometer  registers  113°,  what  will  be  the  register  by 
the  Reaumur  thermometer  ? 


^^2  25  Reaumur.  — ^ - = 36°  Reaumur. 

To  Convert  Reaumur  Into  Fahrenheit.— (1)  Multiply  by  2.25,  or  multiply  by  |, 
and  add  32. 

If  the  Reaumur  thermometer  registers  36°,  what  will  be  the  register  by 
the  Fahrenheit  thermometer? 

36  X 2.25  + 32  = 113°  Fahrenheit.  32  = 113°  Fahrenheit. 

4 

To  Convert  Reaumur  Into  Centigrade.— Multiply  by  1.25. 

If  a Reaumur  thermometer  registers  32°,  what  will  be  the  register  by 
a Centigrade  thermometer? 

32  X 1.25  = 40°  Centigrade. 

To  Convert  Centigrade  Into  Reaumur.— Multiply  by  .8. 

If  a Centigrade  thermometer  registers  40°,  what  will  be  the  register  by 
a Reaumur  thermometer? 

40  X .8  = 32°  Reaumur. 

Calculation  of  Mine  Resistance.— The  mine  resistance  is  equal  to  the  total 
pressure  p a that  it  causes.  This  mine  resistance  is  dependent  upon  three 
factors:  (a)  The  resistance  k offered  by  1 sq.  ft.  of  rubbing  surface  to 
a current  having  a velocity  of  1 ft.  per  minute.  The  coefficient  of  friction  k, 
pr  the  unit  of  resistance,  is  the  resistance  offered  by  the  unit  of  rubbing  sur- 
face to  a current  of  a velocity.  This  unit  resistance  has  been  variously 
estimated  by  different  authorities  (see  following  table).  The  value  most 
iiniversally  accepted,  however,  is  that  known  as  the  Atkinson  coefficient 


THE  EQUIVALENT  ORIFICE. 


367 


(.0000000217).  (6)  The  mine  resistance,  which  varies  as  the  square  of  the 
velocity,  (c)  The  rubbing  surface.  Hence,  if  we  multiply  the  unit  resist- 
ance by  the  square  of  the  velocity,  and  by  the  rubbing  surface,  we  will 
obtain  the  total  mine  resistance  as  expressed  by  the  formula  pa  = ksv^. 


Table  of  Various  Coefficients  of  Friction  of  Air  in  Mines. 


Pressure  per 
Sq.  Ft.  Decimals 
of  a Pound. 

J.  J.  Atkinson’s  treatise 0000000217 

A.  Devillez  in  Ventilation  des  Mines: 

Forchies .000000008211 

Crachet-Picquery  000000008928 

Grand  Baisson .'. 000000008611 

Average  of  2,  3,  and  4 000000008585 

Used  in  Ventilation  des  Mines 000000009511 

Arched  Tunnels 000000002113 

Along  a working  face  of  coal 000000014266 

G.  G.  Andre,  Atmosphere  of  Coal  Mines 000000022424 

Peclet,  Cheminee  (Devillez,  p.  112) 000000003697 

D.  K.  Clark .000000002272 


According  to  Goupilliere’s  Cours  d’  Exploitation  des  Mines, 
Vol.  II,  p.  389: 

D’Aubuisson 

Navier 

W.  Fairley 

J.  Stanley  James.. 

D.  Murgue 


.000000001955 

.000000001872 

.00000001 

.00000000929 

.000000008242 


It  will  be  observed  that  J.  J.  Atkinson’s  coeificient  is  greatly  in  excess  of 
any  other,  with  the  exception  of  Andre’s.  Fairley’s  is  derived  from  an 
average  taken  between  Atkinson,  Devillez,  and  Clark,  and,  undoubtedly,  it 
is  an  exceedingly  simple  coefficient  to  work  out  calculations  with,  as  it  will 
save  a great  mass  of  figures.  James,  in  his  work  on  colliery  ventilation, 
reduces  the  coefficient  still  further  on  the  authority  of  the  Belgian  Mine 
Commission,  but  he  gives  a most  unwieldy  figure  to  use. 

Atkinson’s  figure  is  the  one  most  in  use,  and  if  it  is  too  high,  it  errs  on  the 
side  of  safety,  and  it  is  always  advisable  to  have  plenty  of  spare  ventilating 
power  at  a mine.  For  this  reason,  and  until  a regular  and  thorough  investi- 
gation, made  by  a commission  of  competent  men,  provides  a standard  coef- 
ficient, we  prefer  to  abide  by  Atkinson’s  coefficient,  and  it  is  used  in  all  our 
calculations. 

Calculation  of  Power,  or  Units  of  Work  per  Minute.— If  we  multiply  the  total 
pressure  by  the  velocity  (feet  per  minute)  with  which  it  moves,  we  obtain  the 
units  of  work  per  minute,  or  the  power  upon  the  air.  Hence,  u = pav  = 
k s v%  which  is  the  fundamental  expression  for  work  per  minute^  or  power. 

The  Equivalent  Orifice.— This  term,  often  used  in  regard  to  ventilation, 
evaluates  the  mine  resistance,  or,  as  will  be  seen  from  the  equation  given 
below  for  its  value,  it  expresses  the  ratio  that  exists  between  the  quantity 
of  air  passing  in  an  airway  and  the  pressure  or  water  gauge  that  is  produced 
by  the  circulation.  This  term  was  suggested  by  M.  Daniel  Murgue,  and 
refers  to  the  flow  of  a fluid  through  an  orifice  in  a thin  plate,  under  a given 
head.  The  formula  expressing  the  velocity  of  flow  through  such  an  orifice 
is  V = y 2gh\  multiplying  both  members  of  this  equation  by  A,  and  substi- 
tuting for  the  first  member  A v,  its  value  q,  we  have,  after  transposing  and 

correcting  for  vena  contracta,  A = , in  which  .62  is  the  coefficient  for 

.621/2 

the  vena  contracta  of  the  flow.  Reducing  this  to  cubic  feet  per  minute  and 
inches  of  water  gauge  represented  by  t,  we  have,  finally,  the  equation 

A = .0004  X — By  this  formula,  Murgue  has  suggested  assimilating  the 
V i 

flow  of  air  through  a mine  to  the  flow  of  a fluid  through  a thin  plate;  since, 
in  each  case,  the  quantity  and  the  head  or  pressure  vary  in  the  same  ratio. 
Thus,  applying  this  formula  to  a mine,  Murgue  multiplies  the  ratio  of  the 
quantity  of  air  passing  (cubic  feet  per  minute)  and  the  square  root  of  the 
water  gauge  (inches)  by  .0004,  and  obtains  an  area  A,  which  he  calls 
the  equivalent  orifice  of  the  mine. 

Potential  Factor  of  a Mine.  {Proposed  by  J.  T.  Reard.)— Equations  8 and  27, 


368 


VENTILATION  OF  MINES. 


pages  370-371,  give,  respectively,  the  pressure  and  the  power  that  will  circu* 
late  a given  quantity  of  air  per  minute  in  a given  airway.  These  equations 
may  be  written  as  equal  ratios,  expressed  in  factors  of  the  current  and  the 

airway,  respectively;  thus,  ^ and  ^ which  show  that  the  ratio 

between  the  pressure  and  the  square  of  the  quantity  it  circulates  in  any 
given  airway  is  equal  to  the  ratio  between  the  power  and  the  cube  of  the 
quantity  it  circulates.  Solving  each  of  these  equations  with  respect  to  g, 
we  have  the  following: 

With  respect  to  pressure,  

With  respect  to  power, 

Hence,  we  observe  that,  in  any  airway,  /or  a constant  pressure,  the  quan- 
tity of  air  in  circulation  is  proportional  to  the  expression  and, /or  a 

constant  power,  the  quantity  is  proportional  to  the  expression  , which 

y ks 

terms  are  called  the  potentials  of  the  mine  with  respect  to  pressure  and 

power,  respectively;  and  their  values  -4=  and  are  the  potentials  of  the 

\/  p y u 

current  with  respect  to  pressure  and  power,  respectively.  These  factors,  it 
will  be  observed,  evaluate  the  airway,  as  they  determine  the  quantity  of  air 
a given  pressure  or  power  will  circulate  in  that  airway  (cubic  feet  per 
minute).  By  their  use,  the  relative  quantities  of  air  any  given  pressure  or 
power  will  circulate  in  different  airways  are  readily  determined.  The  rule 
may  be  stated  as  follows: 

Rule. — For  any  given  pressure  or  power,  the  quantity  of  air  in  circulation  is 
always  proportional  to  the  potential  for  pressure,  or  the  potential  for  power,  as 
the  case  may  he. 

This  rule  finds  important  application  in  splitting  (see  Calculation  of 
Natural  Splitting).  In  all  cases  where  the  potential  is  used  as  a ratio,  the 
relative  potential  may  be  employed  by  omitting  the  factor  k',  or  it  may  be 
employed  to  obtain  the  pressure  and  power,  in  several  splits  by  multiplying 
the  final  result  by  k (see  Formulas  46,  47,  etc.,  page  378). 

Example. — 20,000  cu.  ft.  of  air  is  passing  in  a mine  in  which  the  airway 
is  6 ft.  X 8 ft.,  and  10,000  ft.  long,  under  a certain  pressure;  it  is  required  to 
find  what  quantity  of  air  this  same  pressure  will  circulate  in  a mine  in  which 
the  airway  is  6 ft.  X 12  ft.,  and  8,000  ft.  long. 

Calculating  the  potential  Xp  with  respect  to  the  pressure  for  each 
of  these  mines,  or  airways,  we  have,  using  the  relative  potential, 

-Xi  = 6 X ^^-^6  + 8)  X 10,000  ""  ^2  = 6 X 2(6  -}- 12)  X 8,000 

= 1.1384.  Since  the  ratio  of  the  quantities  is  equal  to  the  ratio  of  the 
potentials  with  respect  to  pressure,  in  these  two  mines,  we  write  the  propor- 

90  non  V 1 1^84 

tion  20,000  : ga  : : .62845  : 1.1384,  and  gg  = ’ - = 36,229  cu.  ft.  per 

min.  .62840 

Example.—  20,000  cu.  ft.  of  air  is  passing  in  a mine  in  which  the  airway 
is  6 ft.  X 8 ft.,  and  10,000  ft.  long,  under  a certain  power;  it  is  required  to  find 
what  quantity  of  air  will  be  circulated  by  this  same  power  in  a mine  in 
which  the  airway  is  6 ft.  X 12  ft.,  and  8,000  ft.  long. 

We  calculate  the  potential  with  respect  to  power  for  each  of  these 

6x8 

mines,  using,  as  before,  the  relative  potential.  Thus,  Xi  = -■  

6y  12  r 2(6  + 8)  X 10,000 

= .7337,  and  X^  = , . — = 1.0905.  Then,  in  this  case,  since  the 

F 2(6  + 12)  X 8,000 

ratio  of  the  quantities  is  equal  to  the  ratio  of  the  potentials  with 


POTENTIAL  FACTOR. 


369 


respect  to  power,  we  write  the  proportion,  20,000  : 
20,000  X 1.0905 

92  = — ^ = 29,726  cu.  ft.  per  min. 

.7337 


.7337  : 1.0905,  and 


The  following  table  will  serve  to  illustrate  the  use  of  the  formulas 
employed  in  these  calculations.  It  will  be  observed  that  there  are 
several  formulas  for  quantity,  and  for  velocity,  and  for  work  or  horse- 
power, but  in  each  respective  case  the  several  formulas  are  derived  by 
simple  transposition  of  the  terms  of  the  original  formula,  and  are  tabulated 
here  for  convenience.  Choice  must  be  made  in  the  use  of  any  of  these  for- 
mulas, according  to  the  known  terms  in  each  example.  Thus,  an  example 
may  ask:  What  pressure  will  be  produced  in  passing  a given  quantity  of  air 
through  a certain  mine,  the  size  and  length  of  the  airways  being  given  ? 

We  then  use  the  formula  p = — But  if  the  question  asks  what  quan- 


tity of  air  a given  pressure  will  produce  in  this  same  mine,  we  use  the 
formula  q = X It  will  be  observed  that  this  second  formula  is  a 
simple  transposition  of  the  first. 

In  like  manner  the  question  may  be  asked,  what  power  will  produce  a 
certain  quantity  of  air  in  a certain  airway;  and  the  expression  used,  in  this 

case,  is  u = Or,  the  question  may  be  asked,  what  quantity  of  air  will 


be  produced  in  a given  airway  by  means  of  a certain  power^  work  applied 
to  the  airway.  In  this  case,  the  formula  used  is  9 = H the  ques- 

tion asks  for  the  power  required  to  produce  a given  velocity  in  a given  air- 
way, the  formula  employed  is  = ksv^.  All  of  these  formulas  are  derived 

by  combining  the  simple  formulas  p = — q = av,  and  u = qp. 

To  illustrate  the  use  of  the  formulas,  we  take  as  an  example  an  under- 
ground road,  5 ft.  wide  by  4 ft.  high,  and  2,000  ft.  in  length,  and  calculate  the 
value  of  each  symbol  or  letter,  assuming  a velocity  of  500  ft.  per  minute. 


Symbol. 

Value  of  Symbol  for  this 
Particular  Example. 

Area  of  airway  (5  ft.  X 4 ft.) 

a 

20  sq.  ft. 

Horsepower*  

h 

2.959  H.  P. 

Coefficient  of  friction  f -.r 

k 

.0000000217  lb. 

Length  of  airway  

1 

2,000  ft. 

Perimeter  of  airway,  2('5  ft.  + 4 ft.)  

0 

18  ft. 

Pressure  (lb.  per  sq.  ft.)  

P 

9.765  lb. 

Quantity  of  air  (cu.  ft.  per  min.)  

q 

10,000  cu.  ft. 

Area  of  rubbing  surface 

s 

36,000  sq.  ft. 

Units  of  work  per  minute  (power) 

u 

97,650  ft.-lb. 

Velocity  (ft.  per  min.) 

V 

500  ft. 

Water  gauge 

i 

1.87788  in. 

Equivalent  orifice  of  the  mine 

A 

2.919  sq.  ft. 

Potential  for  power  

217.16  units. 

Potential  for  pressure  

3,200  units. 

Weight  of  1 CO.  ft.  of  downcast  air 

vf 

.08098  lb. 

Motive  column  (downcast  air)  

M 

120.5  ft. 

Depth  of  furnace  shaft 

D 

306.77  ft. 

Average  temperature  of  the  upcast  column.. 

T 

350°  F. 

Average  temperature  of  the  downcast  column 

t 

32°  F. 

*A  horsepower  is  equal  to  33,000  units  of  work. 

tThis  coefficient  of  friction  is  an  invariable  quantity,  and  is  the  same  in  every  calculation 
relating  to  the  friction  of  air  in  mines. 

Note.— The  water  gauge  is  calculated  to  five  decimal  places  to  enable  all 
the  other  values  to  be  accurately  arrived  at.  In  practice,  it  is  only  read  to 
one  decimal  place. 


370 


VENTILATION  OF  MINES. 


FORMULAS. 

On  the  right  side  of  each  formula,  the  various  calculations,  based  on  the 
example  given,  are  worked  out  in  figures. 


To  Find: 

No. 

Formula. 

Specimen  Calculation. 

Rubbing  sur- 
face of  an  air- 
way. (Sq.ft.) 

1 

s = lo 

2,000  X 18  = 36,000  sq.  ft. 

Area  of  an 
airway.  (Sq.ft.) 

2 

11 

- = 20  sq.  ft.  of  area. 

Velocity. 
(Ft.  per  min.) 

3 

a 

4 

si  u 

~ 'yjks 

3 / 97,650 

\ .0000000217  X 36,000 

5 

^ = \k- 

\ ks 

1 9.765  X 20 

\ .0000000217  X 36,000 

u 

97,650  _ 

9.765  X 20 

6 

~ pa 

Pressure. 

7 

ksv- 

.0000000217  X 36,000  X 5002  ^ 

(Lh.  per  sq.  ft.) 

20  “ 

8 

ks(fi 

.0000000217  X 36,000  X 10,0002 

203 

= 9.765  lb. 

9 

u 

p = — 

<1 

97,650  _ __  „ 

iPoo  = 

10 

p = Mw 

120.58  X .08098  = 9.765  lb. 

11 

p = 5.2  i 

5.2  X 1.87788  = 9.765  lb. 

12 

11 

13 

Water  gauge. 
(Inches.) 

14 

^ 5.2 

= 1.87788  in. 

Resistance  of 
an  airway. 
(Total  pressure, 
lb.) 

15 

16 

pa  = k sv^ 

n 

pa  = - 
^ V 

.0000000217  X 36,000  X 5002  = 195.3  ib. 

97,650  ^ „ 

FORMULAS. 


371 


To  Find: 

No. 

Formula. 

Specimen  Calculation. 

Quantity. 
(Cu.ft.per  min) 

17 

q = 

a V 

20  X 500  = 10,000  cu.  ft. 

18 

u 

97,650 

Q = 

~ P 

■^7-65 

19 

1 9.765X20 

q = ^ 

\ .0000000217  X 36,000  ^ 

= 10,000  cu.  ft. 

20 

fcx- 

3/  97,050 

\ .0000000217  X 36,000  ^ 

= 10,000  cu.  ft. 

21 

11 

1 

SI 

217.16  X if 97,650  = 10,000  cu.  ft. 

22 

11 

S 

if 3,2002  X 97,650  = 10,000  cu.  ft. 

23 

q = Xpl/  p 

3,200  X 1/ 9.765  = 10,000  cu.  ft. 

Units  of  work 
per  minute,  or 
power  on  the 

24 

u = 

avp 

20  X 500  X 9.765  = 97,650  ft.-lb. 

25 

u = 

qp 

10,000  X 9.765  = 97,650  ft.-lb. 

air. 

(Ft.-lb.permin) 

26 

u = 

ksv^ 

.0000000217  X 36,000  X 500" 

= 97,650  ft.-lb. 

27 

u = 

ks  q^ 

.0000000217  X 36,000  X 10,0003 

203 

= 97,650  ft.-lb. 

28 

u = ^33,000 

2.959  X 33,000  = 97,650  ft.-lb. 

29 

u — 

q^ 

Xu^ 

S = 97.650 

30 

u = 

JL 

= 97.650  ft-lb. 

Xp^ 

3,2002  ’ 

Horsepower. 

31 

h = 

u 

?^-  2 959H  P 

33,000  “ 

Power  poten- 

Xu = 

a 

20 

tial. 

(Units.) 

32 

217.16  units. 

-^ks 

r:6d00000217  X 36,600 

33 

Xu,  = 

3iq^ 

MJ 

-<1  9:765  - 217.16  units. 

34 

X — 

10,000  — ^ ^ jg  units 

fu 

U97,650 

372 


VENTILATION  OF  MINES. 


To  Find: 

No. 

Formula. 

Specimen  Calculation. 

Pressure  poten- 
tial. 
(Units.) 

35 

36 

II 

II 

1 

0000000217  X 36,000 
= 3,200  units. 

- ^ ^ = 3,200  units. 

1/9.765 

Equivalent 

orifice. 

(Sq.  ft.) 

37 

^ _ .0004 Q 

i/r 

y 1.87788 

Motivecolumn, 
downcast  air. 
(Feet.) 

38 

39 

^“^^459  + T 

M = ^ 
w 

- 120.5  ft. 

Motivecolumn, 
upcast  air. 
(Feet.) 

40 

39 

M = ^ 
w 

+ 198.7  ft. 

Variation  of  the  Elements.— In  the  illustration  of  the  foregoing  table,  we 
have  assumed  fixed  conditions  of  motive  column,  as  well  as  fixed  conditions 
in  the  mine  airways.  It  is  often  convenient,  however,  to  know  how  the 
different  elements,  as  velocity  v,  quantity  q,  pressure  p,  power  tt,  etc.,  will 
vary  in  different  circulations;  since  we  may,  by  this  means,  compare  the 
circulations  in  different  airways,  or  the  results  obtained  by  applying  different 
pressures  and  powers  to  the  same  airway.  These  laws  of  variation  must 
always  be  applied  with  great  care.  For  example,  before  we  can  ascertain 
how  the  quantity  in  circulation  will  vary  in  different  airways,  we  must 
know  whether  the  pressure  or  the  power  is  constant  or  the  same  for  each 
airway.  The  following  rules  may  always  be  applied: 


For  a constant  pressure:  v varies  as  Q.  varies  as  (relative  poten- 
tial for  pressure). 

For  a constant  power:  v varies  as-^^;  q varies  as-r^  (relative  potential 
V lo 

for  power). 

For  a constant  velocity:  q varies  as  a;  p varies  as  — ; u varies  as 


For  a constant  quantity:  v varies  inversely  as  a;  p varies  inversely  slS,  XJ 
(potential  for  power);  u varies  inversely  as  (potential  for  power)  or 
directly  as  p. 

For  the  same  airway:  The  following  terms  vary  as  each  other:  v,  q, 
l/p,  -^u. 

Similar  Airways. 


r = length  of  similar  side,  or  similar  dimension.  _ 

For  a constant  pressure:  v varies  as  q varies  as  r^  X rvariesas 

Iv^t  or  Iq^. 


DISTRIBUTION  OF  AIR. 


373 


1 3 \T^ 

For  a constant  power;  wanes  as — — ; q varies  as  r X r varies  as 


3 IT^ 

Yy;  r varies  as 


For  a constant  velocity:  q varies  as  r*;  p varies  as  u varies  as  Ir; 


/-I  w 
r vanes  as  y , or  y 


For  a constant  quantity:  v varies  inversely  as  p and  u vary  inversely  as 


Furnace  Ventilation.  _ 

p (motive  column)  varies  as*"  Z);  q varies  as  i/X). 
Fan  Ventilation. 


It  has  been  customary  in  calculations  pertaining  to  the  yield  of  centrif- 
ugal ventilators  to  assume  as  follows:  q varies  as  n;  p varies  as  n^; 
u varies  as  n^. 

More  recent  investigation,  however,  shows  that  when  we  double  the 
speed  we  do  not  obtain  double  the  quantity  of  air  in  circulation;  or,  in  other 
words,  the  quantity  does  not  vary  exactly  as  the  number  of  revolutions  of 
the  fan.  Investigation  also  points  to  the  fact  that  the  efficiency  of  centrif- 
ugal ventilators  decreases  as  the  speed  increases.  To  what  extent  this  is  the 
case  has  not  been  thoroughly  established.  The  variation  between  the  speed 
of  a fan  and  the  quantity,  pressure,  power,  and  efficiency,  as  calculated  from 
a large  number  of  reliable  fan  tests,  may  be  stated  as  follows: 

For  the  same  fan,  discharging  against  a constant  potential:  q varies  as 
p varies  as  n^-^.  Complement  of  ^ciency  {1  — K)  varies  as 

The  efficiency  here  referred  to  is  the  mechanical  efficiency,  or  the  ratio 
between  the  effective  work  qp  and  the  theoretical  work  of  the  fan. 


DISTRIBUTION  OF  AIR  IN  MINE  VENTILATION. 


When  a mine  is  first  opened,  the  air  is  conducted  in  a single  current 
around  the  face  of  all  the  headings  and  workings,  and  returns  again  to  the 
upcast  shaft,  where  it  is  discharged  into  the  atmosphere.  As  the  develop- 
ment of  the  mine  advances,  however,  it  becomes  necessary  to  divide  the  air 
into  two  or  more  splits  or  currents.  This  division  or  splitting  of  the  air- 
current  is  usually  accomplished  at  the  foot  of  the  downcast,  or  as  soon  as 
possible  after  the  current  enters  the  mine.  There  are  several  reasons  why 
the  air-current  should  be  thus  divided.  The  most  important  reason  is  that 
the  mine  is  thereby  divided  into  separate  districts,  each  of  which  has  its 
own  ventilating  current,  which  may  be  increased  or  decreased  at  will. 
Fresh  air  is  thus  obtained  at  the  face  of  the  workings,  and  the  ventilation  is 
under  more  perfect  control.  It  often  happens  that  certain  portions  of  a mine 
are  more  gaseous  than  others,  and  it  is  necessary  to  increase  the  volume  of 
air  in  these  portions,  which  can  be  readily  accomplished  when  each  district 
has  its  own  separate  circulation.  Again,  the  gases  and  foul  air  are  not 
conducted  from  one  district  to  another,  but  each  district  is  supplied  with 
fresh  air  direct  from  the  main  intake.  Should  an  explosion  occur  in  any 
part  of  the  mine,  it  is  more  apt  to  be  confined  to  one  locality  when  a mine  is 
thus  divided  into  separate  districts.  Another  consideration  is  the  reduced 
power  necessary  to  accomplish  the  same  circulation  in  the  mine;  or  the 
increased  circulation  obtained  by  the  use  of  the  same  power. 

Requirements  of  Law  in  Regard  to  Splitting.— The  Anthracite  Mine  Law  of 
Pennsylvania  specifies  that  every  mine  employing  more  than  75  persons 
must  be  divided  into  two  or  more  ventilating  districts,  thus  limiting  the 
number  that  are  allowed  to  work  on  one  air-current  to  75  persons.  The 
Bituminous  Mine  Law  of  Pennsylvania  limits  the  number  allowed  to  work 
upon  one  current  to  65  persons,  except  in  special  cases,  where  this  number 
may  be  increased  to  100  persons  at  the  discretion  of  the  mine  inspector. 

Practical  Splitting  of  the  Air-Current. — When  the  air-current  is  divided  into 
two  or  more  branches,  it  is  said  to  be  split.  The  current  may  be  divided  one 
gr  more  times;  when  split  or  divided  once,  the  current  is  said  to  be  traveling 


374 


VENTILATION  OF  MINES, 


in  two  splits,  each  branch  being  termed  a split.  The  number  of  splits  in 
which  a current  is  made  to  travel  is  understood  as  the  number  of  separate 
currents  in  the  mine,  and  not  as  the  number  of  divisions  of  the  current. 

Primary  Splits.— When  the  main  air-current  is  divided  into  two  or  more 
splits,  each  of  these  is  called  a primary  split. 

Secondary  Splits.— Secondary  splits  are  the  divisions  of  a primary  split. 

Tertiary  Splits.— Tertiary  splits  result  from  the  division  of  a secondary  split. 

Equal  Splits  of  Air.— When  a mine  is  spoken  of  as  having  two  or  more  equal 
splits,  it  is  understood  to  mean  that  the  length  and  the  size  of  the  separate 
airways  forming  those  splits  are  equal  in  each  case.  It  follows,  of  course, 
from  this  that  the  ventilating  current  traveling  in  each  split  wdll  be  the 
same,  inasmuch  as  they  are  all  subject  to  the  same  ventilating  pressure. 
When  an  equal  circulation  is  obtained  in  two  or  more  splits  by  the  use  of 
regulators,  these  splits  cannot  be  spoken  of  as  equal  splits. 

Unequal  Splits  of  Air.— By  this  is  meant  that  the  airways  forming  the  splits 
are  of  unequal  size  or  length.  Under  this  head  we  will  consider  (a)  Natural 
Division  of  the  Air- Current;  (ft)  Proportionate  Division  of  the  Air- Current. 

Natural  Division  of  the  Air-Current.— By  natural  division  of  air  is  meant  any 
division  of  the  air  that  is  accomplished  without  the  use  of  regulators;  or,  in 
other  words,  such  division  of  the  air-current  as  results  from  natural  means. 
If  the  main  air-current  at  any  given  point  in  a mine  is  free  to  traverse  two 
separate  airways  in  passing  to  the  foot  of  the  upcast  shaft,  and  each  of  these 
airways  is  free  or  an  open  split,  i.  e.,  contains  no  regulator,  the  division  of 
the  air  will  be  a natural  division.  In  such  a case,  the  larger  quantity  of  air 
will  always  traverse  the  shorter  split  of  airway.  In  other  words,  an  air-cur- 
rent  always  seeks  the  shortest  way  out  of  a mine.  A comparatively  small 
current,  however,  will  always  traverse  the  long  split  or  airway. 

Calculation  of  Natural  Splitting. — It  is  always  assumed,  in  the  calculation 
of  the  splitting  of  air-currents,  that  the  pressure  at  the  mouth  of  each  split, 
starting  from  any  given  point,  is  the  same.  Since  this  is  the  case,  in  order 
to  find  the  quantity  of  air  passing  in  each  of  several  splits  starting  from  a 
common  point,  the  rule  given  under  Potential  Factor  of  a Mine  is  applied. 
This  rule  may  be  stated  as  follows: 

The  ratio  between  the  quantity  of  air  passing  in  any  split  and  the  pressure 
potential  of  that  split  is  the  same  for  all  splits  starting  from  a common  point. 
Also,  the  ratio  between  the  entire  quantity  of  air  in  circulation  in  the  several 
splits  and  the  sum  of  the  pressure  potentials  of  those  splits  is  the  same  as  the 
above  ratio,  and  is  equal  to  the  square  root  of  the  pressure. 

Expressed  as  a formula,  indicating  the  sum  of  the  pressure  potentials 


(Xi  -1-  X2  + etc.)  by  the  expression 


Hence,  p ==  7.^^  ^ and  u = 


(2  X^y 


this  rule  is 

2 p 

express  the  pressure 


and  power. 


respectively,  absorbed  by  the  circulation  of  the  splits.  These  are  the  basal 
formulas  for  splitting,  from  which  any  of  the  factors  may  be  calculated  by 
transposition.  They  will  be  found  illustrated  in  the  table  at  the  end  of  this 
section.  We  will  give  here  two  examples  only,  showing  the  calculation  oi 
the  natural  division  of  an  air-current  between  several  splits.  We  have,  from 

Xi 


Example. — In  a certain  mine,  an  air-current  of  60,000  cu.  ft.  per  minute 
is  traveling  in  two  splits  as  follows:  Split  A,  6 ft.  X 8 ft.,  5,000  ft.  long; 
split  B,  5 ft.  X 8 ft.,  10,000  ft.  long.  It  is  required  to  find  the  natural  division 
of  this  air-current. 

Calculating  the  relative  potentials  for  pressure  in  each  split,  we  have 


for  split  A,  Xi 


48 


2(6+8)5,000 
40 


for  split  B,  Xa  40  ^ 8)10, 000 

and  substituting  these  values,  we  have, 

.8888 


= .8888 


= .4961 


and  2 X„  = 1.3849; 


qi  = X 60,000  = 38,506  cu.  ft.  per  min.; 


and 


72  = 


X 60,000 

1.3849 


21,494  cu.  ft.  per  min. 


DISTRIBUTION  OF  AIR. 


375 


Example.— In  a certain  mine,  there  is  an  air-current  of  100,000  cu.  ft.  per 
minute  traveling  in  three  splits  as  follows:  Split  A,  6 ft.  X 10  ft.,  8,000  ft.  long; 
split  B,  6 ft.  X 12  ft.,  15,000  ft.  long;  split  C,  5 ft.  X 10  ft.,  6,000  ft.  long.  Find 
the  natural  division  of  this  current  of  air. 

Calcul  iting  the  respective  relative  potentials  with  respect  to  pressure, 
we  have 

for  split  X,  = 60^2(6 +-loTx  8,000  ^ 
for  split  B,  X,  = + 1^X16,000  = 

for  split  C,  X,  = 50^2(5  ^,oTx '6.000  = 

Adding  these  potentials,  we  have  2 = .9185  4-  .8314  + .8333  = 2.5832. 

Then,  applying  the  foregoing  rule,  we  have 
9185 

qi  = X 100,000  = 35,556  CU.  ft.  per  min.; 

X 100,000  = 32,184  cu.  ft.  per  min.; 

^•OooZ 

QOOO 

and  ^^3  = ~ X 100,000  = 32,260  cu.  ft.  per  min. 

^.UOO^ 


Total,  100,000 

Proportional  Division  of  the  Air-Current.— It  continually  happens  that  differ- 
ent proportions  of  air  are  required  in  the  several  splits  of  a mine  than  would 
he  obtained  by  the  natural  division  of  the  air-current.  It  is  usually  the  case 
that  the  longer  splits  employ  a larger  number  of  men,  and  require  a larger 
quantity  of  air  passing  through  them.  They,  moreover,  liberate  a larger 
quantity  of  mine  gases,  for  which  they  require  a larger  quantity  of  air  than 
is  passing  in  the  smaller  splits.  The  natural  division  of  the  air-current 
would  give  to  these  longer  splits  less  air,  and  to  the  shorter  ones  a larger 
amount  of  air,  which  is  directly  the  reverse  of  what  is  needed.  On  this 
account,  recourse  must  be  had  to  some  means  of  dividing  this  air  pro- 
portionately, as  required.  This  is  accomplished  by  the  use  of  regulators,  of 
which  there  are  two  general  types,  the  box  regulator  and  the  door  regulator. 

Box  Regulator. — This  is  simply  an  obstruction  placed  in  those  airways  that 
would  naturally  take  more  air  than  the  amount  required.  It  consists  of  a 
brattice  or  door  placed  in  the  entry,  and  having  a small  shutter  that  can  be 
opened  to  a greater  or  less  amount.  The  shutter  is  so  arranged  as  to  allow 
the  passage  of  more  or  less  air,  according  to  the  requirements.  The  box 
regulator  is,  as  a rule,  placed  at  the  end  or  near  the  end  of  the  return  air- 
way of  a split.  It  is  usually  placed  at  this  point  as  a matter  of  convenience, 
because,  in  this  position,  it  obstructs  the  roads  to  a less  extent,  the  haulage 
from  the  back  entry  in  this  split  being  carried  over  to  the  main  haulway, 
through  a cross-cut,  before  this  point  is  reached.  The  difficulty,  however, 
can  be  avoided,  in  most  cases,  by  proper  consideration  in  the  planning  of 
the  mine  with  respect  to  haulage  and  ventilation.  The  objection  to  this 
form  of  regulator  is  that,  in  effect,  it  lengthens  the  airway,  or  increases  its 
resistance,  making  the  resistance  of  all  the  airways,  per  foot  of  area,  the 
same.  It  is  readily  observed  that,  by  thus  increasing  the  resistance  of  the 
mine,  the  horsepower  of  the  ventilation  is  largely  increased,  for  the  same 
circulation.  This  is  an  important  point,  as  it  will  be  found  that  the  power 
required  for  ventilation  is  thus  increased  anywhere  from  50fc  to  100^  over 
the  power  required  when  the  other  form  of  regulator  can  be  adopted. 

Door  Regulator.— In  this  form  of  regulator,  which  was  first  introduced  by 
Beard,  the  division  of  the  air  is  made  at  the  mouth  of  the  split.  The  regu- 
lator consists  of  a door  hung  from  a point  of  the  rib  between  two  entries, 
and  swung  into  the  current  so  as  to  cut  the  air  like  a knife.  The  door  is 
provided  with  a set  lock,  so  that  it  may  be  secured  in  any  position,  to  give 
' more  or  less  air  to  the  one  or  the  other  of  the  splits,  as  required.  The  posi- 
tion of  this  regulator  door,  as  well  as  the  position  of  the  shutter  in  the  box 
regulator,  is  always  ascertained  practically  by  trial.  The  door  is  set  so  as 
to  divide  the  area  of  the  airway  proportionate  to  the  work  absorbed  in  the 


376 


VENTILATION  OF  MINES. 


respective  splits.  The  pressure  in  any  split  is  not  increased,  each  split 
retaining  its  natural  pressure. 

Calculation  of  Pressure  for  Box  Regulators.— When  any  required  division  of 
the  air-current  is  to  be  obtained  by  the  use  of  box  regulators,  these  are 
placed  in  all  the  splits,  save  one.  This  split  is  called  the  open,  or  free,  split, 

k S 

and  its  pressure  is  calculated  in  the  usual  way  by  the  formula  p = — 

The  natural  pressure  in  this  open  split  determines  the  pressure  of  the  entire 
mine,  since  all  the  splits  are  subject  to  the  same  pressure  in  this  form  of 
splitting. 

First,  determine  in  which  splits  regulators  will  have  to  be  placed,  in  order 
to  accomplish  the  required  division  of  the  air.  Calculate  the  natural  pres- 
sure, or  pressure  due  to  the  circulation  of  the  air-current,  for  each  split, 

kso^ 

when  passing  its  required  amount  of  air,  using  the  formula  p = — The 

split  showing  the  greatest  natural  pressure  is  taken  as  the  free  split.  In  each 
of  the  other  splits,  box  regulators  must  be  placed,  to  increase  the  pressure 
in  those  splits;  or,  in  other  words,  to  increase  the  resistance  of  those  splits 
per  unit  of  area. 

Example.— The  ventilation  required  in  a certain  mine  is: 

split  A,  6 ft.  X 9 ft.,  8,000  ft.  long;  40,000  cu.  ft.  per  min. 

split  B,  5 ft.  X 8 ft.,  6,000  ft.  long;  40,000  cu.  ft.  per  min. 

split  C,  9 ft.  X 9 ft.,  8,000  ft.  long;  10,000  cu.  ft.  per  min. 

split  D,  6 ft.  X 8 ft.,  10,000  ft.  long;  30,000  cu.  ft.  per  min. 

In  which  of  these  splits  should  regulators  be  placed,  to  accomplish  the 
required  division  of  air,  and  what  will  be  the  mine  pressure  ? 

Calculating  the  pressure  due  to  friction  in  each  split  when  passing  its 
required  amount  of  air,  we  find, 

. , , .0000000217  X 2(6  -f  9)8,000  X 40,0002 

for  split  A,  p = ' '543 " ^ 


for  split  B,p  = 
for  split  C,  p = 
for  split  D,p  = 


.0000000217  X 2(5  + 8)6,000  X 40,0002 
403 

.0000000217  X 2(9  -f  9)8,000  X 10,0002 
813 

.0000000217  X 2(6  + 8)10,000  X 30,0002 
483 


= 84.63  lb.  per  sq.  ft.; 
= 1.176  lb.  per  sq.  ft; 


= 49.45  lb.  per  sq.  ft. 


Split  B has  the  greatest  pressure,  and  is  therefore  the  free  split.  Box 
regulators  are  placed  in  each  of  the  other  splits  to  increase  their  respective 
pressures  to  the  pressure  of  the  free  split  or  the  mine  pressure.  Therefore, 
the  mine  pressure  in  this  circulation  is  84.63  lb.  per  sq.  ft. 

The  Size  of  opening  in  a box  regulator  is  calculated  by  the  formula  for 
determining  the  flow  of  air  through  an  orifice  in  a thin  plate  under  a certain 
head  or  pressure.  The  difference  in  pressure  between  the  two  sides  of  a box 
regulator  is  the  pressure  establishing  the  flow  through  the  opening,  which 
corresponds  to  the  head  h in  the  formula  v = \/  2 gh.  This  regulator  is 
usually  placed  at  the  end  of  a split  or  airway,  and  since  the  regulator 
increases  the  pressure  in  the  lesser  split  so  as  to  make  it  equal  to  the  pressure 
in  the  other  split,  the  pressure  due  to  the  regulator  will  be  equal  to  the 
ventilating  pressure  at  the  mouth  of  the  split,  less  the  natural  pressure  or 
the  pressure  due  to  friction  in  this  split.  Hence,  when  the  position  of  the 
regulator  is  at  the  end  of  the  split,  the  pressure  due  to  friction  in  the  split  is 

k s 0^ 

first  calculated  by  the  formula  p = — and  this  pressure  is  deducted  from 


the  ventilating  pressure  of  the  free  or  open  split,  which  gives  the  pressure 
due  to  the  regulator.  This  is  then  reduced  to  inches  of  water  gauge,  and 

substituted  for  i in  the  formula  A = The  value  of  A thus  obtained  is 

V i 

the  area  (square  feet)  of  the  opening  in  the  regulator. 

Example. — 50,000  cu.  ft.  of  air  is  passing  per  minute  in  a certain  mine, 
in  two  equal  splits,  under  a pressure  equal  to  2 in.  of  water  gauge,  and  it  is 
required  to  reduce  the  quantity  of  air  passing  in  one  of  these  splits,  by  a box 
re^lator  placed  at  the  end  of  the  split,  so  as  to  pass  but  15,000  cu.  ft.  per 


DISTRIBUTION  OF  AIR. 


377 


minute  in  this  split.  Find  the  area  of  the  opening  in  the  regulator,  assu- 
ming that  the  ventilating  power  is  decreased  to  maintain  the  pressure  con- 
stant at  the  mouth  of  the  splits  after  placing  the  regulator.  The  size  and 
length  of  each  split  is  6 ft.  X 10  ft.  and  10,000  ft.  long. 

The  natural  pressure  for  the  split  in  which  the  regulator  is  placed  will  be 
ksq'^  .0000000217  X 2(6  + 10)  X 10,000  X 15,000^ 


(6  X 10)=“ 


= 7.233  lb.  per  sq.  ft. 


7 233 

Then,  = 1-4  in.  of  water  gauge  (nearly),  due  to  friction  of  the  air- 
current  in  this  split.  And,  2 — 1.4  = .6  in.  water  gauge  due  to  regulator. 


Finally,  A = - — j—  = 

V.6 


.0004  g _ .0004  X 15,000 


l/.6 


= 7.746  sq.  ft.,  area  of  opening. 


Size  of  Opening  for  a Door  Reguiator.— The  sectional  area  at  the  regulator  is 
divided  proportionately  to  the  work  to  be  performed  in  the  respective  splits 
according  to  the  proportion  Ai\  A^wui'.  u^.  Or  since  Ai-\-  A^  = a,  we  have 

Ai : a : : Wi : and  Ai  = — ^ — ■ X a.  This  furnishes  a method  of  pro- 

U\  “T  U2 


portionate  splitting  in  which  each  split  is  ventilated  under  its  own  natural 
pressure.  The  same  result  would  be  obtained  by  the  placing  of  the  box 
regulator  at  the  intake  of  any  split,  thereby  regulating  the  amount  of  air 
passing  into  that  split,  but  the  door  regulator  presents  less  resistance  to  the 
flow  of  the  air-current.  The  practical  difference  between  these  two  forms 
of  regulators  is  that  in  the  use  of  the  box  regulator  each  split  is  ventilated 
under  a pressure  equal  to  the  natural  pressure  of  the  open  or  free  split, 
which  very  largely  increases  the  horsepower  required  for  the  ventilation  of 
the  mine;  while  in  the  use  of  the  door  regulator  each  split  is  ventilated 
under  its  own  natural  pressure,  and  the  proportionate  division  of  the  air  is 
accomplished  without  any  increase  of  horsepower.  This  is  more  clearly 
explained  in  the  two  following  paragraphs,  and  the  table  showing  the  com- 
parative horsepowers  of  the  two  methods. 

Calculation  of  Horsepower  for  Box  Regulators.— By  the  use  of  the  box  regu- 
lator, the  pressure  in  all  the  splits  is  made  equal  to  the  greatest  natural 
pressure  in  any  one.  This  split  is  made  the  open  or  free  split,  and  its  natural 
pressure  becomes  the  pressure  for  all  the  splits,  or  the  mine  pressure.  This 
mine  pressure,  multiplied  by  the  total  quantity  of  air  in  circulation  (the  sum 
of  the  quantities  passing  in  the  several  splits),  and  divided  by  33,000,  gives 
the  horsepower  upon  the  air,  or  the  horsepower  of  the  circulation.  Thus, 
in  the  first  example  given  on  page  376,  in  which  for  split  B the  pressure 
p = 84.63  lb.  per  sq.  ft.  and  the  total  quantity  of  air  passing  per  minute 
is  120,000  cu.  ft.,  we  have 


84.63  X 120,000 
33,000  ' 


307.745  H.  P. 


Calculation  of  Horsepower  for  Door  Regulators.— In  the  use  of  the  door 
regulator,  each  split  is  ventilated  under  its  own  natural  pressure,  and, 
hence,  in  the  calculation  of  the  horsepower  of  such  a circulation,  the  power 
of  each  split  must  be  calculated  separately,  and  the  sum  of  these  several 
powers  will  be  the  entire  power  of  the  circulation.  For  the  purpose  of  com- 
parison, we  tabulate  below  the  results  obtained  in  the  application  of  these 
two  methods  of  dividing  the  air  in  the  above  example. 


Splits. 

Natural 

Division. 

Required 

Division. 

Horsepower. 

Door 

Regulator. 

Box 

Regulator. 

Split  A,  6 ft.  X 9 ft.,  8,000  ft.  long 
Split  B,  5 ft.  X 8 ft.,  6,000  ft.  long 
Split  Cy  9 ft.  X 9 ft,,  8,000  ft.  long 
Split  Z>,  6 ft.  X 8 ft.,10,000  ft.  long 

Totals 

28,277 

22,360 

47,423 

21,940 

40,000 

40.000 

10.000 
30,000 

64.145 

102.582 

.356 

44.955 

102.582 

102.582 

25.645 

76.936 

120,000 

120,000 

212.038 

307.745 

378 


VENTILATION  OF  MINES. 


SPLITTING  FORMULAS. 

The  following  table  of  formulas  will  serve  to  illustrate  the  methods  of 
calculation  in  splitting.  The  example  assumes  the  same  airway  as  that  given 
on  page  369  and  used  to  illustrate  the  table  of  formulas,  page  370,  but  the  air- 
current  is  divided,  as  specified  in  the  table: 

Natural  Division. 

Primary  Splits.— Split  (1)  = 4 ft.  X 5 ft.,  800  ft.  long.  Split  (2)  = 4 ft.  X 5 ft., 
1,200  ft.  long. 


To  Find: 

No. 

Formula. 

Specimen  Calculation. 

Potential  for 
pressure. 

35 

(X1  + X2 
+ etc.). 

i 20 

^^\.0000000217X  14,400  ~ 

/'o\  on-t.  / 4 1^1 

^^^.0000000217X21,600  ’ 

5,060  + 4,131  = 9,191. 

Natural  divi- 
sion. 

41 

(1)  X 10,000  = 5,505  cu.  ft. 

(2)  X 10,000  = 4,495  cu.  ft. 

Or  the  natural  division  may  be  calculated  from  the  pressure  at  the  mouth 
of  the  several  splits  by  using  formula  (23);  thus. 


23 

q = Xp}/  p. 

(1)  5,060  i/l.l838  = 5,505  CU.  ft. 

(2)  4,131 1/ 1.1838  = 4,495  CU.  ft. 

See  formula  (42). 

Pressure. 

42 

^ (2Xy)2- 

Power. 

43 

“ (2X„)2- 

S = units- 

Quantity. 

44 

45 

Q = 2 XpV'p- 
Q = f (2Xp)%. 

9,191  p 1.1838  = 10,000  CU.  ft. 

#'9,1912  X 11,838  = 10,000  CU.  ft. 

Increase  of 
quantity  due 
to  splitting. 
(Pressure  con- 
stant.) 

46 

2 X„ 

Q = X Qo- 

Q 1Q1 

^ X 10,000  = 28,722  cu.  ft. 

Increase  in 
quantity  due 
to  splitting. 

( Power  con- 
stant. ) 

47 

Hm' 

10,000  ^(^^y=20,mcn.  ft. 

SPLITTING  FORMULAS. 


379  . 


Secondary  Splits.— (1)  4 ft.  X 5 ft.,  800  ft.  long.  (2)  4 ft.  X 5 ft.,  500  ft.  long. 
(3)  4 ft.  X 5 ft.,  400  ft.  long.  (4)  4 ft.  X 5 ft.,  300  ft.  long. 

The  calculation  is  often  shortened,  when  many  splits  are  concerned,  by 
using  the  relative  potential,  omitting  the  factor  k;  but  the  final  result  must 
then  be  multiplied  by  k to  obtain  the  pressure  or  power;  or,  these  factors 
must  be  divided  by  A:,  when  finding  the  quantity,  as  in  formulas  (49)  to  (51). 


380 


VENTILATION  OF  MINES. 


Proportionate  Division. 

Primary  Splits  (only). — (1)  4 ft.  X 5 ft.,  800  ft.  long  = 3,500  cu.  ft.  (2) 
4 ft.  X 5 ft.,  1,200  ft.  long  = 6,500  cu.  ft. 


To  Find; 

No. 

Formula. 

Specimen  Calculation. 

Pressure  due  to 
friction. 

13 

(2)  = 2.4757  lb. 

To  accomplish  this  division  of  air,  the  pressure  in  split  (1)  mlist  he 
increased  by  means  of  a regulator  to  make  it  equal  to  the  pressure  in  the 
free  or  open  split  (2),  and,  hence,  the  pressure  due  to  the  regulator  is 
equal  to  the  diff’erence  between  the  natural  pressures  in  these  splits. 

Pressure  due  to 
the  regulator 
in  split  (1). 

53 

11 

1 

2.4757  — .47845  = 1.99725  lb. 

Area  of  the 
opening  in 
regulator. 

37 

, .0004  q 

1.99725 
\ 5.2 

Secondary  Splits.— (1)  4 ft.  X5  ft.,  800  ft.  — 3,500  cu.  ft.  (2)  4 ft.  X5  ft., 
500  ft.  — 6,500  cu.  ft.  (3)  4 ft.  X 5 ft.,  400  ft.  — 4,000  cu.  ft.  (4)  4 ft.  X 5 ft., 
300  ft.  — 2,500  cu.  ft. 

Note — When  using  the  relative  jxitential,  multiply  the  result  by  fc,  to 
obtain  the  pressure,  or  the  power. 

Pressure  due  to 
friction.  Free 
split-second- 
ary pressure. 

13 

(.1)  .0000000217(^1^^^=  .47848  lb. 

(2)  .0000000217 1.0314  lb. 

(3)  .0000000217 .31248  lb. 

(4)  .0000000217 .0915461b. 

Since  the  natural  pressure  in  (3)  is  greater  than  that  in  (4),  (3)  is  the  free 
split,  and  its  natural  pressure  is  the  pressure  for  the  secondary  splits.  The 
pressure  for  the  primary  splits  is  then  found  by  first  adding  the  pressures  in 
(2)  and  (3),  and  if  their  sum  is  greater  than  the  natural  pressure  for  (1),  it 
becomes  the  pressure  for  the  primary  splits,  or  the  mine  pressure.  If  the 
natural  pressure  for  (1)  is  the  greater,  this  is  made  the  free  split,  and  its 
natural  pressure  becomes  the  primary  or  mine  pressure.  In  this  case,  the 
secondary  pressure  must  be  increased  by  placing  a regulator  in  split  (3). 


Primary  or 
mine  pressure. 

1 

P2+P3. 

1.0314  + .31248  = 1.34388. 

Pressure  due  to 
the  regula- 
tors. 

P3-P4- 

(P2+P3)-Pl. 

(4)  .31248  — .091546  = .220934  lb. 

(1)  (1.0314  + .31248)  — .47848 

= .86540  lb. 

Areas  of  open- 
ings in  the 
regulators. 

37 

, .0004  q 

Vi  ■ 

m •<>««  X 2,500 
/.220934 

V 5.2 

(1)  = 3.4328  sq.ft. 

.8654 
\ 6.2 

METHODS  AND  APPLIANCES, 


381 


METHODS  AND  APPLIANCES  IN  THE  VENTILATION 
OF  MINES. 

Ascensional  Ventilation.— Every  mine,  as  far  as  practicable,  should  be  venti- 
lated upon  the  plan  known  as  ascensional  ventilation.  This  term  refers 
particularly  to  the  ventilation  of  inclined  seams.  The  air  should  enter  the 
mine  at  its  lowest  point,  as  nearly  as  possible,  and  from  thence  be  conducted 
through  the  mine  to  the  higher  points,  and  there  escape  by  a separate 
shaft,  if  such  an  arrangement  is  practicable.  Where  the  seam  is  dipping 
considerably  and  is  mined  through  a vertical  shaft,  the  upcast  shaft  should 
be  located  as  far  to  the  rise  of  the  downcast  shaft  as  possible.  The  intake  air 
is  then  first  conducted  to  the  lowest  point  of  the  dip  workings,  which  it 
traverses  upon  its  way  to  the  higher  workings.  In  the  case  of  a slope 
working  where  a pair  of  entries  is  driven  to  the  dip,  one  being  used  as  the 
intake  and  the  other  the  return,  there  being  cross-entries  or  levels  driven  at 
regular  intervals  along  the  slope,  the  air  should  be  conducted  at  once  to  the 
inside  workings,  from  which  point  it  returns,  ventilating  each  pair  of  cross- 
entries from  the  inside,  outwards.  Where  the  development  of  the  cross- 
entries or  levels  is  considerable,  their  circulation  is  considered  separately, 
and  a fresh  air  split  is  made  in  the  intake  at  each  pair  of  levels.  In  all 
ventilation,  the  main  point  to  be  observed  is  to  conduct  the  air-current  first 
to  the  inside  workings,  from  whence  it  is  distributed  along  the  working  face 
as  it  returns  toward  the  upcast. 

General  Arrangement  of  Mine  Plan.— Every  mine  should  be  planned  with 
respect  to  three  main  requirements,  viz.:  (a)  haulage;  {h)  drainage;  (c) 
ventilation.  These  requirements  are  so  closely  connected  with  one  another 
that  the  consideration  of  one  of  them  necessitates  a reference  to  all.  The 
mine  should  be  planned  so  that  the  coal  and  the  water  will  gravitate  toward 
the  opening,  as  far  as  possible.  There  are  many  reasons,  in  the  consideration 
of  non-gaseous  mines,  why  the  haulage  should  be  effected  upon  the  return 
airways.  The  haulage  road  is  always  a dusty  road,  caused  by  the  traveling 
of  men  and  mules,  as  well  as  by  the  loss  of  coal  in  transit,  which  becomes 
reduced  to  fine  slack  and  powder.  If  the  haulage  is  accomplished  upon  the 
intake  entry  or  air-course,  this  dust  is  carried  continually  into  the  mine  and 
working  places,  which  should  be  avoided  whenever  possible.  When  the 
loaded  cars  move  in  the  same  direction  as  the  return  air,  the  ventilation  of 
the  mine  is  not  as  seriously  impeded.  It  is  often  the  case  that  fewer  doors  are 
required  upon  the  return  airway  than  upon  the  intake,  which  is  a feature 
favorable  to  haulage  roads.  Again,  in  this  arrangement,  the  hoisting  shaft 
is  made  the  upcast  shaft,  which  prevents  the  formation  of  ice,  and  conse- 
quent delay  in  hoisting  in  the  winter  season.  The  arrangement,  however, 
presupposes  the  use  of  the  force  fan  or  blower,  since  if  a furnace  or  exhaust 
fan  is  employed,  a door,  or  probably  double  doors,  would  have  to  be  placed 
upon  the  main  haulage  road  at  the  shaft  bottom,  which  would  be  a great 
hindrance. 

In  the  ventilation  of  gaseous  mines,  however,  other  and  more  important 
considerations  demand  attention.  The  gaseous  character  of  the  return 
current  prevents  making  the  return  airway  a haulage  way.  In  such  mines, 
the  haulage  should  always  be  accomplished  upon  the  intake  air,  as  any  other 
system  would  often  result  in  serious  consequences.  In  such  gaseous  mine, 
men  and  animals  must  be  kept  off  the  return  airways  as  far  as  this  is 
possible. 

As  far  as  practicable,  ventilation  should  be  accomplished  in  sections 
or  districts,  each  district  having  its  own  split  of  air  from  the  main  intake,  and 
its  own  return  connecting  with  the  main  return  of  the  mine.  Reference 
has  been  made  to  this  under  Distribution  of  the  Air  in  Mine  Ventilation. 
This  splitting  of  the  air-current  is  accomplished  preferably  by  means  of  an 
air  bridge,  either  an  under  crossing  or  an  over  crossing.  There  are,  in 
general,  three  systems  of  ventilation,  with  respect  to  the  ventilating  motor 
employed:  (a)  natural  ventilation;  (b)  furnace  ventilation;  (c)  mechanical 
ventilation. 

Natural  ventilation  means  such  ventilation  as  is  secured  by  natural  means, 
or  without  the  intervention  of  artificial  appliances,  such  as  the  furnace, 
or  any  mechanical  appliances  by  which  the  circulation  of  air  is  maintained. 
In  natural  ventilation,  the  ventilating  motor  or  air  motor  is  an  air  column 
that  exists  in  the  downcast  shaft  by  virtue  of  the  greater  weight  of  the 
downcast  air,  This  air  column  acts  to  force  thC  air  through  the  airways 


382 


VENTILATION  OF  MINES. 


of  the  mine.  An  air  column  always  exists  where  the  intake  and  return 
currents  of  air  pass  through  a certain  vertical  height,  and  have  different 
temperatures.  This  is  the  case  whether  the  opening  is  a shaft  or  a slope; 
since,  in  either  case,  there  is  a vertical  height,  which  in  part  determines 
the  height  of  air  column.  The  other  factor  determining  the  height  of  air 
column  is  the  difference  of  temperature  between  the  intake  and  return. 
The  calculation  of  the  ventilating  pressure  in  natural  ventilation  is  identical 
with  that  of  furnace  ventilation,  which  is  described  later. 

Ventilation  of  Rise  and  Dip  Workings.— We  have  referred  to  the  air  column 
existing  either  in  vertical  shafts  or  slopes  as  the  motive  column  or  venti- 
lating motor.  Such  an  air  column  will  be  readily  seen  to  exist  in  any  rise 
or  dip  workings  within  the  mine,  and  may  assist  or  retard  the  circulation 
of  the  air-current  through  the  mine.  It  is  this  air  column  that  renders  the 
ventilation  of  dip  workings  easy,  and  that  of  rise  workings  correspondingly 
difficult,  depending,  however,  on  the  relative  temperature  of  the  intake  and 
return  currents;  the  latter  usually  is  the  warmer  of  the  two,  which  gives 
rise  to  the  air  column.  The  influence  of  such  air  columns  must  always  be 
taken  into  account  in  the  calculation  of  any  ventilation.  This  is  often 
neglected. 

The  influence  of  air  columns  in  rise  or  dip  workings,  within  the  mine, 
becomes  very  manifest  where,  from  any  reason,  the  main  intake  current  is 
increased  or  decreased.  For  example,  a mine  is  ventilated  in  two  splits,  a 
rise  and  a dip  split;  a current  of  50,000  cu.  ft.  of  air  is  passing  in  the  main 
airway,  30,000  cu.  ft.  passing  into  the  dip  workings,  and  20,000  into  the  rise 
workings.  A fall  of  roof  in  the  main  intake  airway,  or  other  cause,  reduces 
the  main  current  from  50,000  to  35,000  cu.  ft.  Instead,  now,  of  21,000  cu.  ft. 
going  to  the  dip  workings  and  14,000  to  the  rise  workings,  we  find  that  this 
proportion  no  longer  exists,  but  that  the  dip  workings  are  taking  more  than 
their  proportion  of  air,  and  the  rise  workings  Zess.  Thus,  the  circulation 
being  decreased  to  35,000  cu.  ft.,  the  dip  workings  will  probably  take  25,000 
cu.  ft.,  and  the  rise  workings  10,000  cu.  ft.  On  the  other  hand,  had  the 
intake  current  been  increased  instead  of  decreased,  the  rise  workings  would 
then  take  more  than  their  proportion,  while  the  dip  workings  would  take 
less.  The  reason  for  this  distribution  is  evident;  suppose,  for  example,  the 
intake  or  mine  pressure  is  3 in.  of  water  gauge,  and  in  the  dip  workings 
there  is  i in.  of  water  gauge  acting  to  assist  ventilation,  while  a like  water 
gauge  of  i in.  in  the  rise  workings  acts  to  retard  ventilation.  The  effective 
water  gauge  in  the  dip  workings  is  therefore  3^  in.,  while  the  effective 
water  gauge  in  the  rise  workings  is  2i  in.,  or  they  are  to  each  other  as  7 : 6. 
If,  now,  the  mine  pressure  is  decreased  to,  say,  2 in.,  the  effective  rise  and 
dip  pressures  will  be,  respectively,  2\  in.  and  li  in.,  or  as  5 ; 3.  We  observe, 
before  the  decrease,  the  dip  pressure  was  or  1.4,  times  the  rise  pressure, 
while  after  the  decrease  took  place  in  the  mine  pressure,  the  dip  pressure 
became  f,  or  1.66,  times  the  rise  pressure.  The  relative  quantities  passing  in 
the  dip  split  before  and  after  the  decrease  took  place,  as  compared  with  the 

quantities  passing  in  the  rise  split,  will  be  as  the  y 1.4  : ]/l.66,  showing  an 
increase  of- proportion.  Now,  instead  of  a decrease  taking  place  in  the  mine 
pressure,  let  us  suppose  it  is  increased,  say,  from  3 in.  to  4 in.  The  effective 
pressures  in  the  dip  and  rise  workings  will  then  be,  respectively,  4i  in. 
and  3i  in.,  or  they  will  be  to  each  other  as  9:7,  instead  of  7 : 5.  Here  we 
observe  that  the  dip  pressure  is  If,  or  1.15,  times  the  rise  pressure,  instead 
of  1.4.  The  relative  quantities,  therefore,  passing  in  the  dip  split,  before 
and  after  the  increase  of  the  mine  pressure,  as  compared  with  the  quantities 

passing  in  the  rise  split,  will  be  in  the  ratio  of  i/l.4 : \/ 1.15,  showing  a 
decrease  of  proportion.  We  observe  that  any  alteration  of  the  mine  pres- 
sure by  which  it  is  increased  or  decreased  does  not  affect  the  inside  dip  or 
rise  columns,  and  hence  the  disproportion  obtains.  In  case  of  a decrease  of 
the  mine  pressure,  the  dip  workings  receive  more  than  their  proportion 
of  air,  and  in  case  of  an  increase  of  the  mine  pressure,  they  receive  less 
than  their  proportion  of  air. 

Influence  of  Seasons.— In  any  ventilation,  air  columns  are  always  established 
in  slopes  and  shafts,  owing  to  the  relative  temperatures  of  the  outside  and 
inside  air.  The  temperature  of  the  upcast,  or  return  column,  may  always  be 
assumed  to  be  the  same  as  that  of  the  inside  air.  The  temperature  of  the 
downcast,  or  intake  column,  generally  approximates  the  temperature  of  the 
outside  air,  although,  in  deep  shafts  or  long  slopes,  this  temperature  may  be 
changed  considerably  before  the  bottom  of  the  shaft  or  slope  is  reached,  and 


METHODS  AND  APPLIANCES. 


383 


consequently  the  average  temperature  of  the  downcast,  or  intake,  is  often 
different  from  that  of  the  outside  air.  The  difference  of  temperatures  will 
also  vary  with  the  season  of  the  year.  In  winter  the  outside  temperature  is 
below  that  of  the  mine,  and  the  circulation  in  shafts  and  slopes  is  assisted, 
since  the  return  columns  are  warmer  and  lighter  than  the  intake  columns 
for  the  same  circulation.  In  the  summer  season,  however,  the  reverse  of 
this  is  the  case.  The  course  of  the  air-current  will  thus  often  be  changed. 
When  the  outside  temperature  approaches  the  average  temperature  of  the 
mine,  there  will  be  no  ventilation  at  all  in  such  mines,  except  such  as  is 
caused  by  accidental  wind  pressure. 

In  furnace  ventilation  the  temperature  of  the  upcast  column  is  increased 
above  that  of  the  downcast  column  by  means  of  a furnace.  The  chief 
points  to  be  considered  in  furnace  ventilation  are  in  regard  to  the  arrange- 
ment and  size  of  the  furnace.  Furnace  ventilation  should  not  be  applied  to 
gaseous  seams,  and  in  some  cases  is  prohibited  by  law.  It  is,  however,  in 
use  in  many  mines  liberating  gas.  In  such  cases  the  furnace  fire  is  fed  by  a 
current  of  air  taken  directly  from  the  air-course,  sufficient  to  maintain  the 
fire,  and  the  return  current  from  the  mine  is  conducted  by  means  of  a dumb 
drift,  or  an  inclined  passageway,  into  the  shaft,  at  a point  from  50  to  100  ft. 
above  the  seam.  At  this  point,  the  heat  of  the  furnace  gases  is  not  sufficient 
for  the  ignition  of  the  mine  gases.  The  presence  of  carbonic-acid  gas  in  the 
furnace  gases  also  renders  the  mine  gases  inexplosive.  In  other  cases, 
where  the  dumib  drift  is  not  used,  a sufficient  amount  of  fresh  air  is  allowed 
to  pass  into  the  return  current  to  insure  its  dilution  below  the  explosive 
point  before  it  reaches  the  furnace. 

Construction  of  a Mine  Furnace.— In  the  construction  of  a mine  furnace,  a 
sufficient  area  of  passage  must  be  maintained  over  the  fire  and  around  the 
furnace  to  allow  the  passage  of  the  air-current  circulating  in  the  mine.  The 
velocity  of  the  current  at  the  furnace  should  be  estimated  not  to  exceed 
20  ft.  per  second,  and  the  entire  area  of  passage  calculated  from  this  velocity. 
Thus,  for  a current  of  50,000  cu.  ft.  of  air  per  minute,  the  area  of  passage 
through  and  around  the  furnace  should  be  not  less  than 


50,000 

60X20 


41|  sq.  ft. 


This  is  a safe  method  of  calculation,  notwithstanding  the  fact  that  the 
velocity  of  the  air  is  often  much  more  than  20  ft.  per  second,  yet  the  volume 
of  the  air  is  largely  increased  owing  to  the  increase  of  temperature. 

The  length  of  the  furnace  bars  is  limited  to  the  distance  in  which  good 
firing  can  be  accomplished,  and  should  not  exceed  5 ft.  The  width  of  the  grate 
will  therefore  determine  the  grate  area.  The  grate  area  must,  in  every  case, 
be  sufficient  for  the  heating  of  the  air  of  the  current  to  a temperature  such 
as  to  maintain  the  average  temperature  of  the  furnace  shaft  high  enough  to 
produce  the  required  air  column,  or  ventilating  pressure,  in  the  mine. 
The  area  A of  the  grate  of  the  furnace  is  best  determined  by  the  formula 
34 

A = — X H.  P.,  in  which  A = grate  area  in  square  feet;  H.  P.  = horse- 

V D 

power  of  the  circulation;  and  D = depth  of  shaft  in  feet.  The  horsepower 
for  any  proposed  circulation  may  always  be  determined  by  dividing  the 
quantity  of  air  (cubic  feet  per  minute)  by  the  mine  potential  , and  cubing 
and. dividing  the  result  by  33,000;  thus. 


H.  P.  = 


\X^I  ^ 33,000 


The  furnace  should  have  proper  cooling  spaces  above  and  at  each  side; 
upon  one  side,  at  least,  should  be  a passageway  or  manway.  The  furnace 
should  be  located  at  a point  from  10  to  15  yd.  back  from  the  foot  of  the  shaft, 
at  a place  in  the  airway  where  the  roof  is  strong.  This  is  well  secured 
by  railroad  iron  immediatley  . over  the  furnace.  A good  foundation  is 
obtained  in  the  floor,  and  the  walls  of  the  furnace  carried  up  above  the 
level  of  the  grate  bars,  when  the  furnace  arch  is  sprung.  If  possible,  a 
full  semicircle  should  be  used  in  preference  to  a flat  arch.  The  sides  and 
arch  of  the  furnace  should  be  carried  backwards  to  the  shaft;  this  is 
necessary  in  order  to  prevent  ignition  of  the  coal.  The  walls  and  arch 
are  constructed  of  firebrick  a sufficient  distance  from  the  furnace,  and  after- 
wards of  a good  quality  of  hard  brick;  the  shaft  is  also  lined  with  brick 
or  protected  by  sheet  iron  a sufficient  height  to  prevent  the  ignition  of 
the  curbing. 


384 


VENTILATION  OF  MINES, 


Air  Columns  in  Furnace  Ventilation.— As  previously  stated,  natural  ventilation 
and  furnace  ventilation  are  identical,  in  so  far  as  in  each  the  ventilating 
motor  is  an  air  column.  This  air  column  is  an  imaginary  column  of  air 
whose  weight  is  equal  to  the  difference  between  the  weights  of  the  upcast 
and  downcast  columns.  The  upcast  and  downcast  columns  in  furnace 
ventilation  are  sometimes  referred  to  as  the  primary  and  secondary 
columns,  respectively.  The  primary  or  furnace  column  is,  in  nearly  every 
case,  a vertical  column,  and  consists  of  a single  air  column  whose  average 
temperature  is  easily  approximated.  According  to  the  manner  of  opening 
the  mine,  whether  by  shaft,  slope,  or  drift,  the  secondary  column  may  be 
a vertical  column  in  the  shaft,  an  inclined  column  in  the  slope,  or  an  outside 
air  column  in  case  of  a drift  opening.  Again,  it  is  to  be  observed  that  in 
case  of  a slope  opening  where  the  top  of  the  furnace  shaft  is  much  higher 
than  the  mouth  of  the  slope,  and  the  dip  of  the  slope  is  considerable,  the 
secondary  column  consists  of  two  columns  of  different  temperatures,  an 
outside  air  column  and  the  slope  column.  These  two  parts  of  the  secondary 
column  must  be  calculated  separately,  and  their  sum  taken  for  the  weight  of 
the  secondary  column.  The  level  of  the  top  of  the  furnace  shaft  determines 
the  top  of  both  the  primary  and  secondary  columns,  whether  these  columns 
are  in  the  outer  air  or  in  the  mine.  The  weight  of  the  upcast  or  primary 
column  is  largely  affected  by  its  gaseous  condition.  For  example,  if  the 
return  cu^'ent  from  the  mine  is  laden  with  blackdamp  CO2 , its  weight  will 
be  much  increased,  since  this  gas  is  practically  li  times  as  heavy  as  air, 
while,  if  laden  with  marsh  gas,  or  firedamp  mix- 
ture, its  weight  will  be  considerably  reduced. 
These  causes  decrease  and  increase,  respectively, 
the  ventifating  pressure  in  the  mine. 

Inclined  Air  Columns.— In  a slope  opening,  the 
air  column  is  inclined;  it  is  none  the  less,  how- 
ever, an  air  column,  and  must  be  calculated  in 
the  same  manner  as  a vertical  column  whose  ver- 
tical height  corresponds  to  the  amount  of  dip  of 
the  slope.  Fig.  7 shows  a vertical  shaft  and  a 
slope,  the  air  column  in  each  of  these  being  the  same  for  the  same  tem- 
perature. The  air  column  in  all  dips  and  rises  must  be  estimated  in  like 
manner,  by  ascertaining  the  vertical  height  of  the  dip. 

Calculation  of  Ventilating  Pressure  in  Furnace  Ventilation. — The  ventilating 
ressure  in  the  mine  airways,  in  natural  or  in  furnace  ventilation,  is  caused 
y the  difference  of  the  weights  of  the  primary  and  secondary  columns.  Air 
always  moves  from  a point  of  higher  pressure  toward  a point  of  lower 
pressure,  and  this  movement  of  the  air  is  caused  by  the  difference  between 
these  two  pressures.  In  this  calculation  each  column  is  supposed  to  have 
an  area  of  base  of  1 sq.  ft.  Hence,  if  we  multiply  the  weight  of  1 cu.  ft.  of 
air  at  a given  barometric  pressure,  and  having  a temperature  equal  to  the 
average  temperature  of  the  column,  by  the  vertical  height  D of  the  column, 
we  obtain  not  only  the  weight  of  the  column  but  the  pressure  at  its  base  due 
to  its  weight.  Now,  since  the  ventilating  pressure  per  square  foot  in  the 
airway  is  equal  to  the  difference  of  the  weights  of  the  primary  and  secondary 
columns,  we  write 

/ 1.3253  X B 1.3253  X ^ 

^ V 459  + « 459  + T * 

Example. — Find  the  ventilating  pressure  in  a mine  ventilated  by  a 
furnace,  the  temperatures  of  the  upcast  and  downcast  columns  being, 
respectively,  350°  F.  and  40°  F.,  the  depth  of  the  upcast  and  downcast  shafts 
being  each  600  ft.,  and  the  barometer  30  in. 

Substituting  the  given  values  in  the  above  equation,  we  have 

p = 1.3253  X 30  X 600  ( = 18.32  lb.  per  sq.  ft. 

Calculation  of  Motive  Column  or  Air  Column. — It  is  often  convenient  to 
express  the  ventilating  pressure  p (lb.  per  sq.  ft.)  in  terms  of  air  column  or 
motive  column  M,  in  feet.  The  height  of  the  air  column  M is  equal  to  the 

pressure  p divided  by  the  weight  wofl  cu.  ft.  of  air,  or  = £•  The  expres- 
sion for  motive  column  may  be  written  either  in  terms  of  the  upcast  air  or 
of  the  downcast  air,  the  former  giving  a higher  motive  column  than  the 
latter  for  the  same  pressure,  since  the  upcast  air  is  lighter  than  that  of  th^ 


Fig.  7. 


MECHANICAL  VENTILATORS, 


385 


downcast.  As  the  surplus  weight  of  the  downcast  column  of  air  produces 
the  ventilating  pressure,  it  is  preferable  to  write  the  air  column  in  terms  of 
the  downcast  air,  or,  in  other  words,  to  consider  the  air  column  as  being 
located  in  the  downcast  shaft,  and  pressing  the  air  downwards  and  through 
the  airways  of  the  mine.  If  we  divide  the  expression  previously  given  for  the 

/ 1 3253  X \ 

ventilating  pressure  by  the  weight  of  1 cu.  ft.  of  downcast  air  459  _|.^  J » 

(y I \ 

459  + t)  ^ 

which  is  the  expression  for  motive  column  in  terms  of  the  downcast  air. 

If,  on  the  other  hand,  we  divide  the  expression  for  the  ventilating 

/ 1 3253  'X.  E\ 

pressure  by  the  weight  of  1 cu.  ft.  of  upcast  air  ( *459  + 'r~)*  obtain 

(y I \ 

7377 — 7 ) X D.  which  is  the  expression  for  motive  column  in  terms  of 
459  + c / 
the  upcast  air. 

Influence  of  Furnace  Stack.— To  increase  the  height  of  the  primary  or 
furnace  column,  a stack  is  often  erected  over  the  mouth  of  the  furnace  shaft. 
The  effect  of  this  is  to  increase  the  ventilating  pressure  in  the  mine  in 
proportion  to  the  increased  height  of  the  primary  column,  and  to  increase 
the  quantity  of  air  passing  in  the  mine  in  proportion  to  the  square  root  ot 
this  height.  Thus,  the  square  root  of  the  ratio  of  the  heights  of  the  primary 
column,  before  and  after  the  stack  is  erected,  is  equal  to  the  ratio  of  the 
quantities  of  air  passing  before  and  after  the  erection  of  the  stack.  Or, 
calling  these  quantities  qi  and  and  the  height  of  stack  d,  we  have 


MECHANICAL  VENTILATORS, 


A large  number  of  mechanical  ventilators  have  been  invented  and  applied, 
with  more  or  less  success,  to  the  ventilation  of  mines.  The  earliest  type  of 
ventilator  was  the  wind  cowl,  by  which  the  pressure  of  the  wind  at  the  sur- 
face was  brought  to  bear  effectively  upon  the  mine  airways  by  the  action  of 
a cowl  whose  mouth  could  be  turned  toward  the  wind;  this  was  naturally 
very  unreliable.  The  waterfall  was  also  extensively  applied  at  one  time,  but 
its  application  could  only  be  made  where  there  was  a reliable  source  of 
water  supply,  and  where  the  drainage  of  the  mine  could  be  effected  through 
a tunnel,  or  where  the  mine  opening  could  be  placed  in  connection  with 
such  a waterfall  outside  of  the  mine.  Where  these  conditions  are  obtained, 
as  is  the  case  in  some  mountainous  districts,  the  waterfall  is  still  in  use,  as 
it  is  an  effective  means  of  ventilation,  and  is  economical.  Its  application, 
however,  must  be  limited  'to  the  ventilation  of  small  mines.  The  steam  jet 
is  another  mechanical  device  for  producing  an  air-current  in  the  mine.  The 
steam  is  allowed  to  issue  from  a jet  at  the  bottom  of  an  upcast  shaft,  and, 
by  the  force  of  its  discharge,  causes  an  upward  current  in  the  shaft.  Its  use, 
however,  is  very  limited,  and  is  practically  restricted  to  the  ventilation  of 
shafts  while  sinking.  In  this  connection  it  may  be  mentioned,  however, 
that  the  discharged  steam  from  the  mine  pumps,  where  practicable,  may  be 
conducted  into  the  upcast  shaft;  or  the  discharge  pipe  from  the  pumps  may 
be  carried  up  the  upcast  shaft,  its  heat  increasing  the  temperature  of  the 
shaft,  and  thereby  increasing  the  motive  column  and  the  ventilation. 

Fan  Ventilation. — Mechanical  motors  of  this  type  present  two  distinct 
modes  of  action  in  producing  an  air-current:  (a)  by  propulsion  of  the  air; 
and  (6)  by  establishing  a pressure  due  to  the  centrifugal  force  incident  to 
the  revolution  of  the  fan.  Fans  have  been  constructed  to  act  wholly  on 
one  or  the  other  of  these  principles,  while  others  have  been  constructed  to 
act  on  both  of  these  principles  combined. 

Disk  Fans.— The  action  of  this  type  of  fan  resembles  that  of  a windmill, 
except  that  in  the  latter  the  wind  drives  the  mill,  while  in  the  former  the 
fan  propels  the  air  or  produces  the  wind.  This  type  of  fan  consists  of  a 
number  of  vanes  radiating  from  a central  shaft,  and  inclined  to  the  plane  of 
revolution.  The  fan  is  set  up  in  the  passageway  between  the  outer  air  and 
the  mine  airways.  Power  being  applied  to  the  shaft,  the  revolution  of  the 


386 


VENTILATION  OF  MINES, 


vanes  propels  the  air,  and  produces  a current  in  the  airways.  The  fan  may 
force  the  air  through,  or  exhaust  the  air  from,  the  airways,  according  to  the 
direction  of  its  revolution.  This  type  of  fan  is  most  efficient  under  light 
pressures.  It  has  found  an  extensive  application  in  mining  practice,  and 
has  a large  number  of  devotees,  but  has  been  replaced  to  a large  degree 
in  the  ventilation  of  extensive  mines.  This  type  of  fan  acts  wholly  by 
propulsion. 

Centrifugal  fans  include  all  fans  that  act  solely  on  the  centrifugal  principle, 
and  those  that  combine  the  centrifugal  and  propulsion  principles.  The 
action  of  the  fan,  whether  by  centrifugal  force  alone,  or  combined  with 
propulsion,  depends  on  the  form  of  the  fan  blades.  In  this  type  of  fan,  the 
blades  are  all  set  at  right  angles  to  the  plane  of  revolution,  and  not  inclined, 
as  in  the  disk  fan  just  described.  The  blades  may,  however,  be  either  radial 
blades,  sometimes  spoken  of  as  paddle  blades,  or  they  may  be  inclined  to  the 
radius  either  forward  in  the  direction  of  revolution,  or  backward.  When 
the  blades  are  radial,  the  action  of  the  fan  is  centrifugal  only.  The  inclina- 
tion of  the  blades  backward  from  the  direction  of  motion  gives  rise  to  an 
action  of  propulsion,  in  addition  to  the  centrifugal  action  of  the  fan.  The 
blades  in  this  position  may  be  either  straight  blades  in  an  inclined  position, 
as  in  the  original  Guibal  fan,  or  they  may  be  curved  backward  in  the  form 
of  a spiral,  as  in  the  Schiele  and  Waddle  fans. 

Centrifugal  fans  may  be  (a)  exhaust  fans  or  {h)  force  fans  or  blowers.  In 
each,  the  action  of  the  fan  is  essentially  the  same;  i.  e.,  to  credXe  a difference 
of  pressure  between  its  intake  or  central  opening,  and  its  discharge  at  the 
circumference.  The  centrifugal  force  developed  by  the  revolution  of  the  air 
between  the  blades  of  the  fan  causes  the  air  within  the  fan  to  crowd  toward 
the  circumference;  as  a result,  a depression  is  caused  at  the  center  and  a 
compression  at  the  circumference,  giving  rise  to  a difference  of  pressure 
between  the  intake  and  the  discharge  of  the  fan. 

Exhaust  Fans.— If  the  intake  opening  of  the  fan  be  placed  in  connection 
with  the  mine  airways,  and  the  discharge  be  open  to  the  atmosphere,  the 
fan  will  act  to  create  a depression  in  the  fan  drift  leading  to  the  mine,  which 
will  cause  a flow  of  air  through  the  mine  airways  and  into  and  through  the 
fan.  In  this  case,  the  fan  is  exhausting,  its  position  being  ahead  of  the 
current  that  it  produces  in  the  airway.  The  atmospheric  pressure  at 
the  intake  of  the  mine  forces  the  air  or  propels  the  current  toward  the 
depression  in  the  fan  drift  caused  by  the  fan’s  action. 

Force  Fans  and  Blowers.— If  the  discharge  opening  of  the  fan  be  placed  in 
connection  with  the  mine  airways,  a compression  will  result  in  the  fan  drift 
owing  to  the  fan’s  action,  and  the  air  will  flow  from  this  point  of  compres- 
sion through  the  airways  of  the  mine,  and  be  discharged  into  the  upcast, 
and  thence  into  the  atmosphere.  The  ventilating  pressure  in  the  case  of 
either  the  exhaust  fan  or  the  force  fan  is  equal  to  the  difference  of  pressure 
created  by  the  fan’s  action.  In  the  former  case,  when  the  fan  is  exhausting, 
the  absolute  pressure  in  the  fan  drift  is  equal  to  the  atmospheric  pressure 
less  the  ventilating  pressure,  while  in  the  latter  case,  when  a fan  is  forcing, 
the  absolute  pressure  in  the  fan  drift  is  equal  to  the  atmospheric  pressure 
increased  by  the  ventilating  pressure.  This  gives  rise  to  two  distinct  systems 
of  ventilation,  known  as  (a)  vacuum  system  and  (6)  plenum  system. 

Vacuum  System  of  Ventilation.— In  this  system,  the  ventilation  of  the  mine 
is  accomplished  by  creating  a depression  in  the  return  airway  of  the  mine. 
This  depression  may  be  created  by  the  action  of  an  exhaust  fan,  as  just 
described,  or  by  the  action  of  a furnace.  In  either  case,  the  absolute  pres- 
sure in  the  mine  is  below  that  of  the  atmosphere,  or,  we  may  say,  the  mine 
is  ventilated  under  a pressure  below  the  atmospheric  pressure.  This  system 
has  many  points  of  advantage  over  the  plenum  system,  and  for  years  was 
considered  by  many  the  only  practicable  system  of  ventilation.  Its  appli- 
cation, however,  is  controlled  by  conditions  in  the  mine  with  respect  to 
the  gases  liberated,  the  arrangement  of  the  haulage  system,  etc. 

Plenum  System  of  Ventilation.— In  this  system,  the  air-current  is  propelled 
through  the  mine  airways  by  means  of  the  compression  or  ventilating 
pressure  created  at  the  intake  opening  of  the  mine.  This  ventilating  pres- 
sure may  be  established  by  a fan,  waterfall,  wind  cowl,  or  any  other 
mechanical  means  at  hand.  In  this  system,  the  absolute  pressure  in  the  mine 
is  above  that  of  the  atmosphere;  or,  as  we  say,  the  mine  is  ventilated  under 
a pressure  above  the  atmospheric  pressure. 

Comparison  of  Vacuum  and  Plenum  Systems.— No  hard-and-fast  rule  can  be 
made  to  apply  in  every  case,  as  each  system  has  its  particular  advantages. 


TYPES  OF  FANS. 


387 


In  case  of  a sudden  stoppage  of  the  ventilating  motor  at  a mine,  there  is, 
in  the  vacuum  system,  a rise  of  mine  pressure,  instead  of  a fall,  and  the 
gases  are  driven  back  into  the  workings  for  a while,  while,  in  the  plenum 
system,  any  stoppage  of  the  ventilating  motor  is  followed  at  once  by  a fall  of 
pressure  in  the  mine,  and  mine  gases  expand  more  freely  into  the  passage- 
ways at  the  very  moment  when  their  presence  is  most  dangerous.  This 
point  must  be  carefully  considered  in  the  ventilation  of  deep  workings.  In 
shallow  workings,  the  plenum  system  is  often  advantageous,  especially  if 
there  is  a large  area  of  abandoned  workings  that  have  a vent  or  opening  to 
the  atmosphere,  either  through  an  old  shaft  or  through  crevices  extending 
to  the  surface.  Every  crevice  or  other  vent  becomes  a discharge  opening  by 
which  the  mine  gases  find  their  way  to  the  surface,  and  the  gases  accumu- 
lating in  the  old  workings  are  driven  back  into  the  workings,  and  find  their 
way  to  the  surface  instead  of  being  drawn  into  the  mine  airways,  as  would  be 
the  case  in  an  exhaust  system.  Any  given  fall  of  the  barometer  affects  the 
expansion  of  mine  gases  to  a less  extent  in  the  plenum  system  than  in 
the  vacuum  system,  but  this  small  advantage  would  not  give  it  consider- 
ation in  determining  between  the  adoption  of  the  one  or  the  other  of  these 
two  systems;  regard  must  be  had,  however,  to  other  conditions  more  vital 
than  this.  In  the  ventilation  of  gaseous  seams,  owing  to  the  necessity  of 
making  the  intake  airway  the  haulage  road,  the  exhaust  system  has  usually 
been  adopted,  as  the  main  road  is  thereby  left  unobstructed  by  doors. 


TYPES  OF  CENTRIFUGAL  FANS. 

We  shall  only  mention  the  more  prominent  types  of  fans  that  have  been 
or  are  still  in  use,  giving  the 
characteristic  features,  as  nearly 
as  possible,  of  each  fan.  Many 
fans  have  been  built,  however, 
combining  many  of  the  features 
that  originally  characterized  a 
single  type  of  fan. 

Nasmyth  Fan.— Fig.  8 is  the 
original  type  of  fan  representing 
straight  paddle  blades  radiating 
from  the  center,  which  is  its 
characteristic  feature.  This  was 
probably  the  earliest  attempt  to 
apply  the  centrifugal  principle 
to  a mine  ventilator,  and  al- 
though not  recognized  at  the 
time,  the  fan  embodied  some  of  the  most  essential  principles  in  centrifugal 
ventilation.  > It  possessed  certain  disadvantages,  however,  chief  of  which  was 
a contracted  central  or  intake  opening.  The  blades,  also,  were  straight 
throughout  their  entire  length,  being  normal 
both  to  the  inner  and  outer  circles  of  the  fan, 
and  thus  did  not  provide  for  receiving  the  air 
without  shock  at  the  throat  of  the  fan.  The 
depth  of  Nasmyth’s  blades  equaled  one-half  the 
radius  of  the  fan,  which  was,  under  ordinary 
conditions  of  mine  practice,  far  too  great,  and 
gave  the  fan  a low  efficiency. 

Biram’s  Ventilator.  — About  1850,  Biram  at- 
tempted to  improve  upon  the  Nasmyth  ventilator 
by  reducing  the  depth  of  blade  so  that  it  was 
but  one-tenth  of  the  radius.  The  blades  were 
straight,  as  in  Nasmyth’s  ventilator,  but  inclined 
backwards  from  the  direction  of  motion  at  a 
considerable  angle.  A large  number  of  these 
blades  were  employed.  This  fan  was  run  at  a 
considerable  speed,  but  proved  very  inefficient.  It  depended  more  on  the 
effort  of  propulsion  given  to  the  air  than  on  the  centrifugal  principle,  as 
the  depth  of  the  blade  was  as  much  too  small  as  that  of  Nasmyth’s  was  too 
great.  The  intake  or  central  opening  in  this  fan  was  as  contracted  as  in 
the  former  type.  See  Fig.  9. 

Waddle  Ventilator.— In  this  fan.  Fig.  10,  the  inventor  attempted  to  reenforce 
the  discharge  pressure  at  the  circumference  against  the  pressure  of  the 


Fig.  9. 


388 


VENTILATION  OF  MINES. 


atmosphere.  The  discharge  took  place  all  around  the  entire  circumference 
of  the  fan,  which  was  entirely  opened  to  the  atmosphere.  The  blades  were 
curved  backward  from  the  direction  of  motion  in  spiral  form.  The  width 
of  the  blade  decreased  from  the  throat  toward  the  circumference,  so  as  to 
present  an  inverse  ratio  to  the  length  of  radius.  Thus,  the  area  of  passage 

between  the  fan  blades  was 
maintained  constant  from 
the  throat  to  the  circumfer- 
ence of  the  fan.  The  pur- 
pose of  this  was  to  maintain 
the  velocity  of  the  air 
through  the  fan  constant, 
and  to  fortify  the  pressure 
due  to  the  fan  against  the 
atmospheric  pressure  at  the 
point  of  discharge.  The  es- 
sential features  of  the  Wad- 
dle ventilator  were,  there- 
fore, curved  blades  tapered 
toward  the  circumference, 
and  a free  discharge  into 
the  atmosphere  all  around 
the  circumference.  This 
type  is  the  best  type  of  the 
open-running  fan  having  no  peripheral  casing,  and  discharging  air  into 
the  atmosphere  all  around  the  circumference. 

Schiele  Ventilator.— This  ventilator.  Fig.  11,  was  constructed  on  the  same 
principles  as  the  Waddle  ventilator  just  described,  but  differed  from  the 
latter,  as  the  discharge  was  made  into  a spiral  chamber  surrounding  the 
fan  and  leading  to  an  expanding  or  6vase  chimney.  There  was  some  advan- 
tage in  this  feature,  as  it  protected  the  fan  against  the  direct  influence  of 
the  atmosphere,  and  reduced  the  velocity  of  discharge;  but,  in  each  of 
these  fans,  the  intake  opening  was  contracted,  and  the  depth  of  blade  was 
very  great,  yielding  a comparatively  low  efficiency. 

Guibal  Ventilator.— The  next  important  step  in  the  improvement  of  centrif- 
ugal ventilators  was  introduced  by  M.  Guibal,  who  constructed  a fan. 
Fig.  12,  embodying  the*features  of  the  Nasmyth  ventilator,  with  the  addition 
of  a casing  built  over  the  fan  to  protect  its  circumference.  This  casing  was, 
however,  a tight-fitting  casing,  and  as  such,  differed  very  materially  from  the 
Schiele  casing.  In  the  Guibal  fan  the  blades  were  arranged  upon  a series  of 
parallel  bars  passing  upon  each  side  of  the  center  and  at  some  distance  from 
it.  By  this  construction,  the  blades  were  not  radial  at  their  inner  edge  or 
the  throat  of  the  fan.  They  were  curved,  however,  as  they  approached  the 
circumference  of  the  fan,  so  as  to  be  normal  or  radial  at  the  circumference. 


Fig.  11.  Fig.  12. 

The  advantage  of  this  construction  was  to  give  a strong  skeleton  or  frame- 
work to  the  revolving  parts,  and,  further,  each  blade  was  inclined  to  the 
radius  at  its  inner  extremity,  the  effect  of  which  was  to  receive  the  air  upon 
the  blade  with  less  shock  than  was  the  case  in  the  Nasmyth  ventilator.  The 
intake  or  central  opening,  however,  was  very  contracted,  and  the  tight-fitting 


EFFICIENCY  OF  FANS. 


389 


casing  about  the  circumference  prevented  the  effective  action  of  the  fan 
during  a considerable  portion  of  its  revolution.  The  fan  was  supplied 
with  an  6vase  chimney,  which  was  a feature  of  the  Schiele  fan,  but 
vibration  was  so  strong  that  a shutter  was  required  at  the  cut-off  below 


the  chimney,  to  prevent  it.  This  shutter  was  made  adjustable,  and  is  known 
as  the  Walker  shutter,  having  been  applied  to  the  fan  later. 

The  Guibal  ventilator  presents  some  important  and  valuable  features 
in  the  protecting  cover,  and  in  the  blades  meeting  the  outer  circumference 
radiallj^,  and  in  the  air  being  received  with  less  shock  than  before.  On  the 
whole,  it  has  proved  a very  efficient  ventilator,  although  much  work  is  lost 
by  reason  of  its  contracted  central  orifice  and  tight  casing,  where  the  same 
is  used. 

» Ventilator. — Fig.  13  consists  of  twin  fans  supported  on  the  same 
set  a few  feet  apart.  Each  fan  receives  its  air  on  one  side  only, 
the  openings  being  turned  toward  each  other.  This  ventilator  is  built  with 
a small  diameter,  and  is  run  at  a high  speed.  The  blades  are  curved  back- 
wards from  the  direction  of  motion.  The  intake  opening  is  considerably 
enlarged;  a spiral  casing  generally  surrounds  the  fan,  and  in  every  respect 
this  fan  makes  an  efficient  high-speed  motor.  It  has  received  considerable 
favor  in  the  United  States,  where  it  has  been  introduced  into  a large  number 
of  mines. 

Capell  Ventilator.— Perhaps  none  of  the  centrifugal  ventilators  have  been 
as  little  understood  in  regard  to  their  principle  of  action  as  the  Capell  fan. 
The  fan  is  constructed  along  the  lines  of  the  Schiele  ventilator,  but  differs 
from  that  ventilator  in  the  manner  of  receiving  its  intake  air  and  delivering 
the  same  into  the  main  body  of  the  fan.  Here,  and  revolving  with  it,  is  a set 
of  smaller  supernumerary  blades.  These  blades  occupy  a cylindrical  space 
within  the  main  body  of  the  fan,  and  are  inclined  to  the  plane  of  revolu- 
tion so  as  to  assist  in  deflecting  the  entering  air  through  small  ports  or 
openings  into  the  main  body  of  the  fan,  where  it  is  revolved  and  discharged 
at  the  circumference  into  a spiral  space  resembling  that  surrounding  the 
Schiele  fan.  The  larger  blades  of  this 
fan  are  curved  backwards  as  the  Schiele 
blades,  but  are  not  tapered  toward  the 
circumference.  The  fan  is  capable  of  giv- 
ing a high  water  gauge,  and  i§  efficient 
as  a mine  ventilator.  The  space  surround- 
ing the  fan  is  extended  to  form  an  ex- 
panding chimney.  The  fan  may  be  used 
either  as  an  exhaust  fan  or  a blower. 
The  best  results  in  the  United  States  have 
been  obtained  by  blowers.  In  Germany, 
where  this  fan  is  in  general  use,  there  are 
no  blowers. 

The  position  of  the  fan,  whether  used  as 
an  exhaust  or  blower,  should  be  suffi- 
ciently removed  from  the  fan  shaft  to 
avoid  damage  to  the  fan  in  case  of  ex- 
plosion in  the  mine.  Even  in  non-gaseous 
mines,  the  fan  should  be  located  a short  distance  back  from  the  shaft 
mouth,  to  avoid  damage  due  to  settlement.  Connection  should  be  made 
with  the  fan  shaft  by  means  of  an  ample  drift,  which  should  be  deflected 
into  the  shaft  so  as  to  produce  as  little  shock  to  the  current  as  possible.  In 


390 


VENTILATION  OF  MINES. 


case  of  gaseous  seams,  explosion  doors  should  be  provided  at  the  shaft 
mouth.  The  ventilator  at  every  large  mine  should  be  arranged  so  that  it 
may  be  converted  from  an  exhaust  to  a blow-down  fan  at  short  notice. 
This  is  managed  by  housing  the  central  orifices  or  intake  of  the  fan  in 
such  a manner  as  to  connect  them  directly  with  the  fan  drift.  A large  door 
abj  Fig.  15,  is  arranged  at  the  foot  of  the  expanding  chimney,  the  latter 

being  placed  between  the  fan 
and  the  shaft.  This  door, 
when  the  fan  is  exhausting, 
is  in  the  lower  position  ab, 
and  then  forms  a portion,  of 
the  spiral  casing  leading  to 
the  chimney.  When  the  fan 
is  blowing,  however,  the  door 
is  swung  upwards  so  as  to  oc- 
cupy the  position  ac,  being 
tangent  to  the  cut-off  at  c, 
thereby  closing  the  discharge 
into  the  chimney  and  causing 
it  to  enter  the  fan  drift  behind 
the  door.  At  the  same  time, 
the  positions  of  the  two  doors, 
ed  and/d,  in  the  fan  drift,  are 
changed  to  e ^ and  fs,  respec- 
tively, to  open  the  fan  drift 
to  the  discharge  from  the  fan, 
and  to  close  the  openings  lead- 
ing from  the  fan  drift  to  the 
housing  upon  each  side  of  the 
fan,  while  another  set  of  doors 
A A upon  each  side  of  the  fan, 
in  the  housing,  which  were 
previously  closed  tightly,  are 
now  set  wide  open  to  admit 
the  outside  air  to  the  intake  openings  of  the  fan.  The  fan  is  thus  made  to . 
draw  its  air  from  the  atmosphere,  and  discharge  it  into  the  fan  drift,  instead  of 
drawing  its  air  from  the  fan  drift  and  discharging  into  the  chimney,  as  before. 

The  manometrical  efficiency  of  a fan  is  the  ratio  between  its  effective  and 
theoretical  'pressures.  It  has  been  assumed  that  the  theoretical  pressure  due 

7^2  N/  2 2 X 12 

to  the  fan’s  action  is  given  by  the  equation  h = ox  i — 

g gx  1,000  ’ 

u being,  as  before,  the  tangential  speed  (feet  per  second),  and  g the  force  of 
gravity  (32.16);  h = head  of  air  column  in  feet;  i = water  gauge  in  inches. 

The  term  mechanical  efficiency,  as  applied  to  the  ventilator,  is  the  ratio 
between  its  effective  and  theoretical  powers.  In  estimating  the  efficiency  of 
a ventilator,  it  is  customary,  though  incorrect,  to  estimate  the  theoretical 
power  of  the  fan  from  an  engine  card  taken  from  the  steam  cylinder  of  the 
fan  engine.  The  efficiency  of  the  steam  engine  is  thus  confused  with  the 
efficiency  of  the  ventilator.  Mr.  Beard  gives  the  following  formula  for 

jnS 1 - 

the  theoretical  work  of  the  fan  per  minute:  U = .001699 r—  y V B?b  n^, 

in  which  m = ratio  between  outer  and  inner  diameters  of  fan  (D  = md), 
and  V = velocity  (feet  per  minute)  of  air  in  fan  drift;  R = outer  radius  of 
fan  blades  (feet);  b = breadth  of  fan  blades  (feet);  n = number  of  revolu- 
tions of  fan  per  minute.  If  we  divide  the  power  upon  the  air,  as  determined 
by  the  expression  qp,  by  the  theoretical  work  given  in  the  last  equation,  we 
obtain  the  value  of  the  coefficient  of  efficiency.  According  to  this  formula 
the  efficiency  of  the  ventilator  changes  with  the  speed,  decreasing  as  the 
speed  increases,  but  not  in  the  same  ratio.  An  expression  for  the  coefficient 

163  600“ 

of  efficiency  of  a ventilator  is  given  by  Beard  as  follows:  K = 

C ^ -f-  lo3,o(X)* 

The  factor  c is  a constant  of  design  whose  value  may  vary  from  2 to  7,  but 
for  an  ordinary  design,  the  value  c = 4 may  be  taken.  This  factor  has  refer- 
ence to  the  equipment  of  the  machine  with  respect  to  its  efficiency  for  pass- 
ing an  air-current  through  itself  with  least  resistance.  Thus,  where  the 
ventilator  is  to  be  equipped  with  intake  blades  for  the  defiection  of  the  air- 
current  into  the  motor,  and  with  straight  radial  blades  having  only  a forward 


FAN  CONSTRUCTION. 


391 


curve  at  the  lip  of  the  blade  to  avoid  the  shock  of  the  entry  air  against  the 
revolving  blades,  and  the  spiral  casing  starting  a short  distance  upon  the 
cut-off  and  extending  uniformly  around  the  circumference  of  the  fan, 
the  value  of  this  constant  may  be  2 or  3.  Where  none  of  these  accessories 
to  the  efficiency  of  the  fan  is  employed,  the  value  of  c may  be  as  high  as  7. 


FAN  CONSTRUCTION. 


Size  of  Central  Orifice.— The  velocity  of  the  intake  should  vary  between 
1,000  ft.  and  1,500  ft.  per  minute,  while  1,200  ft.  may  be  used  for  fan  calcula- 
tions. If  d = diameter  of  opening,  and  q = quantity  of  air  passing  per 

minute,  d = fans,  and  d = -y/^00xT7854 

for  double-intake  fans. 

Upon  entering  the  fan  the  air  travels  in  a radial  direction;  this  change  of 
direction  is  accompanied  by  a slight  reduction  of  the  velocity,  hence  the 
throat  area  of  the  fan  must  be  slightly  in  excess  of  the  intake  area.  The 
throat  is  the  surface  of  the  imaginary  cylinder  that  has  for  its  two  bases  the 
two  intake  openings  of  the  fan,  and  for  its  length  the  width  of  the  fan,  = 
irdb.  [The  throat  area  is  commonly  made  1.25  times  the  total  area  of  the 
intake  orifices,  which  gives  for  breadth  of  blade  b = | d for  double  intake, 
and  5 = 1%  d for  single  intake.— .Beard.] 

Diameter  of  Fan. — Murgue  assumes  the  tangential  velocity  of  the  blade 
tips  (u)  to  create  a depression  double  that  due  to  the  velocity  as  expressed 

by  the  equation  H = or  if  the  manometrical  efficiency  = and  the 

effective  head  produced  = h,  h = KH  = iT  or  w = From  this 

equation,  the  tangential  velocity  (feet  per  second)  may  be  calculated  for 
any  given  effective  head  h.  This  effective  head  h is  the  head  of  air  column 
effective  in  producing  the  circulation  in  the  airway.  To  convert  the 
effective  head  of  air  column  into  inches  of  water  gauge  (i),  we  have 

h = found  the  tangential  speed  required  in  feet  per 

second,  this  is  multiplied  by  60,  to  obtain  the  speed  in  feet  per  minute, 
and  dividing  this  result  by  the  desired  number  of  revolutions  per  minute,  or 
the  desired  speed  of  the  ventilator,  the  outer  circumference  of  the  fan 
blades  is  obtained.  No  reference  is  made  in  the  equation  to  the  quantity 
of  air  in  circulation,  which  is  determined  from  the  equivalent  orifice  of 

the  mine  and  of  the  fan  by  the  equation  V = » in  which 

V 1 + ^ 


V = volume  of  air  (cu.  ft.  per  sec.);  a = equivalent  orifice  of  the  mine: 
o = the  equivalent  orifice  of  the  fan.  M.  Murgue  also  uses  the  equation 

h = — ^ and  suggests  that  the  value  of  K for  any  particular  type  of 


machine  should  be  first  decided,  after  which  the  tangential  speed  required 
to  produce  any  given  effective  head  of  air  column  (/i)  is  easily  calculated 
/gh 


from  the  formula  u 


N, 


The  breadth  of  the  blade  is  left  largely  to 


judgment,  while  this  method  of  calculation  gives  the  same  size  of  fan 
for  any  given  effective  head  desired,  regardless  of  the  quantity  of  air  to 
be  circulated,  which  is  the  same  as  saying  that  the  ventilator  will  present 
the  same  efficiency  when  a large  amount  of  air  is  crowded  through  its 
orifice  of  passage  as  when  a smaller  amount  of  air  is  necessary. 

Mr.  Beard  uses  the  following  formulas  for  determining  the  several  dimen- 
sions of  a ventilating  fan: 


m = 3 


Q 


i , 163,600'^  \ 

385,000,000  p 

KV'QV 


+ 1; 


D = 


\/m^- 
|/m3  — 
170  m 


__  3,770  / p , 
a n \/Wv' 


'X3  V 


e = 


392 


VENTILATION  OF  MINES. 


in  which  m = which  is  the  ratio  between  the  outer  diameter  of  the  fan 
a 

blades  D and  the  inner  diameter  of  the  blade  d,  which  equals  the  diameter  of 
the  intake  orifice;  h = width  of  fan  blade;  e = expansion  of  spiral  casing  at 
point  of  cut-off. 

The  other  symbols  stand  for  the  same  quantities  as  previously  indicated. 

Curvature  of  Blades.— It  was  at  one  time  supposed  that  the  curvature  of 
the  blades  should  be  such  that  the  radial  passage  of  the  air-current  would 
be  undisturbed  by  the  revolution  of  the  fan;  but  fans  constructed  on  this 
principle  gave  no  adequate  results,  and  the  theoretical  spiral  thus  developed 
was  entirely  abandoned.  A certain  curvature  of  the  blade  backward, 
however,  is  assumed  by  many  to  increase  the  efficiency  of  the  fan.  This 
has  not  been  proved  in  practice,  but  the  effect  of  the  backward  curvature 
appears  simply  to  necessitate  a higher  speed  of  revolution  in  the  fan,  in 
order  to  obtain  the  same  results  as  are  obtained  with  radial  blades. 

The  Guibal  blade,  radial  at  its  outer  extremity,  or  normal  to  the  outer 
circumference,  and  curved  forward  in  the  direction  of  motion,  at  its  inner 
extremity,  so  that  the  lip  of  the  blade  approaches  tangency  to  the  throat 
circle,  seems  the  most  effective  blade  in  centrifugal  ventilation. 

Tapered  Blades.— The  object  of  the  taper  is  to  produce  a constant  area  of 
passage  from  the  throat  to  the  circumference  of  the  fan,  and  thus  prevent 
the  reduction  of  the  velocity  of  the  current  in  its  passage  through  the 
fan.  This  feature  presents  an  attempt  similar  to  that  attempted  by  the 
curvature  of  the  blades,  to  hasten  the  passage  of  the  air  through  the  fan. 
It  has  not  been  proved,  however,  to  have  produced  any  beneficial  result, 
except  in  the  strengthening  of  the  discharge  pressure  against  the  atmos. 
pheric  pressure,  in  open-running  fans.  On  the  other  hand,  the  slowing  up 
of  the  air  in  its  passage  through  a covered  fan  has  by  no  means  been 
proved  a detriment,  but  is  assumed  by  many  to  be  an  advantage,  inasmuch 
as  the  air  thus  remains  longer  within  the  influence  of  the  fan  blades. 

The  number  of  blades  depends  on  the  size  of  the  fan.  An  increased  number 
strengthens  the  fan’s  action  at  the  circumference,  or  supports  the  air  at  that 
point,  and  thus  prevents  the  backlash  or  the  reentry  of  air  into  the  fan,  due 
to  the  eddies  occurring  at  the  circumference  when  the  blades  are  too  far 
apart.  To  a certain  extent,  the  number  of  blades  is  modified  by  the  speed 
of  revolution,  high-speed  motors  requiring  a somewhat  lesser  number, 
while  low-speed  motors  require  more.  In  any  case,  the  number  of  blades 
should  not  be  so  great  as  to  abnormally  increase  the  resistance  to  the  air- 
current.  In  general,  the  distance  upon  the  outer  circumference  from  tip 
to  tip  of  the  fan  blades  should  be  from  2 to  3 times  the  depth  of  the  blade. 

The  spiral  casing  gradually  reduces  the  velocity  of  the  air  and  reduces  the 
shock  incident  to  the  discharge  of  the  air  into  the  atmosphere.  The  spiral 
casing  should  be  so  proportioned  that  the  velocity  of  the  fiow  from  the  fan 
blades  will  be  maintained  constant  around  the  entire  circumference,  and 
this  should  not  be  less  than  the  velocity  of  the  blade  tips.  The  expansion  e 
of  the  casing  at  the  cut-off  should  be  such  as  to  provide  a velocity  of  the 
air  at  this  point  equal  to  the  velocity  of  the  blade  tips,  according  to  the 

equation  e = — S v.  in  which  D — diameter  of  fan;  n = number  revolu- 
^ TT  Dnh 

tions  per  minute;  h = breadth  of  fan  blade. 

The  evase  chimney  reduces  the  velocity  of  the  air,  as  it  is  discharged  into 
the  atmosphere,  to  a minimum.  The  chirnney  should  be  sufficiently  high 
to  protect  the  fan  from  the  effect  of  high  winds,  but  should  not  extend  too 
far  above  the  fan  casing,  the  point  of  cut-off  being  situated  below  this,  at 
about  the  level  of  a tangent  to  the  throat  circle  at  its  lower  side. 

High-Speed  and  Low-Speed  Motors.— The  question  of  speed  of  the  venti- 
lating motor  is  largely  an  open  one,  inasmuch  as  the  same  work  may  be 
performed  by  a small, ventilator  running  at  a high  speed  as  is  performed  by 
a large  ventilator  running  at  a low  speed. 

It  is  important  to  design  a mine  ventilator  at  a speed  such  as  to  admit  of 
its  being  increased  in  case  of  emergency.  If  the  ventilator  has  been 
designed  at  a high  speed,  a demand  for  an  increase  of  speed  cannot  be  met 
as  readily  as  when  the  ventilator  is  designed  at  a medium  or  low  speed;  in 
other  words,  the  exigencies  of  mine  ventilation  demand  that  a ventilator 
shall  be  capable  of  greatly  increased  speed. 

Fan  Testa.— A large  number  of  fan  tests  hav$  been  made,  from  time  to 


CONDUCTING  AIR-CURRENTS. 


393 


) 

time,  on  different  types  of  fans  and  under  different  conditions,  with  respect 
to  the  resistance  against  which  the  fan  is  operated,  and  the  quantity  of  air 
required,  and  the  speed  of  the  ventilator.  The  experiments  have  resulted, 
to  a large  extent,  in  tabulating  a mass  of  contradictory  data.  The  condi- 
tions that  affect  the  yield  of  the  centrifugal  ventilator  are  so  numerous,  and 
the  tabulation  of  the  necessary  data  has  been  so  often  neglected  in  these 
experiments,  as  to  render  them  practically  useless  for  the  purpose  of 
scientific  investigation.  In  conducting  a reliable  fan  test,  the  following 
points  should  be  observed:  (1)  Take  the  velocity,  pressure,  and  temperature 
of  the  air  at  the  same  point  in  the  airway,  as  nearly  as  practicable.  This 
point  should  be  selected  near  the  foot  of  the  downcast  shaft,  or  in  the  fan 
drift  at  a suitable  distance  from  the  fan,  to  avoid  oscillations  of  pressure  and 
velocity.  (2)  The  area  of  the  fan  drift  should  be  uniform  for  a suitable 
distance  in  each  direction  from  the  point  of  observation,  and  this  area 
should  be  carefully  measured.  (3)  Take  the  anemometer  readings  at  differ- 
ent positions  in  the  airway,  so  as  to  obtain  an  average  reading  over  the  entire 
sectional  area.  Do  not  interpose  the  body  in  this  area  so  as  to  decrease  the 
sectional  area  of  the  airway.  (4)  Take  outside  temperature  of  the  air  and 
the  barometric  pressure  at  the  time  of  making  the  test.  (5)  The  intake  and 
discharge  openings  of  the  fan  should  be  protected  against  wind  pressure. 
(6)  At  least  three  observations  should  be  made,  at  as  many  different  speeds 
of  the  ventilator,  and  the  number  of  revolutions  of  the  fan  carefully  observed 
and  recorded  for  each  observation. 

Mr.  R.  Van  A.  Norris  (Trans.  A.  I.  M.  E.,  Vol.  XX,  page  637)  gives  the 
results  of  a large  number  of  experiments  performed  upon  different  mine 
ventilating  fans.  This  table,  like  all  other  tabulated  fan  tests,  shows  a large 
amount  of  contradictory  data.  The  conclusions  drawn  by  Mr.  Norris  from 
these  tests  are  interesting  and  would  be  given  here  excepting  that  they 
might  be  misleading  if  considered  apart  from  the  description  of  the  experi- 
ments and  the  discussion  leading  up  to  the  conclusions. 


CONDUCTING  AIR-CURRENTS. 

Doors.— A mine  door  is  used  for  the  purpose  of  deflecting  the  air-current 
from  its  course  in  one  entry  so  as  to  cause  it  to  traverse  another  entry,  at  the 
same  time  permitting  the  passage  of  mine  cars  through  the  first  entry.  The 
essential  points  in  the  construction  of  a mine  door  are  that  it  shall  be  hung 
from  a strong  door  frame  in  such  a manner  as  to  close  with  the  current.  The 
door  should  be  hung  so  as  to  have  a slight  fall.  If  necessary,  canvas  flaps 
may  be  supplied  to  prevent  leakage  around  the  door,  and  particularly  at  the 
bottom.  Double  doors  are  used  on  main  entries  at  the  shaft  bottom,  or  at 
any  point  where  the  opening  of  the  door  causes  a stoppage  of  the  entire  cir- 
culation of  the  mine.  Such  doors  should  be  placed  a sufiicient  distance 
apart  to  allow  an  entire  trip  of  mine  cars  to  stand  between  them,  so  that  one 
of  the  doors  will  always  be  closed  while  the  other  is  open. 

Stoppings.— Stoppings  are  used  to  close  break-throughs  that  have  been 
made  through  two  entries,  or  rooms,  for  the  purpose  of  maintaining  the  cir- 
culation as  the  workings  advance;  also  to  close  or  seal  off  abandoned  rooms 
or  working  places.  Stoppings  must  be  air-tight  and  substantially  built.  A 
good  form  of  stopping  is  constructed  by  laying  up  a double  wall  of  slate, 
having  about  8 or  10  in.  of  space  between  the  two  walls.  This  space  is  filled, 
as  the  building  progresses,  with  dirt  taken  from  the  roadways,  or  other  fine 
material.  In  the  building  of  stoppings  to  seal  off  mine  fires,  it  is  important 
to  begin  the  work  at  the  end  nearest  the  return  air,  and  work  toward  the 
intake  end,  which  should  be  sealed  off  last.  This  method  avoids  the  danger 
of  an  explosion  occurring  within  the  workings  that  are  being  sealed  off,  as 
the  necessary  dilution  of  the  gases  within  is  accomplished  by  the  fresh  air- 
current,  until  the  intake  is  finally  sealed.  Where  the  intake  is  sealed  first, 
an  explosion  is  almost  inevitable,  as  has  been  proved  in  many  instances. 

Air  Bridges.— An  air  bridge  is  a bridge  constructed  for  the  passage  of  air 
across  and  over  another  airway,  this  being  called  an  overcast;  or,  the  cross- 
ing may  be  made  to  pass  under  the  airway,  this  being  called  an  undercast. 
In  almost  every  instance,  overcasts  are  preferable  to  undercasts  for  several 
reasons.  An  undercast  is  liable  to  be  filled  with  water  accumulating  from 
mine  drainage;  it  is  also  liable  to  fill  with  heavy  damps  from  the  mine,  when 
the  ventilation  is  sluggish,  and  to  offer  considerable  resistance  to  the  free 
passage  of  the  air-current.  An  undercast  can  never  be  maintained  as  air- 
tight as  an  overcast,  on  account  of  the  continual  travel  through  the 


394 


HOISTING  AND  HA  VLAGE. 


haulageway  or  passageway  leading  over  it.  This  continual  passing  over 
the  bridge  causes  a fine  dust  to  sift  into  the  airway  and  mingle  with  the 
air-current.  All  these  objections  are  overcome  in  the  construction  of  the 
overcast. 

An  air  brattice  is  any  partition  erected  in  an  airway  for  the  purpose  of 
deflecting  the  current.  A thin  board  stopping  is  sometimes  spoken  of  as  a 
brattice;  but  the  term  applies  more  particularly  to  a thin  board  or  canvas 
partition  running  the  length  of  an  entry  or  room  and  dividing  it  into  two 
airways,  so  that  the  air  will  be  obliged  to  pass  up  one  side  of  the  partition 
and  return  on  the  other  side  of  the  partition,  thus  sweeping  the  face  of  the 
heading  or  chamber.  Such  a temporary  brattice  is  often  constructed  by 
nailing  brattice  cloth  or  heavy  duck  canvas  to  upright  posts  set  from  4 to  6 ft. 
apart  along  one  side  of  the  entry  a short  distance  from  the  rib. 

Curtains.— These  are  sometimes  called  canvas  doors.  Heavy  duck,  or 
canvas,  is  hung  from  the  roof  of  the  entry  to  divide  the  air  or  deflect  a 
portion  of  it  into  another  chamber  or  entry.  Curtains  are  thus  used  very 
often  previous  to  setting  a permanent  door  frame.  They  are  of  much  use 
in  longwall  work,  or  where  there  is  a continued  settlement  of  the  roof, 
which  would  prevent  the  construction  of  a permanent  door;  also,  in  tempo- 
rary openings  where  a door  is  not  required. 


HOISTING  AND  HAULAGE. 


HOISTING. 

There  are  two  general  systems  of  hoisting  in  use:  (a)  Hoisting  without 
attempting  to  balance  the  load.  In  this  system,  the  cage  and  its  load  are  hoisted 
by  an  engine  and  lowered  by  gravity,  (b)  Hoisting  in  balance.  In  this 
system,  the  descending  cage  or  a special  counterbalance  assists  the  engine  to 
hoist  the  loaded  ascending  cage.  Hoisting  in  balance  is  usually  effected  by 
the  use  of  (1)  double  cylindrical  drums;  (2)  flat  ropes  winding  on  reels; 
(3)  conical  drums;  (4)  the  Koepe  system;  (5)  the  Whiting  system. 

1.  Double  cylindrical  drums  are  widely  used:  they  consist  essentially  of  an 
engine  coupled  directly  or  else  geared  to  the  common  axis  of  the  drums. 
The  drums  are  usually  provided  with  friction  or  positive  clutches,  and 
brakes,  so  that  they  can  be  run  singly  if  desired,  or  the  load  can  be  lowered 
by  gravity  and  the  brake. 

2.  Flat  ropes  wound  on  reels  are  sometimes  used  either  for  unbalanced 
hoisting  with  a single  reel  or  for  balanced  hoisting  with  a double  reel.  With 

the  double  reels,  the  load  on 
the  engine  is  balanced 
throughout  the  entire  hoist, 
for,  as  the  rope  is  wound  on 
the  reel,  the  diameter  of  the 
reel  is  increased,  and  the 
lever  arm  through  which 
the  power,  of  the  engine  is 
applied  is  also  increased  and 
the  mechanical  efficiency  of 
the  hoisting  system  de- 
creased. Thus,  when  the 
cage  is  at  the  bottom  of  the 
shaft  and  the  entire  weight 
of  the  rope  is  out,  giving  the 
maximum  load  to  be  hoisted, 
the  drum  is  of  a minimum 
diameter  and  the  engine  has, 
therefore,  its  greatest  lever- 
age to  start  the  load.  A flat 
rope  has  the  advantage  of 
preventing  fleeting,  but  its  first  cost,  extra  weight,  wear,  and  difficulty  of 
repairing  have  prevented  its  very  general  adoption. 

3.  Conical  Drums.— A conical  drum,  Fig.  1,  equalizes  the  load  on  an  engine 

i*ust  as  a flat  rope  on  a reel  does.  On  account  of  the  fleeting  of  the  rope, 
lowever,  the  drum  must  be  set  at  a considerable  distance  from  the  shaft  to 
prevent  the  rope  leaving  the  head-sheave.  A tail-rope  gives  the  most 


HOISTING. 


395 


perfect  counterbalance,  the  weight  of  the  cage  and  rope  on  each  side  being 
exactly  equal. 

4.  In  the  Koepe  system.  Fig.  2,  one  rope  runs  over  and  the  other  under 
driving  sheaves  S.  A tail-rope  R is  used,  and  the  head-sheaves  x,  x'  are 
placed  vertically  and  at  such  an 
angle  to  each  other  that  their 
grooves  and  the  groove  in  the  dri- 
ving sheave  are  in  line.  As  the 
main  driving  shaft  is  short,  the  en- 
gines can  be  placed  close  together, 
thus  requiring  a smaller  foundation 
and  engine  house  than  for  a drum 
hoist.  The  objection  to  the  system 
is  the  liabilitjr  of  the  rope  to  slipping 
about  the  driving  sheave,  and  for 
this  reason  a hoisting  indicator  can- 
not be  depended  on.  The  system  is 
also  inconvenient  for  hoisting  from  different 
levels  in  the  same  shaft,  and,  in  case  of  the  rope 
breaking,  both  cages  fall  to  the  bottom. 

5.  The  Whiting  system,  Fig.  3,  uses  two  narrow- 

frooved  drums  placed  tandem  instead  of  a single- 
riving  sheave  as  is  used  in  the  Koepe  system. 

The  rope  passes  from  the  cage  A over  a head-sheave, 
under  the  guide  sheave  T and  around  the  sheaves 
My  F three  times,  then  out  to  the  fleet  sheave  (7, 
back  under  another  guide  sheave,  and  up  over 
another  head-sheave  to  the  cage  B.  The  sheave  M 
is  driven  by  a motor  either  coupled  direct  to  its 
shaft,  or  geared.  The  drums  F and  M are  coupled 
together  by  a pair  of  connecting-rods  like  the 
drivers  of  a locomotive,  and  this  arrangement  Fig.  2. 

makes  it  possible  to  utilize  all  the  friction  of  both 

drums  to  drive  the  rope.  Thus  a tail-rope  is  not  depended  on  to  produce 
more  friction,  though  one  is  generally  used  as  a balance  to  the  loads. 

It  is  best  to  incline  the  follower  sheave  F from  the  vertical  an  amount 


c 

0 

< 

• 

1 

equal  in  its  diameter  to  the  distance  between 
the  centers  of  two  adjacent  grooves,  the  object 
being  to  eliminate  chafing  between  the  ropes 
around  the  drums  and  to  prevent  them  from 
running  off  by  enabling  the  rope  to  run  from 
each  groove  in  one  drum  straight  to  the  proper 
groove  in  the  other.  This  throws  the  shaft  and 
crankpins  out  of  parallel  with  those  of  the  main 
drum,  but  this  difficulty  is  overcome  by  the 
connections  in  the  ends  of  the  parallel  rods. 

The  fleet  sheave  C is  arranged  to  travel  back- 
wards and  forwards,  as  shown  by  the  dotted 
lines,  in  order  to  change  the  working  length  of 
the  rope,  whereby  hoisting  can  be  done  from  different  levels  in  the  shaft. 

The  power  used  for  hoisting  is  generally  steam  for  the  main  hoists.  Elec- 
tricity is,  however,  coming  rapidly  into  use,  particularly  for  smaller  hoists 


396 


HOISTING  AND  HAULAGE. 


and  local  installations,  and  for  main  hoists  in  locations  where  fuel  is 
expensive  and  water-power  available.  Gasoline  engines  are  also  being  used 
to  an  increasing  degree,  particularly  for  smaller  hoists  and  in  local  installa- 
tions, and  they  are  said  to  give  very  satisfactory  results. 


PROBLEMS  IN  HOISTING. 

To  Balance  a Conical  Drum.— Having  given  the  diameter  of  one  end  of  a 
conical  drum,  to  determine  the  diameter  of  the  other  end  that  will  equalize 
the  load  on  the  engines.  In  Fig.  1,  call  total  load  at  bottom  A,  empty  cage 
at  top  By  loaded  cage  at  top  0,  empty  cage  plus  rope  at  bottom  D,  small 
diameter  of  drum  Xy  and  large  diameter  j/;  then.  Ax—  By  = Cy  — Dx. 

Example.— In  a shaft,  the  cage  weighs  2 tons,  the  empty  car  1 ton,  the 
loaded  car  3 tons,  and  the  rope  2 tons.  What  should  be  the  small  diameter  of 
a conical  drum  whose  large  diameter  is  30  ft.? 

(2  + 2 -h  3)a;  - (2  + 1)30  = (2  + 3)30  - (2  + 2 + l)Xy 
or  7 X — 90  = 150  — 5x. 

12  a;  = 240, 
a;  = 20  ft. 


To  Find  the  Size  of  the  Hoisting  Engine.— Let  D = diameter  of  cylinder, 
P = mean  effective  steam  pressure  in  cylinders,  r = ratio  of  stroke  to  diam- 
eter of  cylinder,  and  w = work  per  revolution  required  to  be  done;  then,  by 
making  one  cylinder  capable  of  doing  the  work,  n = number  of  strokes, 
u = work  per  minute  (ft.-lb.). 

D = 1.97^/^,  or  P = 

\Pr  . \ .7854:  Frn 

Example.— What  should  be  the  size  of  the  cylinders  of  a hoisting  engine 
that  is  to  perform  152,580  ft.-lb.  of  work  per  revolution,  if  the  mean  effective 
pressure  is  45  lb.  per  sq.  in.  and  the  stroke  of  the  piston  is  twice  its  diameter  ? 


D = 1.97 


3ll52,580 

\45X2 


23.5  in. 


To  get  up  speed  in  a few  seconds,  more  power  than  would  be  represented 
by  the  load  to  be  lifted  is  required.  Mr.  Percy  gives  the  following  rule  for 
this  case:  In  a properly  balanced  winding  arrangement,  with  uniform  load, 
multiply  the  weight  of  coal  in  pounds  by  the  average  speed  of  the  cage  in 
feet  per  minute;  add  one-half  to  cover  the  frictional  resistances,  and  call 
ihat  the  load.  Then  the  power  that  must  equal  this  must  be  the  average 
effective  pressure  of  steam  in  pounds  per  square  inch  on  the  piston,  multi- 
plied by  the  area  of  one  cylinder  in  square  inches,  and  multiplied  again  by 
the  average  speed  of  the  piston  in  feet  per  minute. 

Approximately,  the  average  effective  pressure  of  steam  will  be  two-thirds 
of  the  pressure  shown  on  the  gauge  near  the  engines.  A good  average  piston 
speed  is  400  ft.  per  minute. 

To  Find  the  Actual  Horsepower  of  an  Engine  for  Hoisting  Any  Load  Out  of  a Shaft 
at  a Given  Rate  of  Speed.— To  the  weight  of  the  loaded  car  add  the  weight  of 
the  rope  and  cage.  This  will  give  the  gross  weight. 


Then,  H.  P. 


gross  weight  in  lb.  X speed  in  ft.  per  minute. 

33,000  * 


addi  for 


.contingencies,  friction,  etc. 

Example.— Having  a shaft  600  ft.  deep,  gross  weight  of  load  20,000  lb.,  to 
be  hoisted  in  minutes,  what  horsepower  is  required  ? 

20  000  V 400 

= * oo  nnfi — = 243  H.  P.,  nearly.  To  which  add  i for  contingen- 

oOjOOO 


cies,  and  we  have  324  H.  P. 

In  a shaft  with  two  hoistways,  use  the  net  weight  -h  the  weight  of  one 
rope,  instead  of  the  gross  weight. 

The  following  rules  regarding  winding  engines  are  given  by  Percy: 

1.  To  Find  the  Load  That  a Given  Pair  of  Direct-Acting  Engines  Will  Start. 
Multiply  the  area  of  one  cylinder  by  the  average  pressure  of  the  steam 
per  square  inch  in  the  cylinder,  and  twice  the  length  of  the  stroke.  Divide 
this  by  the  circumference  of  the  drum,  and  deduct  i for  friction,  etc. 


HBAD-FRAMES, 


397 


Example.— Given  a pair  of  engines,  cylinders  20  in,  diameter  by  40  in. 
stroke,  the  drum  12  ft.  diameter,  and  the  i)ressure  at  steam  gauge  50  lb., 
steam  cut-off  at  average  pressure  of  steam  in  cylinder  48.2  lb. 

Then,  area  of  cylinder  = 314.16  sq.  in.  314.16  X 48.2  X 80  = 1,211,400.96. 

The  circumference  of  the  drum  = 452.4  in.  1,211,400.96  -t-  452.4  = 2,677. 
I of  2,677  = 1,784  lb.,  or  the  net  load. 

The  gross  load  would  include  the  weight  of  rope,  cage,  and  car,  but  as 
these  are  balanced  by  the  descending  rope,  cage,  and  car,  the  net  load  only 
is  found.  The  drum  mentioned  is  cylindrical. 

2.  Knowing  the  Load  and  the  Diameter  of  a Cylindrical  Drum,  and  the  Length  of 
Stroke,  the  Cut-off  and  Pressure  of  Steam  at  Steam  Gauge,  to  Find  the  Area  and 
Diameter  of  Cylinders  of  a Pair  of  Direct-Acting  Engines.— Multiply  the  load  by 
the  circumference  of  the  drum,  and  add  one-half  for  friction,  etc.  Divide 
this  by  the  mean  average  steam  pressure,  multiplied  by  twice  the  length  of 
the  stroke. 

Example.— Having  the  drum  10  ft.  in  diameter,  the  stroke  6 ft.,  the  steam 
pressure  at  gauge  60  lb.,  the  cut-off  at  ^ of  stroke,  and  the  load  5 tons,  or 
11,200  lb. 

Then  11,200  X 31.416  (circumference  of  drum)  =*  351,859.  351,859  -f  i of 
351,859  (or  175,930)  = 527,789. 

The  mean  average  pressure  = 56.2  lb.  56.2  X (6  X 2)  = 674.4.  527,789 
-7-  674.4  = 782.6  sq.  in.,  area  of  piston. 

782.6  .7854  = 996.  i/  ^ = 31.56  in.,  or  diameter  of  cylinder. 

3.  To  Find  the  Approximate  Period  of  Winding  on  a Cylindrical  Drum  With  a Pair 
of  Direct-Acting  Engines.— Assume  the  piston  to  travel  at  an  average  velocity  of 
400  ft.  per  minute,  and  divide  this  by  twice  the  length  of  the  stroke,  and 
multiply  by  the  circumference  of  the  drum.  This  gives  the  speed  of  cage  in 
feet  per  minute.  Divide  the  depth  of  shaft  by  this,  and  the  result  will  be  the 
period  of  winding. 

Example. — Drum,  31.416  ft.  circumference;  stroke,  6 ft.;  depth  of  shaft, 
1,500  ft. 

Then,  400  ^ 12  = 33.33.  33.33  X 31.416  = 1,047.1.  1,500  1,047.1  = 1.43 

min.,  or  about  1 min.  26  sec. 

4.  To  Find  the  Useful  Horsepower  During  a Winding.— Multiply  the  depth  of 
shaft  by  net  weight  raised;  divide  this  by  number  of  minutes  occupied  in 
winding,  and  divide  again  by  33.000. 

Example.— Net  weight,  2 tons  = 4,4801b.;  depth,  1,500  ft.;  period  of  wind- 
ing, 1.43  minutes. 

Then,  4,480  X 1,500  = 6,720,000.  6,720,000  -r- 1.43  = 4,699,301.  4,699,301 

-r-  33,000  = 142-f  H.  P.  


HEAD-FRAMES. 

Head-frames  are  built  of  wood  or  steel,  and  some  of  the  typical  forms  are 
shown  on  pages  275  and  276.  They  vary  in 
height  from  30  to  100  ft.,  depending  on  local 
conditions. 

The  inclined  leg  of  a head-frame  should  be 
placed  so  as  to  take  up  the  resultant  strain  due 
to  the  load  hanging  down  the  shaft  and  the 
pull  of  an  engine.  Fig.  4 shows  the  graphical 
method  of  determining  the  direction  and  mag- 
nitude of  this  resultant  force.  Produce  the 
direction  of  the  two  portions  of  the  rope  lead- 
ing to  the  drum  and  down  the  shaft  until 
they  intersect  at  G,  measure  off  a distance  G K 
to  scale  to  represent  the  load  hanging  down  the 
shaft;  similarly,  measure  off  GH  to  the  same 
scale  to  represent  the  pull  of  the  engine,  com- 
plete the  parallelogram  GHLK;  the  direction 
of  the  line  G L represents  the  direction  of  the 
resultant  force,  and  its  length  represents  the 
amount  of  this  force.  The  inclined  leg  of 
the  head-frame  should  be  placed  as  nearly  as 
Fig.  4.  possible  parallel  to  this  resultant  line,  and 

should  be  designed  to  withstand  a compressive 
Strain  equal  to  this  resultant. 

Ile8d-9ne9v*9  are  made  of  iron,  being  sometimes  entirely  cast,  or  else  the 


398 


HOISTING  AND  HAULAGE. 


rim  and  hub  are  cast  separately  and  wrought-iron  spokes  are  used.  The 
former  are  cheaper  and  quite  satisfactory,  but  the  latter  are  lighter  and 
stronger,  and  therefore  usually  better.  The  diameter  of  the  sheave  depends 
on  the  diameter  of  the  rope,  and  the  table  giving  this  will  be  found  on 
page  120.  The  groove  in  the  sheave  should  be  wood-lined,  to  reduce  wear 
on  the  rope.  Wrought-iron  spokes  should  be  staggered  in  the  hub  and  not 
placed  radially. 

Guides  and  conductors  are  usually  of  timber  rigidly  attached  to  the  sides  of 
a shaft.  In  England  and  certain  parts  of  Europe,  wire  ropes  are  used  for  guides 
and  are  strongly  advocated,  but  they  have  never  found  favor  in  America. 
These  ropes  when  used  are  weighted  at  the  bottom,  and  Percy  gives  1 ton 
for  each  600  ft.  in  depth  for  each  wire  as  a good  weight  to  be  used.  When 
not  thus  weighted,  the  ropes  are  fastened  at  the  bottom  and  attached  to 
levers  at  the  top,  the  levers  being  weighted  to  produce  the  requisite  tension. 

Safety  catches  usually  consist  of  a pair  of  toothed  cams  placed  on  either 
side  of  the  cages  and  enclosing  the  guides.  When  the  load  is  on  the  hoisting 
rope,  these  cams  are  kept  away  from  the  guides  by  suitable  springs;  but  if 
the  rope  breaks,  the  springs  come  into  action  and  throw  the  catches  or 
dogs  so  that  they  grip  the  guides,  and  the  tendency  to  fall  increases  the 
grip  on  the  guides. 

Detaching  hooks  are  devices  that  automatically  disconnect  the  rope  from 
the  cage  in  case  of  overwinding. 


HAULAGE. 

The  magnitude  of  modern  mines  and  the  practice  of  loading  or  of  treating 
the  coal  or  ore  at  a large  central  station  makes  the  underground  haulage  of 
the  material  one  of  the  most  important  problems  in  connection  with 
mining.  A good  haulage  system  is  now  essential  to  make  most  mines  a 
commercial  success.  Haulage  may  be  considered  under  the  following  heads: 

1.  Inclined  Roads. — Gravity  planes,  engine  planes. 

2.  Level  Roads.— Mule  haulage,  rope  haulage  (tail-rope  and  endless  rope), 
motor  haulage  (steam,  electricity,  compressed  air,  or  gasoline). 

Gravity  Planes.— The  loaded  car  or  trip  hauls  the  empty  car  up  the  grade. 
Two  ropes  are  attached  to  a drum  so  that  the  rope  attached  to  the  loaded 
car  unwinds  from  the  drum  as  the  car  de- 
i scends,  while  the  rope  attached  to  the  empty 

^ car  is  wound  on  the  drum  and  the  car  thus 

T hauled  up  the  plane.  The  natural  slope  of 

nor/zontaL  ground,  in  a large  measure,  determines 

Fig.  5.  the  grade  of  the  incline,  but  where  it  is  pos- 

sible to  alter  the  direction  of  the  incline, 
the  grade  may  be  lessened  by  constructing  the  incline  across  the  slope  of 
the  ground.  The  grade  of  the  incline  may  be  increased  by  carrying  the 
upper  landing  forwards  till  a point  is  reached  from  which  the  required 
grade  is  obtained. 

The  following  rule  gives  suggestions  based  on  practice  that  has  been 
successful:  For  lengths  not  exceeding  500  ft.,  the  minimum  grade  for  the 
incline  should  be  5^  when  the  weight  of  the  descending  load  is  8,000  lb.  and 
that  of  the  ascending  load  2,800  lb.  Or  the  inclination  should  not  be  less 
than  h\io  if  the  respective  descending  and  ascending  loads  are  one-half  of 
those  just  given.  When  the  length  of  the  plane  is  from  500  to  2,000  ft.,  the 
grade  should  be  increased  from  5j^  to  10^,  according  to  the  loads.  A load 
of  4,000  lb.  on  a 10^^  grade  2,000  ft.  long  will  hoist  a weight  of  1,400  lb. 

The  angle  of  inertia  is  that  angle  or  inclination  at  which  a car  will  start  to 
move  down  the  slope  or  plane.  The  car,  when  it  has  once  started  on  this 
grade,  will  continue  to  accelerate  its  speed  as  it  descends  the  plane  A B, 
Fig.  5.  If  we  decrease  the  angle  of  inclination  until  the  plane  A B occupies 
the  position  A C,  such  that  the  moving  car  will  continue  to  move  at  a 
uniform  velocity  instead  of  accelerating  its  speed,  the  angle  D C A will  be 
the  angle  of  rolling  friction,  and  the  tangent  of  this  angle  will  be  the  coefficient 
of  rolling  friction  for  the  car. 

The  upper  portion  of  a plane  is  made  steeper  than  the  lower  portion  so 
that  the  trip  may  start  quickly  at  the  head  and  afterwards  maintain  a 
uniform  velocity.  With  a good  brake  to  control  the  cars,  the  uniform  grade 
of  a central  portion  of  a gravity  plane  should  not  fall  much  below  3°,  which 
corresponds  practically  to  a 5i^  grade. 


HAULAGE. 


399 


The  acceleration  f oi  the  haulage  system  is  given  by  the  formula 


/=: 


- X X sin  a 


Pi  + P2  ' 

where  pi  and  p2  are  the  descending  and  ascending  pulls,  respectively. 
The  length  of  steep  pitch  is  given  by  the  formula 

2/’ 


I = 


where  v = velocity  at  which  the  trip  is  desired  to  run. 

The  maximum  tension  or  pull  on  the  rope  which  may  occur,  if  it  is  required 
to  haul  the  loaded  trip  up,  is 


T = {W  wl)  a -Y  {W  wl)  cos  a X 


where  W = weight  of  loaded  trip;  wl  = weight  of  rope;  a — slope  angle; 
p = coefficient  of  friction. 

Example. — Find  the  possible  tension  of  a rope  used  to  lower  a loaded  trip 
of  two  cars  upon  a plane  800  ft.  long,  having  a uniform  grade  of  5^  at  a 
speed  of  20  miles  per  hour,  using  a factor  of  safety  of  10,  and  letting  ju,  = 
the  empty  cars  weighing  1,000  lb.  each  and  carrying  a load  of  2,000  lb.  each. 

Assuming  w = .88  lb.,  T = (6,000  + .88  X 800)  (.05  + .04994)  = 671  lb. 

To  find  the  nuipber  of  cars  that  must  run  in  a trip  on  a self-acting  incline,  use 
the  formula 

^ (40  sin  a + cos  a)  Wz 

(40  sin  a — cos  a)  Wi  — (40  sin  a + cos  a)  Wf 


in  which  N = number  of  cars;  a = angle  of  inclination  of  plane;  Wi 
= weight  in  pounds  of  one  loaded  car;  W2,  = weight  in  pounds  of  one 
empty  car;  Wz  = weight  in  pounds  of  haulage  rope;  = coefficient  of 
friction. 

Example. — A gravity  plane  has  an  inclination  of  8°;  it  is  2,000  ft.  long,  the 
rope  weighs  4,000  lb.,  a loaded  car  weighs  3,000  lb.,  and  an  empty  car  weighs 
1,800  lb.  What  number  of  cars  must  be  in  the  trip  to  start  it? 

Substituting  values  in  the  above  formula,  we  have 


(40  X .13917  + .99027)4,000  - c 

~ (40  X .13917  — .99027  ) 3,000  — (40  X .13917  + .99027)1,800  “ 

Engine  Planes.— With  an  engine  plane,  the  load  is  delivered  at  the  foot  of 
the  plane  and  has  to  be  hoisted.  The  engine  may  be  either  at  the  top  or  the 
bottom.  The  grade  of  the  plane  is  usually  uniform  from  top  to  bottom,  and 
there  may  be  a single  track,  a double  track,  or  three  rails  with  a turnout. 

Size  of  Engines  Required  for  Engine-Plane  Haulage.— (a)  Engine  at  Head  of 
Plane,  Single  Tracfc.— Calling  the  load  on  the  engine  or  the  tension  of  the 
rope  at  the  winding  drum  T,  the  weight  of  the  ascending  loaded  trip  W,  the 
weight  of  the  rope  per  lineal  foot  w,  and  the  length  of  the  plane  I,  the  angle 
of  inclination  or  the  slope  angle  being  a,  as  before,  we  have 

T=  ( ir+ ^^;^)  (sin  a + ju.  cos  a). 

Assume  an  approximate  value  for  w,  and  determine  T approximately. 
The  size  of  rope  required  for  this  load  is  then  obtained  from  the  table  for 
haulage  ropes,  and  with  this  new  value  of  w,  the  correct  load  on  the  engine 
is  calculated. 

Example.— What  size  of  rope  will  be  required  to  haul  up  an  incline  a 
loaded  trip  of  10  mine  cars  weighing  1,000  lb.  each,  and  carrying  a load  of 
2,000  lb.  each,  the  inclination  of  the  plane  or  the  slope  angle  being  16°  and 
its  length  500  yd.,  assuming  for  the  coefficient  of  friction  /a  = 

W = 30,000  lb.,  and  assuming  w = .89  lb.,  W + wl  = 30,000  + (.89  X 1,500) 

= 31,335  lb.  Sin  a + = .27564  + = .29967.  Hence,  T = 31,320  X 

.29967  = 9,394  lb.  To  provide  against  shock,  we  double  the  load  or  pull  on 
the  rope  in  calculating  the  size  of  rope  required;  thus,  9,394  X 2 = 18,788  lb., 
and  using  a factor  of  safety  of  6,  we  have  for  the  breaking  strain  of  the  rope 
18  788  X 6 

- ’ — = 57  tons.  In  the  table  of  wire  ropes,  a 1|-"  plow-steel  rope 

^)UUU 


400 


HOISTING  AND  HAULAGE. 


presents  % breaking  strain  of  56  tons.  Since  a Ij"  rope  weighs  2 lb.  per 
lineal  fo  jt,  we  have  W w I 80,000  + (2  X 1,500)  = 33,000  lb.  Then  T = 
33,000  X .29967  = 9,889  lb. 

. (b)  Engine  at  Head  of  Incline,  Double  Track. — The  load  on  the  engine 
equals  the  difference  between  the  gravity  pulls  of  the  ascending  and 
descending  trips,  including  the  rope,  plus  the  friction  pull  of  both  the  trips 
and  one  rope,  since  there  is  only  one  rope  on  the  plane  at  any  time.  Calling 
the  Weight  of  the  ascending  trip  W,  as  before,  and  that  of  the  descending 
trip  W\,  we  have  for  the  difference  of  the  gravity  pulls  when  the  loaded  trip 
is  at  the  foot  of  the  incline,  {W  — sin  a,  and  for  the  friction  pull  of 

the  entire  moving  system  {W  -\-Wi-\-wr)  ju.  cos  a,  and  L = {W  — W\  -\-  wl) 
sin  a A-  {W  ^W\  A-  y^l)  y-  cos  a. 

Assuming  the  same  conditions  as  given  in  the  example  of  the  preceding 
paragraph,  we  have  for  the  load  L on  the  engine,  X = [10  X 2,000  + 2 x 

1,500]  .27564  + [10  X (3,000  + 1,000)  + 2 X 1,500]  X = 23,000  X .27564 

4-  43,000  X .02403  = 7,373  lb.  instead  of  9,394,  the  unbalanced  load  for  single 
track. 

(c)  Engine  at  Foot  of  Incline.— load  on  the  engine  is  the  same  as  in 
(a),  except  that  the  gravity  pull  is  the  pull  due  to  the  weight  of  the  loaded 
cars  only,  the  weight  of  the  ascending  rope  being  balanced  by  the  descend- 
ing rope,  while  the  friction  pull  is  increased  by  the  friction  of  the  descend- 
ing rope.  Calling  the  load  on  the  engine  X,  as  before,  we  have,  in  this  case, 

X = TT  sin  a + ( IF  + 2 Z)  /u.  cos  a. 


Assuming  the  conditions  of  the  previous  example  and  calculating  the 
load  on  the  engine  for  this  case,  we  have  X = 30,000  X .27564  + [30,000  -f 
2(2  X 1,500)1.02103  = 9,1341b. 

To  Find  the  Horsepower  of  an  Engine  Required  to  Hoist  a Given  Load  Up  a Single- 
Track  Incline  in  a Given  Time.— Multiply  the  length  of  the  incline  in  feet  by  the 
natural  sine  of  the  angle  of  inclination,  which  will  give  you  the  vertical  lift. 
Divide  the  vertical  lift  by  the  given  time  in  minutes.  Multiply  this  by  the 
gross  load,  including  weight  of  rope,  and  divide  the  product  by  33,000. 

Example.— Length  of  incline,  600  ft.;  angle  of  inclination,  35°;  weight  of 
loaded  car  and  600  ft.  of  rope,  5,000  lb. ; time  of  hoisting,  2 minutes.  Required, 
the  horsepower. 

Sine  of  35°  = .573576.  .573576  X 600  = 344.1456.  344.1456  ^ 2 = 172.728. 


172.728  X 5,000 
33,000 


26+  H.  P. 


Add  from  25^  to  50^  for  contingencies,  friction,  etc.  In  mine  practice,  50^ 
is  not  any  too  much  to  add,  because  the  condition  of  track,  cars,  etc.,  is  not 
as  good,  as  a general  rule,  as  on  railroad  planes. 

To  Find  the  Horsepower  of  an  Engine  Required  to  Hoist  a Given  Load  Up  a Double- 
Track  Incline  in  a Given  Time. — Proceed  as  above,  using  the  net  load,  to  which 
should  be  added  the  weight  of  one  rope,  instead  of  the  gross  load. 


ROPE  HAULAGE. 

The  tail-rope  system  of  haulage  uses  two  ropes  and  a pair  of  drums  on  the 
same  shaft.  The  main  rope  passes  from  one  drum  directly  to  the  front  of  the 
loaded  trip,  and  the  tail-rope  passes  from  the  other  drum  to  the  large  sheave 
wheel  at  the  end  of  the  road  and  back  to  the  rear  of  the  loaded  trip.  While 
hauling  the  loaded  trip,  the  drum  on  which  the  tail-rope  is  wound  is  allowed 
to  turn  freely  on  its  journal  by  throwing  its  clutch  out,  while  the  engine 
turns  the  other  drum.  When  the  empty  trip  is  being  hauled,  the  clutch  on 
the  main-rope  drum  is  thrown  out  and  the  one  on  the  tail-rope  drum  is 
thrown  in.  The  engine  then  turns  the  tail-rope  drum  and  allows  the  other 
one  to  pay  out  rope  as  the  trip  advances. 

The  tail-rope  system  is  suitable  for  steep,  circuitous,  and  undulating 
roads.  The  trip  can  be  kept  stretched  at  all  points,  and  thus  the  cars  will 
be  prevented  from  bumping  together  or  from  being  jerked  apart  as  the  trip  is 
passing  over  changes  in  the  grade.  It  is  undoubtedly  the  most  satisfactory 
system  of  rope  haulage  under  the  natural  conditions  of  most  haulage  roads 
in  mines,  and  especially  so  where  but  one  road  is  available  for  naulage 
purposes. 


ROPE  HAULAGE. 


401 


CALCULATION  OF  THE  TENSION  OF  HAULING  ROPE. 

T — tension  or  pull  upon  rope  (lb.). 

W = weight  of  loaded  trip  (lb.). 

w = weight  of  rope  per  lineal  foot  (lb.). 

I = length  of  two  ropes;  equals  2 times  the  distance  from  winding 
drum  to  tail-sheave  (ft.). 

d = vertical  drop  of  roi)e  (ft.). 

a = slope  angle  of  maximum  grade. 

T = Tr(sin  a + iu.  cos  a)+ (d  + /X  0- 

Example. — What  size  of  steel  wire  rope  will  be  required  to  haul  a trip  of 
20  mine  cars,  the  weight  of  the  loaded  cars  being  3,000  lb.  each,  the  depth  of 
the  shaft  300  ft.,  and  the  distance  from  the  foot  of  the  shaft  to  the  tail-sheave 
900  yd.,  the  maximum  grade  in  this  haulage  being  10°,  fx  = Assuming 
a rope,  weighing  .89  lb.  per  lineal  ft. 

T = 60,000  (.17365  -1-  -f  .89  (3OO  = say  12,300  lb.,  or  some- 

what over  6 tons. 

Referring  to  the  tables  for  steel  haulage  ropes  with  6 strands  of  7 wires 
each,  we  find  the  breaking  strain  of  a rope,  weighing  .89  lb.  per  lineal  ft., 
is  18.6  tons,  which  will  give  a factor  of  safety  of  about  3.  We  would;  however, 
use  a or  even  a 1"  rope,  as  a change  of  ropes  would  then  be  required  less 
often.  Making  the  necessary  corrections  for  1"  rope  weighing  1.58  lb.  per 
lineal  ft.,  T = 12,607  lb. 

The  endless-rope  system  uses  an  endless  rope,  which  is  kept  running  con- 
tinuously by  a pair  of  drums  geared  together  and  set  tandem.  The  drums 
are  comparatively 
narrow  and  provided 
with  grooves  for  the 
rope  to  run  in.  Two 
drums  are  necessary 
to  get  sufficient  fric- 
tion to  drive  the  rope 
when  the  trip  is  at- 
tached to  it.  The 
rope  is  passed  around 
both  drums  a num- 
ber of  times,  depend- 
ing on  the  amount  of 
friction  desired, 
without  completely 
encircling  either.  It 
then  passes  to  a ten- 
sion wheel  at  the  rear 
of  the  drums  and 
thence  to  the  sheave 
wheel  at  the  far  end 
of  the  road  and  back 
to  the  drums.  To  be 
used  to  best  advan-  Fig.  6. 

tage,  this  system  re- 
quires that  the  grade  be  in  one  direction  and  that  it  be  necessary  to  haul  cars 
from  a number  of  places  en  route.  The  cars  are  attached  to  the  rope  by 
friction  grips  in  a manner  quite  similar  to  the  way  in  which  street  cars 
are  attached  to  cable  lines.  It  is  evident,  therefore,  that  any  jerking  due 
to  the  cars  bumping  together  or  stretching  the  hitchings  would  seriously 
injure  the  rope  where  the  grip  takes  hold.  A double  road  is  an  essential 
feature  of  endless-rope  haulage. 

The  endless-rope  system  of  haulage  is  best  adapted  to  roads  presenting  a 
fairly  uniform  grade,  particularly  when  the  trips  are  not  spaced  at  fairly  regu- 
lar intervals  along  the  road.  Owing  to  delays  in  the  delivery  of  the  cars  by  the 
drivers  and  to  irregularity  in  unloading  at  the  tipple,  it  is  practically  im- 
possible to  have  the  several  trips  regularly  spaced,  and  in  consequence  the 
load  on  the  engine  varies  greatlJ^  In  order  to  take  up  any  elongation  of  the 
rope  due  either  to  change  in  temperature  or  to  stretching,  some  form  of 
balance  car  or  balance  weight  is  used.  This  weight  should  be  sufficient  to 
keep  the  empty  rope  taut,  and  any  tendency  of  the  rope  to  slip  on  the 


402 


HOISTING  AND  HA  ULAOE. 


winding  drum  may  be  overcome  by  increasing  the  weight  in  the  bal- 
ance car. 

Fig.  6 shows  a device  for  working  a district  haulage  by  connecting  it  with 
the  main  haulage.  The  main  rope  makes  one  or  two  complete  turns  around  a 
fleet  wheel  located  at  the  mouth  of  each  district,  and  then  continues  on  its 
course.  This  fleet  wheel  d is  directly  connected  with  the  driving  sheave  m 
for  the  district  by  means  of  beveled  gears  g,  h,  as  shown.  The  driving 
sheave  m is  thrown  in  or  out  of  gear  by  levers  o and  q. 

To  Determine  the  Friction  Pull  on  an  Endless-Rope  Haulage.— Let 

0 = output  (lb.  per  min.);  = weight  of  mine  car  (lb.); 

speed  of  winding  (ft.  per  min.);  w = weight  of  rope  (lb.); 


I = length  of  haulage  road  (ft.); 


c = 
Then, 


T ~ load  on  the  rope  (lb.); 
M = coefficient  of  friction. 


capacity  of  mine  car  (lb.); 

^ = weight  of  material  in  transit; 

2 ^ wi  = weight  of  moving  cars,  loaded  and  empty; 
2lw  = weight  of  rope; 

^ ^1  + + 2 wl  = entire  moving  load. 

And  if  the  coefficient  of  friction  equals 


l}. 


H.  P.  = 


JU,  I 

^00 


X 


(l  + -p)  + 


Example.— Find  the  horsepower  for  an  endless-rope  system  5,000  ft.  long 
for  an  output  of  1,000  tons  per  day  of  10  hours  in  a flat  seam,  the  mine  cars 
having  a capacity  of  2,000  lb.  each  and  weighing  1,200  lb.  each. 

Assuming  a speed  of  winding  of  8 miles  per  hour  or  704  ft.  per  minute,  and 
for  the  coefficient  of  friction  /x  = 

r = A (l  + + 2 X 1.58  X 5,00oj  = 1,697,  say  1,700  lb. 

1 + 


H.  P.  = 


704 

5,000 

40  X 33,000 


[3,333  ( 


2X1,200\ 
2,000  ) 


+ 2 X 1.58  X 


704]  = 


36.2  H.P.  or. 


assuming  an  efficiency  for  the  engine  of  60/c, 


36.2 

.60 


= 60  H.  P. 


Inclined  Roads.— The  calculation  of  power  for  inclined  roads  is  the  same  as 
that  just  given,  excepting  that  the  work  due  to  lifting  the  coal  through  a 
height  h must  be  added  to  that  found  by  the  previous  formulas.  If  h equals 
the  elevation  due  to  the  grade  of  the  incline,  the  additional  work  of  the 
engine  due  to  hoisting  the  load  from  this  elevation  will  be  OA  and  the 
total  work  per  minute  u will  be 

u = iOL^[o^l  + ^ + 2 ic  vj  + 0 

Example.— Assuming  the  same  conditions  as  given  above,  and,  in  addi- 
tion, a rise  or  elevation  of  100  ft.  in  the  entire  length  of  the  haulage  way,  we 

have  « = 5^1^3,333(1  + -^p^)  + 2 X 1.58  X 704]  + 3,333  X 100 

= 1,528,050  ft.-lb.  per  minute  = 46.3  H.  P.,  or  assuming  an  efficiency  of  60^^ 

for  the  engine,  = 77  H.  P. 

.60 


MOTOR  HAULAGE. 

Locomotive  Haulage. — Wire-rope  haulage  is  very  efficient  in  headings,  on 
heavy  grades,  and  against  large  loads,  but  in  crooked  passages  it  entails  great 
costs  for  renewals  and  repairs.  When  the  grades  do  not  exceed  5?^  for  short 
distances  and  average  3?^  against,  or  for  short  distances  8^  and  5^  average  in 
favor  of  loads,  locomotives  have  been  found  the  most  economical  form  of 
haulage. 


MOTOR  HAULAGE. 


403 


The  chief  advantages  of  locomotive  over  rope  haulage  are  the  flexibility 
of  the  system,  it  being  able  to  serve  any  number  of  side  tracks  in  various 
parts  of  the  mine,  and  the  closeness  of  the  source  of  power  to  the  point  of 
application.  In  the  event  of  an  accident  due  to  a car  jumping  the  track,  a 
broken  wheel,  etc.,  it  often  happens  that  a large  number  of  cars  are  piled  up 
before  the  man  in  charge  outside  the  mine  is  signaled  to  stop,  whereas  with 
locomotive  haulage  the  engineer  or  trip  rider  affords  immediate  relief. 

In  high  seams  and  under  favorable  conditions,  steam  locomotives  are 
very  economical,  but  there  is  a limit  to  their  use,  for  it  is  not  well  to  fire 
while  running  in  the  mine  when  using  bituminous  coal;  hence  the  length 
of  trip  is  practically  limited  to  the  steam  furnished  with  one  firebox  of  fuel. 
On  account  of  their  many  disadvantages  and  of  the  improvements  in  the 
methods  of  using  other  forms  of  energy,  steam  locomotives  are  fast  going 
out  of  use  and  are  being  replaced  by  locomotives  operated  by  compressed 
air  and  electricity,  of  which  a number  of  types  have  been  designed  in  recent 
years,  and  which  have  been  very  successful  and  have  shown  a marked 
efficiency  over  the  mule. 

Compressed-Air  Haulage.— (See  also  page  194.)  Compressed  air  is  particularly 
applicable  in  gaseous  mines,  as  it  improves  ventilation  and  is  perfectly  safe 
under  all  conditions.  The  great  disadvantage  in  compressed-air  haulage  is 
the  size  of  the  locomotive. 

Mr.  H.  K.  Myers,  of  the  Baldwin  Locomotive  Works,  gives  the  following 
in  regard  to  compressed-air  haulage: 

In  order  that  compressed-air  locomotives  may  be  able  to  make  a fair 
length  of  run,  the  tanks  for  storage  purposes  must  necessarily  be  rather 
cumbersome,  and  constructed  to  carry  high-storage  pressures.  In  order  that 
they  may  be  designed  correctly  and  get  a minimum  of  storage  for  the 
maximum  work  expected,  it  is  necessary  to  have  a complete  profile  of  the 
proposed  haulage  road,  and  to  make  a tabulated  statement  of  the  air  con- 
sumption on  the  various  grades,  noting  the  “ cut-off”  necessary  to  produce  the 
requisite  tractive  effort.  By  making  a summation  of  these  various  amounts, 
and  adding  20^,  we  will  have  the  possible  amount  of  air  used  in  doing  cer- 
tain work  as  specified. 

It  is  necessary,  therefore,  to  provide  storage  on  the  locomotive  for  this 
amount  of  air  at  a much  greater  pressure  than  that  used  in  the  cylinders. 
In  order  that  the  locomotive  may  receive  a quick  charge  at  the  stations 
specially  provided  for  the  purpose,  it  is  necessary  to  have  stationary  storage 
of  adequate  pressure  and  capacity  for  the  purpose. 

At  the  present  time,  it  is  the  custom  to  compress  for  the  stationary  storage 
to  800  lb.,  and  to  have  the  volume  of  this  storage  at  least  double  the  tank 
capacity  of  the  locomotives  comprising  the  system.  This  allows  an  equalized 
pressure  in  the  locomotive  storage  of  approximately  600  lb. 

The  following  formula  is  useful  in  determining  the  capacity  of  stationary 
pV-\-P^ 

storage:  P'  = ^ ; in  which  V = volume  of  storage  on  locomotive; 

X = volume  of  stationary  storage  desired;  p — cylinder  pressure;  P = 
stationary  storage  pressure;  and  P'  = locomotive  storage  pressure. 

If  the  average  time  for  each  trip  is  30  minutes,  the  compressor  must  be 
able  to  compress  in  that  time  to  pressure  P,  the  calculated  amount  of  air 
required  for  one  trip  or  series  of  trips  for  the  various  locomotives  included 
in  the  haulage.  In  general,  it  is  customary  to  extend  extra-strong  pipe  into 
the  mine  and  of  such  length  and  diameter  as  to  have  the  required  volume 
for  the  stationary  storage.  There  are  times  however  when  it  would  be  found 
more  economical  to  arrange  for  tank  storage  either  inside  or  outside  the 
mine,  but  in  general,  especially  when  the  mine  is  advancing,  it  is  the  better 
practice  to  install  pipe  storage  since  it  increases  the  range  of  the  locomotive 
as  the  workings  advance. 

The  following  table  gives  the  various  tractive  efforts  of  different  sizes  of 
compressed-air  locomotives,  when  working  at  100  lb.  cylinder  pressure,  and 
various  cut-offs.  If  other  pressures  or  strokes  are  used,  the  tractive  efforts 
are  directly  proportionate.  This  table  is  calculated  by  means  of  the  formula, 

tractive  effort  = 

in  which  d = diameter  of  cylinder;  D = diameter  of  driver;  I = length  of 
stroke;  p = working  pressure  of  the  cylinders;  and  x = variable  due  to  the 
various  cut-offs. 


404 


HOISTING  AND  HAULAGE. 


Tractive  Efforts  of  Compressed-Air  Locomotives. 


Cylinder. 

Diam- 
eter of 
Driver. 

Inches. 

Weight 

on 

Driver. 

Pounds 

Tractive  Effort  for  Each  100-Lb.  Cylinder 
Pressure  at  Various  Cut-Offs. 

Diam. 

Inches. 

Stroke. 

Inches. 

7 

8 

1 

1 

3 

1 

1 

4 

1 

8 

5 

10 

24 

6,000 

1,020 

990 

920 

835 

710 

530 

325 

6 

10 

24 

8,500 

1,470 

1,425 

1,320 

1,200 

1,020 

760 

445 

7 

12 

26 

13,000 

2,200 

2,150 

1,990 

1,810 

1,540 

1,140 

700 

8 

12 

26 

18,000 

2,880 

2,750 

2,600 

2,360 

2,000 

1,510 

900 

9 

14 

26 

25,000 

4,340 

4,140 

3,840 

3,490 

2,960 

2,220 

1,350 

10 

14 

26 

32,000 

5,280 

5,150 

4,740 

4,310 

3,660 

2,630 

1,670 

11 

16 

28 

42,000 

6,770 

6,450 

5,980 

5,440 

4,620 

3,470 

2,140 

12 

16 

28 

52,000 

8,050 

7,800 

7,200 

6,550 

5,580 

4,150 

2,550 

On  account  of  certain  losses  due  to  radiation,  etc.  for  cut-oif  at  full  length 
of  stroke  in  steam  practice,  x is  taken  as  .85.  While  cylinder  surface  acts  as 
a detriment  to  the  use  of  steam,  it  acts  entirely  opposite  in  the  use  of  air, 
for  the  reason  that,  in  the  expansion  of  the  air,  very  low  temperatures  are 
produced,  and,  with  a maximum  of  cylinder  surface  exi)osed,  we  absorb  a 
maximum  of  heat  from  the  surrounding  air,  which  virtually  adds  new 
energy  to  the  air,  thus  acting  as  a reheater.  Therefore  in  air  practice,  x is 
made  .98  for  full-stroke  cut-off,  with  the  others  proportionately  high.  If 
simple-expansion  cylinders  are  used,  the  working  pressure  should  not 
exceed  130  lb.,  while,  with  compounds,  one  can  easily  use  from  180  to 
225  lb.  with  great  economy.  Where  it  is  imperative  to  have  a minimum- 
sized locomotive  storage  with  a maximum  run,  this  can  be  accomplished 
with  compound  locomotives.  Originally,  it  was  the  custom  to  lag  the  cylin- 
ders as  in  steam  practice,  but  now  it  is  found  advantageous  to  leave  them 
bare  and  to  corrugate  both  sides  and  ends  so  as  to  present  a maximum 
surface  to  the  surrounding  atmosphere  while  running,  thus  absorbing 
new  energy. 

Example.— It  is  desired  to  haul  trips  of  60  cars,  empties  weighing  2,000  lb. 
and  loads  6,000  lb.  each,  over  a track  having  the  following  profile,  and  with 
one  charge  of  air.  All  grades  are  in  favor  of  loads.  (The  following  calcu- 
lations have  been  made  with  the  slide  rule.) 


Profile  of  Road. 


Grade. 

Distance. 

Grade. 

Distance. 

Grade. 

Distance. 

1.3^ 

800  ft. 

0.30^ 

700  ft. 

2.4^ 

400  ft. 

600  ft. 

1.77^ 

1,025  ft. 

3.5^ 

425  ft. 

\.zio 

800  ft. 

0.90^ 

300  ft. 

1.2?^ 

320  ft. 

The  maximum  grade  being  3.5^,  and  the  car  friction  in  this  case  being  1^, 
the  total  resistance  when  ascending  a 3.5^  grade  due  to  cars  is,  hence, 
3.5^  -\-lfo  = 4.b<fo.  Since  it  is  desired  to  haul  60-car  trips,  and  all  grades  are 
in  favor  of  loads,  it  is  only  necessary  to  provide  a locomotive  capable  of 
hauling  60  empties  weighing  120,000  lb.  up  the  above-mentioned  grade.  The 
drawbar  pull  necessary  to  do  this  is  4.5^  of  120,000  lb.  = 5,400  lb.  In  general, 
it  will  require  a locomotive  having  a weight  on  drivers  of  5 times  the 
tractive  effort  desired  if  steel  tires  are  used,  as  is  the  practice  in  the  con- 
struction of  air  locomotives,  and  6 times  the  tractive  effort  if  cast-iron  chilled 
wheels  are  used,  as  is  the  practice  in  electric  locomotives.  We  will  there- 
fore assume  the  necessary  weight  of  the  locomotive  to  give  the  proper 
adhesion  as  32,000  lb.,  and  we  calculate  that  the  tractive  effort  necessary  to 
haul  itself  up  the  3.5^  grade  would  be  3.5^  + .5^  = 4^  (.5^  covering  the  fric- 
tion of  the  locomotive  on  the  level)  of  32,000  lb.,  or  1,280  lb.,  to  which  we 
add  the  necessary  drawbar  pull  to  haul  the  desired  load.  1,280  -I-  5,400,  and 
have  a total  tractive  effort  of  6,680,  which  is  about  the  limit  of  a locomo- 
tive on  dry  rail  with  sand. 


MOTOR  HAULAGE. 


405 


By  consulting  the  table  of  tractive  efforts  of  compressed-air  locomotives, 
we  see  that,  at  100  lb.  working  pressure,  a 10"  X 14",  26"  driver  locomotive  has 
a maximum  tractive  effort  at  | cut-off,  which  is  practically  full  stroke,  of 
5,280  lb.,  and  by  dividing  this  into  our  necessary  tractive  effort,  we  find  that 
the  necessary  working  pressure  would  be  about  130  lb. 

On  this  basis,  we  then  make  up  the  following  table  in  order  to  ascertain 
the  necessary  air  consumption: 


Grade. 

Distance. 

Going  in 
T.  E. 

With  Empties. 
Strokes.  Cut-Off, 

Cu.  In.  Air  Used. 

1.3 

800' 

3,375 

120 

1. 

126,000 

2.0 

600' 

4,450 

80 

1 

176,000 

1.3 

800' 

3,375 

120 

126,000 

0.3 

700' 

1,830 

105 

I 

55,125 

1.77 

1,025' 

4,100 

150 

315,000 

0.9 

300' 

2,750 

40 

A 

42,000 

2.4 

400' 

5,075 

60 

1 

157,500 

3.5 

425' 

6,760 

65 

V 

239,000 

1.2 

320' 

2,220 

50 

1. 

62,500 

0.3 

700' 

Coming 

2,600 

Out  Loaded.* 

105  i 

110,000 

20^  additional 

1,399,125 
279,825 

Total 1,678,950  cu.  in. 


This  equals  975  cu.  ft.  at  130  lb.  pressure  used  in  hauling  the  required  loads 
on  a single  round  trip.  Since  we  should  return  to  the  starting  point  with 
130  lb.  in  the  locomotive  storage,  it  is  evident  that  the  volume  of  the  tanks 
shall  allow  for  the  use  of  975  cu.  ft.  in  addition  to  1 volume  at  130  lb. 

Let  V = volume  of  storage  on  locomotive;  P'  = pressure  of  storage  on 
locomotive;  p = working  pressure;  V'  = volume  at  working  pressure  nec- 
essary to  do  the  work  required. 

Then  the  product  of  the  volume  of  the  locomotive  storage  by  its  pressure 
must  equal  the  sum  of  the  volume  necessary  to  do  the  work  required 
multiplied  by  the  working  pressure,  and  the  locomotive  storage  volume  by 
the  working  pressure,  thus, 

P'F  = i)F  + pF',  or,F=  F' -r/ — . 

P'  — « 

130 

If  P'  = 650,  then  F = 975  X = 244  cu.  ft. 

ooO  — 130 


With  one  locomotive,  making  trips  every  30  minutes, we  must  arrange  for 
a compressor  capable  of  compressing  975  cu.  ft.  at  130  lb.  in  this  time.  Since 
it  is  customary  to  rate  compressors  at  their  capacity  in  free  air  per  minute, 
975  X 130 

the  above  is  equivalent  to  — ^ ^ = 288  cu.  ft.  free  air  per  minute. 

This  must  be  compressed  to  800  lb.  in  the  compressor,  and  stored  in 
stationary  storage.  If  X is  the  volume  of  the  stationary  storage, 

pF+PX 
F+X  • 


^ CT  or  X = 244  X = 846  <m.  ft. 


The  length  of  the  haulage  is  5,370  ft.,  hence  the  cross-section  of  the  pipe 

846 

necessary  to  furnish  the  requisite  storage  is  = .157  sq.  ft. 

From  the  following  table,  this  would  require  a 5F'  pipe,  but  for  practical 
purposes  it  is  possible  that  a 5"  pipe  would  be  selected. 


* Returning  with  loads,  it  is  possible  that  there  is  only  one  grade  that  the  trip  will  have 
te  he  ^ 


406 


HOISTING  AND  HAULAGE, 


Standard  Steam  and  Extra-Strong  Pipe  Used  for  Compressed-Air 
Haulage  Plants. 


Trade 

Diam- 

eter. 

In. 

Cu.  Ft.  in 

1 Lineal 
Ft. 

Lineal  Ft. 
Necessary 
to  Make 

1 Cu.  Ft. 

Steam. 

Extra  Strong. 

Trade 

Diam- 

eter. 

In. 

Thick- 

ness. 

Weight 
per  Ft. 

Thick- 

ness. 

Weight 
per  Ft. 

2 

.0218 

45.41 

.15 

3.61 

.22 

5.02 

2 

2i 

.0341 

29.32 

.20 

5.74 

.28 

7.67 

2k 

3 

.0491 

20.36 

.21 

7.54 

.30 

10.20 

3 

3i 

.0668 

15.00 

.22 

9.00 

.32 

12.50 

3i 

4 

.0873 

11.52 

.23 

10.70 

.34 

15.00 

4 

4i 

.1105 

9.05 

.24 

12.30 

.35 

17.60 

5 

.1364 

7.33 

.25 

14.50 

.37 

20.50 

5 

5i 

.1650 

6.06 

.26 

16.40 

.40 

24.50 

6 

.1963 

5.10 

.28 

18.80 

.43 

28.60 

6 

From  the  following  table  we  see  that  it  would  require  2.88  X 32.5  = 
93.6  H.  P.;  hence,  we  would  be  compelled  to  arrange  for  a boiler  capacity 
of  practically  100  H.  P.,  provided  we  used  a three-stage  compressor,  as  is  the 
general  custom. 

Horsepower  Necessary  to  Compress  100  Cu.  Ft.  of  Free  Air  to  Various 


Pressures  and  With  Two-,  Three-,  and  Four-Stage  Compressors. 


Gauge 

Pres- 

sure. 

Horsepower  Necessary. 

Gauge 

Pressure. 

Horsepower  Necessary. 

Two- 

Stage. 

Three- 

Stage. 

Four- 

Stage. 

Two- 

Stage. 

Three- 

Stage. 

Four- 

Stage. 

100 

15.7 

15.2 

14.2 

900 

36.3 

33.7 

31.0 

200 

21.2 

20.3 

18.8 

1,000 

37.8 

34.9 

31.8 

300 

24.5 

23.1 

21.8 

1,200 

39.7 

36.5 

33.4 

400 

27.7 

25.9 

24.0 

1,400 

41.3 

37.9 

34.5 

500 

29.4 

27.7 

25.9 

1,600 

43.0 

39.4 

35.6 

600 

31.6 

29.5 

27.4 

1,800 

44.5 

40.5 

36.7 

700 

33.4 

31.2 

28.9 

2,000 

45.4 

41.6 

37.8 

800 

34.9 

32.5 

30.1 

2,500 

43.0 

39.0 

Electric  Haulage.— Mr.  H.  K.  Myers  says  in  regard  to  mine  haulage  by 
electricity:  In  general,  it  costs  from  6 to  10  cents  per  ton  to  deliver  coal 
from  face  of  workings  to  shaft,  slope,  or  tipple,  where  the  haul  is  1 mile  and 
the  tracks  approximately  level;  yet  I know  three  mines  that  at  present  haul 
from  parting  with  the  trolley  system,  the  miner  delivering  from  face  of 
room,  making  an  average  round  trip  of  9,000  ft.,  at  a total  cost  of  1 cent  per 
ton.  These  mines  have  never  had  a mule  in  them,  and  it  would  be  almost 
an  impossibility  to  introduce  them,  for  the  reason  that  the  seam  is  of  such 
thickness  that  the  clearance  between  tie  and  roof  is  only  about  4 ft.  Since 
the  advent  of  the  electric-mining  locomotive,  there  has  been  a change  in 
the  mine  wagons  universally  used.  Formerly  it  was  customary  to  find  as 
much  as  60  lb.  per  ton  car  resistance  on  the  level,  while  at  present  it  is  as 
low  as  15  lb. 

In  dimensioning  mining  locomotives,  it  is  customary  to  make  the  weight 
from  6 to  8 times  the  necessary  tractive  effort,  dependent  entirely  on  the 
nature  of  the  work.  If  the  work  is  constant  and  a maximum,  then  the 
weight  will  be  only  6 times  the  torque  of  the  motors,  while  if  the  work  is 
intermittent  with  a short-time  maximum  tractive  effort,  then  the  factor 
will  be  8.  The  weight  of  an  electric  locomotive  running  at  a speed  of  6 to 


MOTOR  HAULAGE. 


407 


8 miles  per  hour  with  intermittent  load  may  also  be  expressed  on  a basis  of 
400  lb.  for  each  rated  horsepower  of  the  motor,  and  the  weight  should  be 
8 times  the  rated  drawbar  pull,  regardless  of  speed.  For  continuous  work, 
these  weights  should  be  decreased  25^. 

Deawbar  Pull  on  Various  Grades  for  Different  Sized  Locomotives. 


Horse- 

power. 

Weight. 

Grades. 

Level. 

l^c 

2fc 

Sfc 

4/. 

5fe 

6fo 

10 

4,000 

500 

460 

420 

380 

340 

300 

260 

20 

8,000 

1,000 

920 

840 

760 

680 

600 

520 

30 

12,000 

1,500 

1,380 

1,260 

1,140 

1,020 

900 

780 

50 

20,000 

2,500 

2,300 

2,100 

1,900 

1,700 

1,500 

1,300 

70 

28,000 

3,500 

3,220 

2,940 

2,660 

2,380 

2,100 

1,820 

100 

40,000 

5,000 

4,600 

4,200 

3,800 

3,400 

3,000 

2,600 

In  mines  it  is  found  that  the  friction  between  wheel  and  rail  is  less  than 
on  the  surface,  due  to  dampness  and  powdered  coal  on  the  rail.  The  tractive 
efforts  with  chilled  wheels  is  usually  considered  i of  the  weight.  The 
table  on  page  408  and  diagram  on  page  409  give  hauling  capacities  of 
locomotives  in  tons  of  2,000  lb. 

For  maximum  continuous  work,  it  is  necessary  to  have  a grade  such 
that  the  efforts  to  haul  the  same  number  of  empty  wagons  as  loaded 
are  equal.  With  the  car  resistance  considered  l<fo  and  the  loaded  cars  weigh- 
ing 3 times  as  much  as  the  empties,  this  is  found  to  be  i of  Ifo.  The  most 
critical  point  in  the  designing  of  mining  locomotives  is  to  make  the  limiting 
dimensions  a minimum.  The  demands  for  various  dimensions  are  wonder- 
ful. The  headings  in  mines  are  never  of  more  generous  proportions  than 
really  necessary,  and  all  clearances  a minimum.  The  minimum  dimensions 
for  mining  locomotives  are  as  small  as  2 ft.  for  wheel  base,  8 ft.  for  length 
over  all,  and  3 ft.  width.  Scarcely  two  orders  carry  the  same  dimensions, 
and  it  is  impossible  to  have  any  kind  of  a standard.  In  consequence  of  this, 
it  is  necessary  to  have  a great  variety  of  motors  suitable  for  gauges  as  nar- 
row as  18  in.  and  for  wheels  as  small  as  20  in.  in  diameter.  With  such  a 
variety,  it  becomes  possible  to  construct  a locomotive  weighing  40,000  lb. 
on  3'  gauge,  having  the  width  over  all  62  in.,  height  35  in.,  and  length 
12  ft.  In  construction,  it  is  necessary  to  have  the  most  modern  form  of 
motors  and  the  most  rigid  mechanical  construction. 

The  motors  now  used  are  of  the  best  possible  construction  and  efficiency. 
They  are  of  the  slow-speed  street-car  type,  6 to  8 miles  per  hour  winding, 
and  range  in  size  from  4 to  50  H.  P.  It  is  customary  to  use  the  rheostatic 
type  of  controller  for  mining  locomotives,  on  account  of  its  small  dimensions 
and  apparent  efficiency  for  this  class  of  work,  but  it  is  doubtless  but  a short 
time  until  a very  compact  form  of  series-parallel  type  will  be  devised.  On 
account  of  the  use  of  this  rheostatic  controller,  it  becomes  necessary  to  pro- 
vide for  large  diverter  capacity,  and  since  the  locomotive  is  designed  for  the 
maximum  tractive  effort,  it  is  hardly  ever  possible  to  run  without  resist- 
ance and,  hence,  a large  amount  of  current  must  be  dispersed  with  the 
consequent  heating.  If  the  motors  are  overloaded,  they  heat  rapidly,  this 
heating  varying  as  the  square  of  the  current.  A motor  that  has  a rating  of 
40  amperes  for  regular  work,  if  worked  for  3 minutes  at  100  amperes,  should 
not  be  subjected  to  such  a strain  oftener  than  once  in  18f  minutes,  as  shown 
by  the  following  equation: 

40'  X ir  = 3 X 1002;  x = 18^  minutes. 

Using  the  same  problem  given  under  compressed-air  locomotives,  in 
which  the  maximum  tractive  effort  was  6,760  lb.,  we  find  from  the  table  of 
drawbar  pulls  that  a locomotive  equipped  with  two  50  H.  P.  motors  (equals 
100  H.  P.)  will  carry  the  load  with  an  overload,  these  motors  being  rated  for 
continuous  work  at  approximately  32  amperes  of  500  volts. 

Using  the  formula = 64,  in  which  t — various  times  at  which 


408 


HOISTING  AND  HAULAGE. 


various  amounts  a of  current  are  used  on  the  corresponding  grades,  2 the 
summation  of  the  items  t calculated  for  each  section  or  grade,  and  T = 
total  time  that  should  he  taken  for  each  trip,  we  calculate  the  following 
table; 


Grade. 

Hist. 

T.  E. 

Time. 

Minutes. 

Amperes. 

ta^ 

1.30 

800 

3,375 

1.5 

114 

Empties. 

19,600 

2.00 

600 

4,450 

1.1 

134 

19,900 

1.30 

800 

3,375 

1.5 

114 

19,600 

.30 

700 

1,830 

4,100 

1.3 

74 

7,100 

1.77 

1,025 

2.0 

128 

32,800 

.90 

300 

2,750 

.6 

100 

6,000 

2.40 

400 

5,075 

.8 

148 

17,300 

3.50 

425 

6,760 

.8 

182 

26,500 

1.20 

320 

2,220 

\6 

86 

4,400 

.30 

700 

2,600 

1.3 

96 

Loads. 

13,900 

167,100  = 

= 64;  4,096  T = 167,100;  T = 40. 

By  this  means  we  can  make  60-car  trips  every  40  minutes  without  injury 
to  the  motors,  based  upon  a speed  of  6 miles  per  hour.  (See  also  page  215.) 

Speed  of  haulage  depends  on  the  system  of  haulage  used  and  on  the  con- 
dition of  the  haulage  road.  The  law  in  Pennsylvania  provides  for  a speed  of 
haulage  not  over  6 miles  per  hour,  and  this  is  the  speed  at  which  electric  and 

Hauling  Capacity  of  Electric  Locomotives. 


Horsepower. 

Weight. 

Drawbar  Pull 
on  Level. 

Frictional  Car 
Resistance  per 
Ton  on  Level. 

Grades. 

(D 

> 

<D 

¥ 

2^ 

2^ 

3^ 

4^ 

5^ 

10 

4,000 

500 

20 

23 

15 

10 

8 

6.3 

5.2 

4.2 

3.5 

3.0 

2.2 

1.6 

30 

15 

11 

8.4 

6.7 

5.4 

4.5 

3.8 

3.2 

2.7 

2.0 

1.5 

40 

12 

9 

7 

5.7 

4.7 

4.0 

3.4 

3.0 

2.5 

1.8 

1.4 

20 

8,000 

1,000 

20 

46 

29 

21 

16 

13 

10.3 

8.4 

7.1 

6.0 

4.3 

3.1 

30 

31 

22 

17 

13 

11 

9 

7.5 

6.4 

5.4 

4.0 

3.0 

40 

23 

18 

14 

11 

9.5 

8 

6.8 

5.9 

5.0 

3.7 

2.8 

30 

12,000 

1,500 

20 

69 

44 

32 

24 

19 

15 

13 

10.7 

9.0 

6.5 

4.7 

30 

43 

33 

25 

20 

16 

13 

11 

9.6 

8.2 

6.0 

4.4 

40 

34 

26 

21 

17 

14 

12 

10 

8.8 

7.5 

5.6 

4.1 

60 

20,000 

2,500 

20 

115 

73 

52 

40 

32 

26 

21 

18 

15 

11 

7.9 

30 

77 

55 

42 

33 

27 

22 

19 

16 

14 

10 

7.3 

40 

58 

44 

35 

29 

24 

20 

17 

15 

13 

9.3 

6.8 

70 

28,000 

3,500 

20 

161 

103 

74 

56 

44 

36 

30 

26 

21 

15 

11 

30 

107 

77 

59 

47 

38 

31 

26 

22 

19 

14 

10 

40 

81 

61 

50 

40 

83 

28 

24 

20 

18 

IS 

9.6 

100 

40,000 

5,000 

20 

230 

147 

105 

80 

63 

62 

42 

36 

30 

22 

16 

30 

153 

110 

84 

67 

54 

45 

38 

32 

27 

20 

16 

40 

115 

88 

70 

57 

47 

40 

1 

34 

29 

25 

19 

14 

MOTOR  HA  ULAGE. 


409 


compressed-air  haulages  are  usually  calculated  and  at  which  loaded  trips 
are  usually  run.  Empty  trips  are  usually  run  at  a slightly  higher  speed. 

The  speed  for  tail-rope  haulage  is  given  by  three  prominent  makers  of 
such  plants,  as  follows:  (a)  600  to  700  ft.  per  minute;  (6)  8 to  10  miles  per 
hour;  (c)  6 to  8 miles  per  hour. 

The  speed  for  endless-rope  haulage  is  given  by  the  same  makers  as  (a) 
140  to  150  ft.  per  minute;  (6)  1 to  2 miles  per  hour;  (c)  150  to  200  ft.  per 
minute.  A slow  speed  for  endless  rope  is  to  be  preferred  as  being  much 
more  economical  in  the  wear  of  the  rope  and  cars,  and  many  prefer  a single- 
car system  to  a trip  system,  thus  doing  away  with  the  trip  rider.  By  han- 
dling* the  cars  singly  or  even  in  trains  of  two  and  at  a slow  speed,  the  load 
can  be  picked  up  without  any  slippage  of  the  rope  through  the  grips;  while 
if  trains  of  from  12  to  25  cars  are  used,  with  the  rope  traveling  3 to  miles 
per  hour,  it  is  impossible  to  pick  up  the  load  without  having  the  rope  slip 


through  the  grip,  thus  heating  the  rope  and  cutting  it.  The  slow-speed, 
single-car  or  small-train,  system  requires  more  cars,  but  this  is  counterbal- 
anced by  the  life  of  the  cars  and  rope.  Those  that  have  tried  both  systems 
prefer  the  slow-speed  small  trip  to  the  high-speed  large  trip. 

It  has  been  found  in  general  practice  that  the  maximum  pulling  power 
of  a mule  as  well  as  a locomotive  is,  approximately,  one-fifth  its  weight,  or, 
in  other  words,  a locomotive  will  pull  as  much  as  the  same  weight  of  mules 
will  pull,  and  at  a speed  about  three  times  as  great. 

Cost  of  Haulage. — So  much  depends  on  local  considerations  that  it  is 
difficult  to  give  costs  of  haulage  that  will  be  of  service.  Mule  haulage 
has  been  given  as  costing,  under  different  conditions,  5.74  cents  and  7.92 
cents  per  ton-mile,  and  in  other  locations  2.35  cents,  2.95  cents,  and  7.15  cents 
per  ton  of  coal  hauled. 

The  Berwind-White  Coal  Mining  Co.,  at  Windber,  Pa.,  uses  30  electric  loco- 
motives at  various  mines,  which  average,  approximately,  400  tons  per  day  of 
9 hours,  per  locomotive,  over  an  average  haul  of  2 miles  for  the  round  trip. 
The  approximate  cost  for  operating  one  of  these  locomotives,  including  the 
wages  of  motorrhan,  trip  rider,  and  proportion  of  power-house  expense,  is 
about  ^6.00  per  day,  or  cents  per  ton  of  coal  haul  per  mile.  If  the  total 
load,  including  weight  of  cars,  is  considered,  it  figures  f of  1 cent  per  ton  per 
mile.  These  figures  do  not,  however,  include  grades,  which  is  an  important 
factor  in  equating  costs  per  ton  per  mile.  In  these  mines  there  are  no  mules 


410 


HOISTING  ANN  HAULAGE. 


whatever,  the  locomotives  distributing  the  empty  cars  to  room  partings,  for 
the  men  to  push  to  the  face.  If  the  haul  is  done  between  side  tracks  and 
under  similar  grade  conditions,  the  same  locomotives  could  easily  handle 
1,000  to  1,200  cars  per  day. 

Mr.  F.  J.  Platt,  of  Scranton,  Pa.,  gives  the  following  comparative  costs  of 
electric  and  mule  haulage  per  ton  of  coal  hauled  and  under  approximately 
the  same  conditions  in  the  same  mine: 


Name  of  Mine. 

Mule  Haulage. 
Cents. 

Electric  Haulage. 
Cents. 

Green  Ridge  Colliery 

7.15 

2.76 

New  York  & Scranton  Coal  Co 

6.58 

2.62 

New  York  & Scranton  Coal  Co 

2.35 

1.07 

Mt.  Pleasant  Colliery 

2.95 

1.27 

Hillside  Coal  & Iron  Co 

10.77 

4.56 

Hillside  Coal  & Iron  Co. 

9.10 

4.65 

The  following  costs  of  electric  haulage,  per  ton  of  material  hauled,  are 
given  in  the  catalogue  of  the  General  Electric  Co.: 


Name  of  Mine. 

Mule  Haulage. 
Cents. 

Electric  Haulage. 
Cents. 

Wythe  Lead  & Zinc  Co 

10 

2.56 

Blossburg  Coal  Co 

7.9 

Cleveland-Clitfs  Iron  Co.  ('94,  '95,  ’96) 

3.9,  4.5,  4.8 

At  Carbondale,  Pa.,  compressed-air  locomotives  have  hauled  coal  for 
1.5  cents  per  ton-mile,  at  Mill  Creek,  Pa.,  for  3.77  cents  per  ton-mile,  and 
at  Glen  Lyon,  Pa.,  for  1.89  to  1.93  cents  per  ton-mile. 


MINE  ROADS  AND  TRACKS. 

Underground  or  mine-car  tracks  should  be  solidly  laid  on  good  sills,  rest- 
ing on  the  solid  floor  of  the  mine.  They  should  be  well  ballasted,  and 
should  have  good  clean  gutters  on  the  lower  side  of  the  entry,  so  that  the 
rails  may  be  protected  as  much  as  possible  from  the  action  of  the  mine 
water.  Much  of  the  following  data,  on  mine  roads  is  based  on  an  article  on 
“Mine  Roads,”  by  Mr.  H.  L.  Auchmuty,  “Mines  and  Minerals,”  March, 
1900. 

Grade. — The  grades  depend  entirely  on  circumstances,  but,  when  possible, 
the  grade  should  be  in  favor  of  the  load,  and  should  be  at  least  5 in.  in  100  ft. 
to  insure  flow  in  the  gutters  alongside  the  track.  On  main  roads,  where 
wagons  having  a capacity  of  1,5  to  2.5  tons  are  hauled  by  animal  power,  the 
grades  should  not  exceed  Vp  to  2^  in  favor  of  the  loaded  wagon.  Such  a rate 
of  grade  provides  for  an  easy  return  haul  of  the  empty  trip  without  wearing 
out  the  stock,  and  likewise  insures  good  drainage.  With  grades  under  1^, 
unless  the  ditches  are  kept  perfectly  clean,  the  drainage  is  apt  to  be  sluggish, 
and  then,  in  low  places,  we  are  sure  to  find  a wet  and  muddy  track,  which 
is  a great  source  of  waste  energy. 

Where  hauling  is  done  by  locomotives,  whether  by  compressed  air  or 
steam,  the  adverse  grades  should  not  be  over  1.556  to  2.5^6  if  it  can  possibly  be 
avoided.  When  gradients  are  heavy,  too  great  a percentage  of  the  tractive 
power  of  the  locomotive  is  consumed  in  drawing  itself  up  the  grade. 

Ties  should  be  spaced  about  2 ft.  apart,  center  to  center,  making  15  to  a 
30'  rail.  The  rail  should  be  well  spiked  to  the  ties  with  four  spikes  to  each 
tie,  the  joint  between  two  rails  on  one  side  of  the  track  being  located  about 
midway  between  two  joints  on  the  opposite  rail.  Care  should  be  taken  in 
locating  the  spikes  that  they  are  not  all  in  the  center  of  the  tie.  thereby 


MINE  ROADS  AND  TRACKS. 


411 


causing  a tendency  to  split  the  same.  It  is  best  to  place  them  each  side  of 
the  center  with  two  spikes  between  the  rails,  on  one  side,  and  the  two  spikes 
on  the  outside  of  the  rail  on  the  other  side  of  the  center  of  the  tie.  With  the 
spikes  so  located,  there  is  no  tendency  for  the  tie  to  slide,  as  there  is  if  an 
outside  and  inside  spike  are  on  the  same  side  of  the  center  of  the  tie.  Ties 
having  a 5 in.  face  and  4 in.  deep  by  ft.  in  length  should  be  used  for  the 
ordinary  sizes  of  rail,  i.  e.,  16  lb.  to  20  lb.,  and,  in  general,  the  thickness 
should  be  sufficiently  great  that  the  spike  does  not  pass  entirely  through  the 
tie,  as  then  its  holding  power  is  greatly  diminished.  On  haulage  tracks 
where  35-lb.  to  40-lb.  rail  is  used,  the  ties  should  be  at  least  5 in.  deep  and 
have  a face  of  6 in.,  the  ties  ordinarily  used  for  lighter  sizes  of  rails  being 
entirely  too  thin  for  rails  of  this  weight,  as  a larger  spike  than  the  ordinary 
3 in.  X f iu.  is  required  to  securely  hold  the  rails  to  place.  The  ends  of  the 
ties  should  be  lined  up  along  one  side  of  the  track,  so  that  they  are  all  the 
same  distance  from  the  rail,  and,  with  each  tie  placed  at  right  angles  to 
the  rail  as  it  should  be,  we  have  a well-spaced,  neat-looking  track,  which, 
when  well  tamped  with  the  ballast,  is  perfectly  solid.  On  curves,  the  ties 
should  be  laid  so  as  to  form  radii  of  the  curves  of  the  track. 

Rails.— The  weight  of  rail  to  be  chosen  in  any  individual  case  depends 
entirely  on  the  weight  of  wagons  used,  and  the  motive  power.  For  wagons 
whose  capacity  is  about  1.5  tons,  the  weight  of  rail,  when  the  motive  power  is 
live  stock,  should  not  be  less  than  16  lb.  per  yd.,  while  for  wagons  having  a 
capacity  of  2 tons  or  over,  a 20-lb.  rail  should  be  used.  There  is  no  economy 
in  using  a very  light  rail,  as  the  base  is  gradually  eaten  away  by  the  mine 
water  when  it  comes  in  contact  with  the  metal,  and  in  the  case  of  a heavy 
sectioni)f  rail,  it  will  be  much  longer  before  the  rail  becomes  weakened. 

On  main  roads,  where  haulage  machinery  of  one  kind  or  another  is  used, 
the  weight  of  rail  for  2-ton  wagons  should  be  from  25  lb.  to  35  lb.  per  yd., 
and  on  steep  slopes  as  high  as  40  lb.  per  yd. 

In  the  case  of  locomotive  haulage,  authorities  claim  that  the  weight  of  rail 
should  be  regulated  by  allowing  1 ton  for  each  driver  for  each  10  lb.  weight 
of  rail  per  yd. 

Gauge. — The  gauge  of  the  track  in  coal  mines  should  not  be  less  than  30  in. 
nor- more  than  48  in.  A mean  between  these  two,  or  a gauge  of  from  38  in.  to 
42  in.  is  desirable,  because  it  combines,  to  a certain  extent,  the  advantages 
claimed  for  the  extremes.  The  advocates  of  broad  gauges  believe  that  the 
greater  stability  of  the  track  and  the  consequent  reduction  in  haulage  expen- 
ses, the  increased  capacity  of  the  broad-gauged  mine  cars,  the  reduction  in 
the  outlay  for  rolling  stock,  and  for  repairs  to  the  same,  more  than  equal 
the  disadvantages  of  broad  as  compared  to  the  narrow  gauges. 

Advocates  of  the  narrow  gauges  think  that  the  ease  of  hauling  around 
sharp  curves,  the  reduction  in  cost  of  construction,  and  the  use  of  mine  cars 
with  inside  wheels,  are  advantages  greater  than  those  advanced  by  the 
advocates  of  the  broad  gauges.  An  allowance  of  about  \ in.  should  always  be 
made  between  the  wheel  gauge  and  the  track  gauge.  By  so  doing,  the  resist- 
ance to  hauling  is  greatly  overcome,  and  there  is  no  binding  of  the  wagons 
on  the  track,  hence  a less  likelihood  of  having  derailed  wagons.  With  an 
average  running  wagon,  there  is  a resistance  of  15  to  20  lb.  per  ton  tractive 
force  on  a level  track,  which  would  be  equal  to  the  resistance  occasioned  by 
a grade  of  .75^  to  1^,  and  with  wagons  that  bind  on  the  track,  this  resistance 
is  greatly  increased. 

Curves  should  be  of  as  large  a radius  as  possible,  and  never,  if  possible,  of 
less  radius  than  25  ft.  The  resistance  of  curves  is  very  considerable.  The 
less  the  radius  of  the  curve,  and  the  greater  the  length  of  the  curved  track 
occupied  by  the  trip,  or  train,  the  greater  the  resistance.  The  length  of 
wheel  bases  of  the  cars,  the  condition  of  rolling  stock  and  of  the  track,  and 
the  rate  of  speed,  all  influence  the  resistance,  and  there  is  no  formula 
that  will  apply  to  all  cases.  In  practice  on  surface  railroads,  engineers 
compensate  for  curves  on  grades  at  the  rate  of  ft.  in  each  hundred  feet 
for  each  degree  of  curvature,  the  grade  being  stated  in  feet  per  hundred. 
In  mine  work,  this  compensation  is  not  made,  as  the  gain  will  not  pay  for 
the  labor  that  must  necessarily  be  employed  to  do  work  in  a thoroughly 
scientific  manner. 

Sharper  curves  can  be  used  on  narrow-gauge  roads  than  on  broad-gauge 
roads,  because  the  difference  in  length  of  the  inner  and  outer  rails  on  curves 
on  the  same  degree  is  not  quite  so  great,  and  also  because  the  wheel  bases 
of  cars  are  less.  The  track  should  be  spread  about  i in.  on  easy  curves,  and 


412 


HOISTING  AND  HAULAGE. 


on  very  short  curves  about  1 in.,  or  as  much  as  the  tread  of  the  wheels  will 
permit.  A good  rule  is  to  widen  the  track  in.  for  each  of  curvature. 
Short  and  irregular  curves  are  to  be  avoided  whenever  possible,  as  they' 
increase  the  load  and  are  destructive  to  rails  and  rolling  stock.  When  a sharp 
curve  is  necessary,  the  rail  should  be  bent  to  the  right  curvature  by  a 
portable  rail  bender,  or  by  a jack  and  clamps. 

To  Bend  Rails  to  Proper  Arc  for  Any  Radius.— Rails  are  usually  30  ft.  long,  and 
the  most  convenient  chord  to  use  in  bending  mine  rails  is  10  ft. 

Then,  having  the  radius  and  chord,  we  find  the  rise  of  middle  ordinate  by 
squaring  the  radius,  and  from  it  take  the  square  of  ^ the  chord.  Extract  the 
square  root  of  the  remainder  and  subtract  it  from  the  radius;  the  result  will 
be  the  rise  of  the  middle  ordinate.  Thus,  having  a radius  of  30  ft.  and  a 
chord  of  10  ft.,  the  middle  ordinate  will  be 

30  - 1/302  - 5-^  or  0.42  ft. 

Rail  Elevation.— In  elevating  rails  on  curves,  consider  whether  the  hauling 
is  to  be  done  by  a rope,  or  by  a locomotive,  or  electric  motor.  For  either  of 
the  latter,  elevate  the  rail  on  the  outside  of  the  curve;  but  for  the  first, 
elevate  the  inner  rail,  since  as  the  power  is  applied  by  a long  flexible  rope, 
there  is  always  a tendency  for  both  rope  and  wagons  to  take  the  long  chord 
of  the  curve  as  soon  as  the  point  of  curve  is  reached.  On  slope  haulages, 
operated  by  a single  rope,  when  the  weight  of  the  wagons  traveling  on  the 
grade  of  the  slope  is  sufficient  to  draw  the  rope  off  the  hoisting  drum,  the 
rails  on  curves  should  be  elevated  on  the  outside,  the  effect  then  being 
similar  to  that  of  a locomotive,  i.  e.,  the  centrifugal  force  teqds  to  throw  the 
wagon  to  the  outside  of  the  track.  In  such  cases,  the  elevation  should  be 
moderate  so  as  not  to  interfere  with  the  trip  when  drawn  out  again  by  the 
rope— the  opposite  effect  being  then  experienced.  On  an  18°  curve  (319  ft. 
radius),  an  elevation  of  2 in.  or  3 in.  in  the  outer  rail,  where  the  haulage  was 
by  slope  rope,  has  never  given  any  trouble  in  operating.  In  general,  the 
elevation  of  rail  necessary  for  different  degrees  of  curvature  for  a 42"  tracl^  • 
gauge  should  be  made  in  accordance  with  the  following  table: 

Table  of  Elevations. 


For  outer  rail  of  curves  for  a speed  of  10  to  15  miles  per  hour  and  a gauge 
of  track  of  42  in.  for  locomotives;  or  for  slope  haulages  where  cars  run  down 
grade  by  gravity. 


Degree 

of 

Curve. 

Radius 

of 

Curve  (Ft.). 

Elevation 
of  Outer 
Rail  (In.). 

Degree 

of 

Curve. 

Radius 

of 

Curve  (Ft.). 

Elevation 
of  Outer 
Rail  (In.). 

1 

5,729.6 

i 

8 

10.0 

573.7 

H 

2 

2,864.9 

12.0 

478.3 

8 

1,910.1 

T^e 

15.0 

383.1 

U 

4 

1,432.7 

18.0 

319.6 

111 

5 

1,146.3 

20.0 

287.9 

2^ 

6 

955.4 

H 

57.3 

100.0 

4i 

7 

819.0 

95.5 

60.0 

4i 

8 

716.8 

T 

114.6 

50.0 

4i 

9 

637.3 

1 

No  elevation  should  be  over  4i  in.,  which  would  be  equivalent  to  an 
elevation  of  6 in.  for  standard  track  gauge  of  4 ft.  9 in.,  the  latter  being  con- 
sidered as  the  maximum  for  standard  gauge. 

Rollers. — The  rollers  on  level  tracks  should  not  be  more  than  about  20  ft. 
apart  to  properly  carry  the  rope,  and  on  gravity  slopes  where  the  lower  end 
of  the  slope  gradually  flattens  oft*  the  distance  between  rollers  should  not 
be  more  than  12  to  15  ft.,  as  this  spacing  allows  the  trip  of  wagons  to  run 
much  farther,  by  keeping  the  rope  well  off  the  ties,  than  if  they  are  farther 
apart,  thereby  not  supporting  the  rope,  and  causing  a great  amount  of 
friction  between  the  rope  and  the  ties.  With  tracks  in  fair  shape  and  rollers 
12  to  15  ft.  apart,  the  resistance,  due  to  the  rope  in  running  empty  wagons 
down  grades  varying  from  to  6.2^,  varied  from  ^ to  159^  of  the  weight  of 
ropes  by  actual  trial. 


MINE  ROADS  AND  TRACKS. 


413 


Fig.  7, 


Switches.— The  switch,  or  latch,  most  commonly  used  in  mines  is  shown 
in  Fig.  7.  When  the  branch  or  siding  is  in  constant  use,  an  ordinary  railway 
frog  is  substituted  for  the  bar  h.  The  latches  a,  a are  wedge-shaped  bars  of 
iron  (made  as  high  as  the  rail)  with  an  eye  in  the  thick  end.  They  are 

sometimes  connected  together  by  a rod 
attached  to  a lever  so  that  they  may 
both  be  moved  at  once  from  the  side  of 
the  track,  or  by  a person  situated  some 
distance  away.  This  switch  is  made  self- 
closing or  automatic  whenever  it  is 
necessary  to  run  all  the  cars  off  at  the 
branch  (the  switch  then  being  used 
only  to  admit  cars  to  the  main  track) 
by  attaching  the  latches  through  a bar 
or  lever  to  a metallic  spring,  a stick  of 
some  elastic  wood,  or  a counter  weight, 
to  pull  them  back  into  a certain  position 
whenever  they  have  been  pushed  to  one 
side  or  the  other  by  the  passage  of  a car 
on  the  main  track.  Figs.  10, 11, 12,  and  13  show  some  of  the  applications  of 
these  spring  latches  or  automatic  switches. 

A modification  of  this  switch  is  shown  in  Fig.  8,  which  represents  a form 
of  double  switch.  These  latches  are  set  by  the  drivers,  who  kick  them  over 
and  drop  a small  square  of  plate  iron  between  them  to  hold  them  in  place. 
This  switch  costs  more  than  the  other  style  and  is  better  adapted  to  outside 
roads  than  to  inside  roads. 

The  ordinary  movable  rail  switch  in  common  use  on  all  surface  railways 
is  sometimes  used  in  mine  roads.  It  is  commonly  used  in  slopes  arranged  as 
shown  by  Fig.  12,  to  replace  latches  set  by  the 
car,  and  is  also  largely  used  in  outside  roads. 

For  crossings,  ordinary  railway  frogs  and 
grade  crossings  are  sometimes  used,  as  is  also 
a small  turntable,  which  then  answers  two  « 
purposes.  More  frequently  the  plan  shown 
in  Fig.  9,  in  which  four  movable  bars  are 
thrown  across  the  main  track  whenever  the 
other  road  is  to  be  used,  is  adopted. 

The  subordinate  road  is  built  from  li  to  2 
in.  higher  than  the  main  road,  to  allow  the 
bars  to  clear  the  main-track  rails. 

Turnouts.— On  gangways  or  headings  used  as  main  haulage  roads,  turnouts 
^ould  be  constructed  at  convenient  intervals  to  allow  the  loaded  and 
empty  trips  to  pass.  These  turnouts  should  be  long  enough  to  accommodate 
from  5 or  6 up  to  15  or  20  cars.  The  switches  at  each  end  may  be  made  self- 
acting so  that  the  empty  trip,  coming  in,  is  thrown  on  the  turnout,  and  in 
running  out  on  the  main  track  at  the  other  end,  the  loaded  cars  open  the 
switch,  which  immediately  closes. 

As  there  is  constant  trouble  with  self-setting  switches,  either  from  small 
fragments  of  coal  or  slate  clogging  them 
up,  or  from  insufficient  power  of  the  spring 
to  move  them,  they  are  viewed  with  dis- 
favor T many  mine  managers,  who  do 
not  ca-  _ to  use  them  under  any  conditions. 

Slope  Bottoms. — At  the  foot  of  a slope, 
or  at  the  landing  on  any  lift,  the  gang- 
way is  widened  out  to  accommodate  at 
least  two  tracks— one  for  the  empty  and 
one  for  the  loaded  cars.  The  empty  track 
should  be  on  the  upper  side  of  the  gang- 
way, or  that  side  nearer  the  fioor  of  the 
seam,  and  the  loaded  track  on  that  side 
of  the  gangway  nearer  the  roof  of  the  seam. 

An  arrangement  of  tracks  often  used 
Is  shown  in  Fig.  10.  At  a distance  of  40 
or  50  ft.  above  the  gangway,  the  slope  is  widened  out  to  accommodate  the 
branch  leading  into  the  gangway  loaded  track.  This  branch  descends 
with  a gradually  lessening  inclination  until  nearly  at  the  level  of  the  gang- 
way it  turns  into  the  maip  loaded  track.  A short  distance  above  the  gangway. 


Fig.  8. 


414 


HOISTING  AND  HAULAGE. 


Ooor: 

Fig.  10. 


a bridge  or  door  is  placed,  which,  when  closed,  forms  a latch  by  which  the 
empty  cars  are  taken  off  the  slope.  The  empty  track  is  about  6 ft.  higher 
than  the  loaded  track,  and  is  carried  over  it  on  a trestle.  The  illustration  in 
Fig.  10  shows  the  plan  as  arranged  for  a single  slope,  or  one  side  only  of  a 
slope  taking  the  coal  from  both  directions. 
When  coal  is  being  raised  from  this  lift, 
the  bridge  is  closed;  the  empty  car  comes 
down  and  is  run  off  over  the  bridge;  the 
car  is  unhooked  from  the  rope,  and  the 
chain  and  hook  attached  to  the  rope  are 
thrown  down  to  the  branch  below  on 
which  a loaded  car  is  standing;  the  loaded 
car  is  attached,  the  signal  given,  the  car 
ascends  to  the  main  track  on  the  slope, 
opening  the  switch — or  the  switch  may  be 
set  each  time  by  the  bottom  men,  by  a lever 
at  the  bottom  of  the  branch.  This  plan  can 
only  be  economically  applied  in  thick 
seams,  as  the  height  necessary  to  allow  one 
track  to  cross  the  other  on  a trestle  cannot 
be  obtained  in  seams  of  moderate  thick- 
ness without  taking  down  a large  amount 
of  top. 

A more  simple  plan,  which  dispenses 
with  the  bridge,  is  often  used.  The  branch 
is  laid  off,  as  shown  by  Fig.  10,  but,  near 
the  point  where  it  enters  the  gangway,  a switch  opening  into  the  empty 
track  is  placed.  By  this  arrangement,  the, tracks  cannot  be  as  well  arranged 
for  handling  the  cars  by  gravity  as  in  the  former  plan,  in  which  the  empty 
cars  when  detached  from  the  rope  run  by 
gravity  into  the  empty  siding,  and  the  loaded 
cars  descend  by  gravity  around  the  curve  to 
the  foot  of  the  branch,  where  they  lie  ready  to 
be  attached  to  the  rope. 

When  the  pitch  of  the  slope  is  so  steep  that 
the  coal  or  ore  falls  out  of  the  cars,  during 
hoisting  a gunboat  is  used  or  the  cars  are 
raised  on  a slope  carriage — ^in  either  case,  the 
arrangement  of  the  tracks  [at  lift  landings  is 
entirely  different.  With  either  a gunboat  or 
a slope  carriage,  the  arrangement  of  tracks 
on  the  slope  is  the  same;  but,  in  the  former 
case,  a connection  between  the  slope  and 

gangway  tracks  is  often  advisable.  When  a , . . i 

gunboat  is  used,  the  gangway  tracks  run  direct  to  the  slope,  and  a tippm,  or 
dump,  is  placed  on  each  side  to  dump  the  mine  cars  over  the  gunboat; 
but  when  the  cars  are  raised  on  a slope  carriage,  the  gangway  tracks 
run  direct  (at  right  angles)  to  the  slope,  to  carry 
the  car  to  the  cage  or  carriage.  The  floor  of  the 
cage  is  horizontal,  and  has  a track  on  it  that  fits 
on  the  end  of  the  gangway  track  when  the  car- 
riage is  at  the  bottom,  and  this  track  is  arranged 
with  stops  similar  to  those  on  cages  used  in  shafts. 

' Another  common  arrangement  of  tracks  at 
the  bottom  of  a slope  is  shown  in  Fig.  11.  A 
branch  is  made  by  widening  the  slope  out  near 
the  bottom,  and  this,  being  a few  feet  higher  than 
the  main  track,  is  used  to  run  off  the  empties  by 
gravity.  The  loaded  cars  run  in  by  gravity 
around  the  curve  to  the  foot  of  the  slope  in 
position  to  be  attached  to  the  rope. 

In  ascending,  the  loaded  car  forces  its  way 
through  the  switch,  or  the  switch  may  be  set  by  a 
lever  located  at  the  foot  of  the  slope.  When  the 
empty  car  descends,  it  runs  in  on  the  branch,  where  the  chain  is  unhooked 
and  thrown  over  in  front  of  the  loaded  car,  and  runs  around  the  curve  into 
the  gangway  by  gravity.  , , , , 

It  will  be  observed  that  in  this  plan  the  loaded  car  (and  consequently  the 


MINE  ROADS  AND  TRACKS. 


415 


bottom  men)  stands  on  the  track  in  line  with  the  slope,  and  is  in  danger  from 
any  objects  falling  down  the  slope,  or  from  the  breakage  of  the  rope  or  coup- 
lings; but  this  can  be  obviated  by  making  the  bottom  on  the  curve.  The 
illustration  in  Fig.  11  shows  only  one  side  of  the  slope;  the  other  side  is,  of 
course,  similar. 

All  these  plans  necessitate  the  location  of  that  part  of  the  gangway  near 
the  slope,  in  the  upper  benches  of  the  coal  or  near  the  top  rock.  The  gang- 
w;ay  is  then  curved  gently  around  toward  the  floor,  so  that,  when  it  has  been 
driven  far  enough  to  leave  a sufficiently  thick  pillar,  the  bottom  bench  is 
reached  and  the  gangway  is  then  driven  along  the  bottom  rock. 

A very  different  bottom  arrangement  is  shown  by  Fig.  12,  which  also 
represents  a plan  frequently  adopted  on  surface  planes.  The  two  slope 
tracks  are  merged  into  one  a short  distance  from  the  bottom  of  the  slope,  and 
on  the  opposite  sides  of  the  bottom  two  tracks  curve  around  into  the  gang- 
way on  opposite  sides  of  the  slope.  As  these  branches  curve  into  the  main 
gangway  tracks,  a switch  sends  off  a side  track  for  the  empty  cars.  The 
switch  on  the  slope  is  either  set  by  the  car— and  this  can  be  done  because 
the  next  loaded  goes  up  on  the  same  side  on  which  the  last  empty  descended 
— or  by  a lever  located  at  the  bottom. 

It  will  at  once  be  seen  that  in  this  plan  no  opportunity  is  afforded  of 
handling  the  cars  by  gravity.  The  curved  branches  are  made  nearly  level, 
and  the  momentum  of  the  descending  car,  if  quickly  detached,  is  often 
sufficient  to  carry  it  partly  or  wholly  around  the  curve,  even  against  a slight 


Fig.  13. 


Fig.  14. 


adverse  grade.  The  disadvantage  above  noted  of  having  the  bottom  in 
direct  line  with  the  slope  (where  there  is  danger  from  breakage  and  falling 
material)  also  obtains  in  this  plan. 

In  the  plan  i^hown  by  Fig.  13,  the  grades  may  be  so  arranged  that  the  cars 
can  be  entirely  handled  by  gravity.  The  latches  on  the  main-slope  track 
may  be  closed  automatically  by  a spring  or  weight,  the  loaded  car  running 
through  them  in  its  ascent  on  the  slope,  or  both  sets  may  be  operated  by  a 
single  lever  at  the  bottom.  The  switch  at  the  upper  end  of  the  central  track 
(loaded)  is  set  by  a hand  lever.  All  three  sets  may  be  linked  together,  so 
that  they  can  all  be  properly  set  by  a single  lever.  Reference  to  Fig.  11  will 
show  that  this  is  only  a modification  of  that  method.  It  requires  space  at 
the  bottom  for  only  three  tracks,  while  Fig.  13  requires  width  to  accom- 
modate four  tracks,  and  is  objectionable  because  it  is  more  complicated. 
The  extra  set  of  latches  at  the  top  of  the  central  track,  and  the  curvature  of 
both  main  tracks  into  this  central  one,  must  inevitably  cause  much  trouble 
and  delay  from  cars  jumping  the  track  at  this  point. 

The  plan  shown  in  Fig.  14  is  open  to  many  of  the  objections  pertaining  to 
some  of  those  already  described,  and  which  need  not  be  reiterated  here.  It 
can  only  be  employed  in  thick  seams,  or  in  seams  of  moderate  thickness 
lying  at  a slight  angle  or  dip. 

In  planning  the  arrangement  of  tracks  on  a slope,  it  is  advisable  to  place 
as  few  switches  as  possible  on  the  slope  itself,  to  keep  the  main  track 


416 


HOISTING  AND  HAULAGE. 


unbroken,  to  make  the  tracks  as  straight  as  possible,  to  have  nothing  stand- 
ing at  the  bottom  in  direct  line  with  the  slope  tracks,  and  to  arrange  the 
tracks  so  that  cars  are  handled  by  gravity. 

The  arrangement  of  tracks  near  the  top  of  the  slope,  and  on  the  surface, 
is  often  very  similar  to  the  bottom  arrangements,  as  already  described;  but 
as  all  loaded  cars  (except  rock  and  slate  cars,  which  are  run  off  on  a separate 
switch)  are  to  be  sent  off  on  one  track,  and  all  the  empties  dome  in  on  the 
same  track  to  the  head  of  the  slope,  and  as  there  is  usually  abundance  of 
room  for  tracks  and  sidings,  these  top  arrangements  are,  in  a measure,  much 
more  easily  designed.  In  some  instances,  the  two  main-slope  tracks  run 
into  a single  track  near  the  head  of  the  slope— a plan  somewhat  similar  to 
the  bottom  arrangement  shown  by  Fig.  12 — and  the  cars  are  then  brought  to 
the  surface  on  one  track,  which,  after  passing  the  knuckle,  bifurcates  into  a 
loaded  and  empty  track.  A similar  arrangement  is  frequently  adopted  at 
slopes  on  which  a carriage  or  gunboat  is  used.  When  the  two  main-slope 
tracks  are  continued  up  over  the  knuckle  to  the  surface — the  most  common 
and  best  plan — the  arrangement  of  tracks  and  switches  may  be  planned 
entirely  with  a view  to  the  quickest  and  most  economical  method  of 
handling  the  cars. 

Vertical  Curves.— The  vertical  curves  at  the  knuckle  and  bottom  of  a slope 
or  plane  should  have  a sufficiently  large  radius,  so  that  when  passing  over 
them  the  car  will  rest  on  the  rail  with  both  front  and  back  wheels.  The 
wheel  base  of  the  car  must  be  considered  in  adopting  the  radius  for  these 
curves,  for  if  the  curve  is  of  too  short  a radius,  there  is  danger  of  the  car 
jumping  the  track  every  time  it  passes  over  the  curve. 

Tracks  for  Bottom  of  Shaft.— Fig.  15  shows  the  arrangement  of  tracks  at  the 
foot  of  a shaft,  with  one  of  the  cages  at  surface.  The  grades  should  be  so 
arranged  that  from  the  inside  latches  of  the  crossings  the  empty  track 
should  have  a slight  down  grade  from 
the  shaft,  and  the  loaded  track  a slight 
down  grade  toward  the  shaft.  The  cross- 
ings and  the  short  straight  piece  of  road 
close  to  the  shaft  should  be  level. 

As  it  is  often  desired  to  move  empty  Fig.  15. 

cars  from  one  side  of  the  shaft  to  the 

other,  without  stopping  the  hoisting,  a narrow  branch  road  should  be  cut 
through  the  shaft  pillar,  and  used  for  this  purpose.  Where  the  pitch  of  the 
seam  prevents  this,  a road  should  be  laid  alongside  the  shaft,  room  to 
accommodate  it  beingr  cut  out  of  the  rock  on  the  side  most  desirable.  (See 
also  Shaft  Bottom,  page  276. ) 

In  arranging  tracks  for  shaft  bottoms,  at  tops  and  bottoms  of  slopes,  on 
coal  bins,  for  mechanical -haulage  landings,  at  foot  of  slopes  or  shafts,  or  in 
the  body  of  the  mine,  it  is  customary  to  provide  double  tracks  of  sufficient 
length  to  hold  the  requisite  number  of  wagons  for  economically  operating 
the  plant  and  with  sufficient  distance  from  center  to  center  of  tracks,  and 
from  centers  of  tracks  to  sides  of  entries,  to  easily  pass  around  the  wagons 
where  it  may  be  necessary,  either  in  handling  them,  or  in  lubricating  the 
wheels.  For  wagons  with  a capacity  of  from  li  to  2 tons,  it  generally 
requires  an  entry  to  be  about  15  to  17  ft.  wide  in  the  clear  for  ordinary  land- 
ings in  the  body  of  the  mine,  while  at  shaft  bottoms  the  necessary  width 
may  attain  17  to  18  ft.  in  the  clear,  owing  largely  to  location  and  local 
requirements.  The  curved  crossovers  connecting  the  tracks  at  shaft  bot- 
toms should  be  designed  with  radii  of  as  great  length  as  can  be  introduced, 
thereby  giving  an  easy  running  track.  They  should  not  be  less  than  from 
20  to  50  ft.  on  center  lines  for  ordinary  gauge  of  tracks,  i.  e.,  36  to  44  in. 

On  landings  constructed  in  the  body  of  the  mine  for  the  reception  of 
empty  and  full  wagons  handled  by  mechanical  haulage  from  shaft  or  slope, 
and  from  this  point  transported  by  animal  power  to  the  various  working 
laces  in  the  mine,  a grade  of  about  1^  in  favor  of  the  loaded  wagons  to  be 
andled  by  the  stock  will  be  found  quite  an  assistance  in  delivering  the 
wagons  to  the  haulage.  The  frogs  and  switches  for  these  landings,  as  well 
as  those  required  at  the  shaft  or  slope,  should  be  formed  of  regular  track 
rails,  and  can  generally  be  arranged  to  be  thrown  by  a spring  or  a con- 
veniently located  hand'lever,  as  has  been  described,  instead  of  being  kicked 
to  position,  as  was  the  custom  at  one  time. 

Besides  these  usual  arrangements  of  shaft-bottom  landings,  at  many 
plants  the  natural  grades  of  the  entries  can  be  taken  advantage  of  in 
designing  convenient  and  economical  methods  for  handling  the  mine  car?. 


MINE  MO  AES  AND  TRACKS. 


417 


For  instance,  where  the  coal  is  to  be  hauled  from  the  dip  workings  of  a 
mine  by  some  form  of  mechanical  haulage,  and  a summit  can  conveniently 
be  arranged  for  in  the  track  on  the  same  side  of  the  hoisting  shaft,  at  the 
proper  distance  therefrom,  to  accommodate  the  requisite  number  of  loaded 
wagons  to  be  hauled,  thus  allowing  them  to  run  by  gravity  over,  say,  a 

grade  to  the  shaft,  several  varieties  of  empty-track  arrangements  can  be 
made.  The  most  simple  form  is  to  have  the  empty  wagon  descend  a short 
grade  of  from  4fo  to  5fo  when  pushed  from  the  cage  by  the  succeeding  full 
one.  The  momentum  thus  secured  is  quite  sufficient  to  carry  the  car  up  an 
opposing  grade  of  about  1.5^.  It  again  descends  on  the  same  track,  and 
passing  through  an  automatic  switch,  continues  to  the  empty-car  siding. 
From  this  latter  point  it  is  handled  by  the  regular  haulage  machinery,  and 
in  its  route  passes  around  the  shaft  through  an  entry  especially  prepared  for 
this  arrangement.  A shaft  bottom  so  constructed  is  very  economical  to 
operate,  requiring  but  few  men  to  handle  the  wagons. 

Occasionally,  it  becomes  more  expedient  to  have  a separate  short  haulage 
to  draw  the  empty  wagons  to  the  main  haulage  when  it  cannot  be  easily 
arranged  to  construct  a complete  gravity  landing.  Several  other  modifica- 
tions of  such  a general  design  can  be  made.  All  the  different  devices, 
however,  depend  largely  on  the  local  requirements  of  the  particular  mine 
under  consideration. 

When  endless-rope  haulage  is  employed,  it  is  generally  found  to  be  most 
convenient  to  have  the  landings  for  full  and  empty  wagons,  in  the  body  of 
the  mine,  reached  by  switches  off  of  the  main-haulage  track,  the  cars 
coming  on  and  leaving  the  main  track  at  slight  knuckles  introduced  in  the 
track,  in  order  to  allow  a place  for  the  passing  of  the  rope,  which  then 
moves  along  through  a short  cut  or  channel  through  the  switch  rails. 
The  flanges  of  the  wagons  pass  over  the  rope  in  this  manner  without  any 
injury  to  it. 

Surface  Tracks  for  Slopes  and  Shafts. — The  arrangement  of  the  tracks  on  the 
surface  naturally  differs  at  every  mine,  owing  to  the  different  existing 
conditions.  All  surface  roads  should  be  so  arranged  that  the  loaded  cars  can 
be  moved  with  the  least  possible  power,  always  looking  out  for  the  return  of 
the  empties  with  as  little  expenditure  of  power  as  possible.  To  secure  the 
running  of  the  loaded  cars  from  the  mouth  of  the  shaft  or  slope  by  gravity,  a 
slight  grade  is  necessary,  the  amount  of  which  depends  on  the  friction  of 
the  cars,  which  varies  greatly.  Care  should  be  take  that  an  excessive  grade 
is  not  constructed,  or  there  will  be  trouble  in  returning  the  empties  from  the 
dump  to  the  head  of  the  shaft  or  slope. 

The  tracks  connecting  the  top  of  the  shaft  and  the  tipple  may  be  very 
short,  or  of  considerable  length,  depending  on  the  conditions  at  each  mine. 
Usually  from  20  to  60  ft.  will  be  sufficient,  although  no  definite  rule  can  be 
given  for  this. 

There  are  two  general  arrangements  of  tracks  about  the  head  of  a shaft: 
First,  where  the  loaded  cars  are  removed  from  the  cage  and  the  empty  cars 
placed  upon  it  from  the  same  side  of  the  shaft;  second,  where  the  loaded 
cars  are  removed  from  one  side  of  the  shaft  and  the  empty  cars  returned  to 
the  cages  from  the  opposite  side  of  the  shaft. 

In  either  case  there  are  usually  several  empty  cars  on  the  platform  ready 
to  be  put  on  the  cages  when  the  loaded  cars  have  been  removed. 

Where  the  conditions  are  such  that  the  loaded  cars  can  be  run  by  gravity 
to  the  dump,  a good  plan  is  to  have  a short  incline,  equipped  with  an  endless 
chain,  in  the  empty  track.  The  empty  cars  can  be  run  to  the  foot  of  this, 
hoisted  by  machinery  to  the  top,  and  thus  gain  height  enough  to  run  them 
back  to  the  shaft  or  slope  by  gravity. 

At  the  Philadelphia  & Reading  Coal  & Iron  Co.’s  Ellangowan  colliery, 
where  the  tipple  at  the  head  of  the  breaker  is  above  the  level  of  the  head 
of  the  shaft,  the  following  plan  is  used:  The  loaded  cars  are  taken  off 
the  east  side  of  the  cages,  and  run  by  gravity  to  the  foot  of  an  incline, 
where  the  axles  of  the  car  are  grasped  by  hooks  on  an  endless  chain 
and  the  car  pulled  up  to  the  tipple.  After  being  dumped,  the  car  is  run 
back  from  the  tipple  to  the  head  of  the  incline,  and  is  carried  to  the 
foot  of  the  empty  track  of  the  incline  by  an  endless  chain.  The  foot  of 
the  empty  track  is  several  feet  higher  than  that  of  the  loaded  track,  and  the 
cars  are  run  by  gravity  around  to  the  west  side  of  the  cages,  and  are  put  on 
from  that  side.  The  empty  cars,  as  they  run  on  the  cage,  have  momentum 
enough  to  start  the  loaded  car  off  the  cage  and  on  toward  the  foot  of  the 
incline.  There  are  a number  of  hooks  attached  to  both  the  empty  and 


418 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


loaded  chain  on  the  incline,  and  there  are  often  several  loaded  and  several 
empty  cars  on  different  parts  of  the  plane  at  once.  This  arrangement 
permits  of  the  hoisting  of  from  700  to  800  cars  per  day  out  of  a shaft  110  yd. 
deep,  with  single-deck  cages. 

Another  excellent  arrangement  for  handling  coal  on  the  surface  is  the 
invention  of  Mr.  Robert  Ramsey,  and  has  been  adopted  by  the  H.  C.  Frick 
Coke  Co.  and  a number  of  other  prominent  operators.  A description  of 
this  arrangement  as  applied  at  the  H.  C.  Frick  Coke  Co.’s  Standard  Shaft 
is  as  follows:  The  landing  of  the  shaft  is  made  slightly  higher  than  the  level 
of  the  tipple,  whieh  is  north  of  the  shaft.  South  of  the  shaft  is  located  a 
double  steam  ram,  one  ram  being  directly  in  line  with  the  track  on  each 
cage.  Directly  in  front  of  the  rams  is  a transfer  truck,  worked  east  and 
west  by  wire  rope.  The  loaded  car  on  the  cage  is  run  by  gravity  to  the 
tipple,  where  it  is  dumped  by  means  of  a nicely  balanced  dumping  arrange- 
ment. As  soon  as  it  is  empty  it  rights  itself  and  runs  by  gravity  alongside 
the  shaft  to  the  transfer  truck,  which  carries  it  up  a grade  to  a point  directly 
in  line  with  the  cage  that  is  at  the  landing,  and  one  of  the  steam  rams 
pushes  it  on  the  cage,  and  at  the  same  time  starts  the  loaded  car  off  toward 
the  tipple.  This  second  loaded  car  is  then  returned  by  the  same  means  to 
the  opposite  cage.  The  whole  mechanism  is  operated  by  one  man,  by  means 
of  conveniently  arranged  levers,  each  of  which  is  automatically  locked, 
except  when  the  proper  time  to  use  it  arrives.  It  is  therefore  impossible 
for  the  topman  to  work  the  wrong  lever  and  put  an  empty  car  into  the 
wrong  compartment  of  the  shaft.  Besides  the  one  man  at  the  levers,  there 
is  but  one  other  man  employed  at  the  tipple,  and  his  work  is  solely  to  look 
after  the  cars  when  dumping.  All  switches  are  worked  automatically,  and 
the  average  hoisting  at  this  shaft  is  at  the  rate  of  3 wagons  per  minute.  The 
shaft  is  about  250  ft.  deep,  and  single-deck  cages  are  used. 

The  Lehigh  & Wilkes-Barre  Coal  Co.  has  a system  in  use  at  a number  of 
collieries  that  has  also  proven  very  effective.  In  this  system  the  loaded  cars 
are  run  by  gravity  from  the  cage  to  the  dump,  and  the  empties  are  hauled 
from  the  dump  back  to  a transfer  truck  by  a system  of  endless-rope  haulage. 
The  transfer  truck  carries  the  car  to  a point  opposite  the  back  of  the 
cage.  The  empty  car  runs  by  gravity  to  the  cage,  and  its  momentum  starts 
the  loaded  car  on  the  cage  on  its  way  to  the  dump.  This  system  necessi- 
tates the  employment  of  more  topmen,  but  is  a very  good  one.  At  the  Not- 
tingham shaft,  which  is  470  ft.  from  landing  to  landing,  from  140  to  150  cars 
per  hour  are  hoisted  on  single-deck  cages. 


ORE  DRESSING  AND  THE  PREPARATION 
OF  COAL. 


CRUSHING  MACHINERY. 

The  object  of  crushing  ore  or  coal  is:  first,  to  free  the  mineral  or  other 
valuable  constituents  from  the  gangue,  slate,  pyrites  (sulphur),  or  other 
worthless  or  objectionable  constituents  so  that  they  can  be  subsequently 
separated;  or,  second,  simply  to  reduce  the  size  of  the  individual  pieces  and 
so  get  the  material  into  a more  salable  or  convenient  condition  for  use. 

Selection  of  a Crusher. — The  style  of  crusher  employed  is  influenced  by  the 
following  conditions:  (a)  The  amount  of  material  to  be  crushed  in  a given 
time.  (5)  The  size  of  the  material  as  it  goes  to  the  crusher,  (c)  The 
physical  characteristics  of  the  material  to  be  crushed;  that  is,  whether  it  is 
hard  or  soft,  tough  or  brittle,  clayey  or  sticky,  (d)  The  object  of  the  crush- 
ing; that  is,  whether  it  is  to  free  the  mineral  constituents  or  simply  to  reduce 
the  size  of  the  individual  pieces,  (e)  The  character  of  the  product  desired; 
that  is,  whether  an  approximately  sized  product  is  desirable  and  whether 
dust  or  fine  material  is  objectionable. 

All  crushing  machinery  may  be  divided  into  the  following  classes:  Jaw 
crushers,  g>Tatory  crushers,  cracking  rolls,  disintegrating  rolls,  crushing 
rolls,  roller  mills,  ball  mills,  stamp  mills,  hammers,  and  miscellaneous 
forms  of  crushers. 


CRUSHING  MACHINERY. 


419 


JAW  CRUSHERS. 

With  jaw  crushers,  the  material  is  crushed  between  two  jaws,  one  or 
both  being  movable.  All  jaw  crushers  have  the  common  defect  of  imparting 
a considerable  amount  of  vibration  or  shake  to  the  framework  of  the  build- 
ing containing  them,  owing  to  the  reciprocating  motion  of  the  heavy  masses 

that  comprise  their  crush- 
ing parts.  There  are  three 
styles  of  jaw  crushers  in 
common  use. 

The  Blake  crusher  is 
shown  in  Fig.  1,  a being  a 
fixed  jaw  and  b a movable 
jaw  that  is  operated  by  a 
toggle  joint  and  the  pitman 
d from  a suitable  crank- 
shaft. The  jaw  b is  hung 
or  pivoted  at  the  top.  The 
advantages  of  this  style  are 
as  follows:  The  large  pieces 
of  rock  to  be  crushed  are 
received  between  the 
upper  part  of  the  jaws, 
where  the  motion  is  least 
and  the  purchase  or  lever- 
age greatest,  so  that  they 
are  broken  with  the  small- 
est possible  expenditure  of 
energy.  The  movement  of  the  jaws  is  greatest  at  the  discharge  opening, 
thus  affording  a free  and  rapid  discharge  of  the  material  crushed,  and 
insuring  a large  capacitjr  for  the  machine.  The  principal  disadvantage  is 
that  the  great  variation  in  the  discharge  opening  results  in  a considerable 
range  in  the  size  of  the  material  delivered. 

This  style  of  crusher  has  found  a wide  field  for  breaking  down  material 

Table  of  Blake  Crushers. 


Fig.  1. 


1 

Size  of  Re- 
ceiving Ca- 
pacity. 

Approximate  Prod- 
uct per  Hour, 
Cubic  Yards,  to 

2 Inches. 

Weight  of 
Heaviest 
Piece. 

Total  Weight. 

Extreme  Dimensions. 

Proper  Speed.  j 

Horsepower 

Required. 

Length. 

Breadth. 

Height. 

Inches. 

Lb. 

Lb. 

Ft. 

In. 

Ft. 

In. 

Ft. 

In. 

3X  U 

Laboratory 

40 

100 

1 

1 

0 

6 

0 

10 

250 

1 

2 

6X  2 

One 

560 

1,200 

2 

10 

2 

1 

2 

3 

250 

4 

10  X 4 

Three 

1,800 

4,900 

4 

0 

3 

3 

3 

9 

250 

6 

10  X 7 

Five  

3,800 

8,000 

5 

1 

3 

9 

4 

5 

250 

8 

15  X 9 

Eight 

7,400 

15,500 

6 

6 

5 

0 

5 

11 

250 

15 

15X10 

Nine  

7,800 

16,000 

6 

6 

5 

5 

5 

11 

250 

15 

20  X 6 

Ten 

5,300 

11,200 

5 

3 

2 

11 

4 

6 

250 

15 

20X  10 

Ten 

8,100 

18,300 

6 

10 

5 

9 

5 

11 

250 

20 

12X30 

Sixteen 

14,200 

33,000 

7 

10 

8 

4 

6 

4 

250 

30 

15X30 

Twenty 

14,200 

35,000 

7 

10 

8 

4 

6 

4 

250 

30 

and  preparing  it  for  other  crushers,  or  for  breaking  large  quantities  of  any 
material  where  an  approximate  sizing  is  not  essential. 

The  Dodge  crusher,  Fig.  2,  has  a fixed  jaw  a and  a movable  jaw  b,  operated 
by  a cam  on  the  shaft  g.  The  movable  jaw  is  pivoted  at  the  bottom,  so  that 
the  minimum  movement  between  the  jaws  is  at  the  discharge  opening.  The 
advantage  of  this  is  that  the  least  movement  occurs  at  the  discharge  opening, 


420 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


and  hence  the  product  is  of  a fairly  uniform  size,  so  that  the  crusher  maj 
be  used  as  a rough  sizing  apparatus.  The  disadvantages  are  that  the  large 
pieces  of  rock  have  to  be  crushed 
in  the  upper  part  of  the  space 
between  the  jaws,  where  the 
motion  is  greatest  and  the  pur- 
chase or  leverage  least,  thus  re- 
quiring an  excessive  amount  of 
power,  especially  when  dealing 
with  hard  material.  The  move- 
ment of  the  jaw  at  the  discharge 
opening  is  so  much  less  than 
that  above  that  there  is  danger 
of  clogging  or  blocking  the  ma- 
chine, especially  when  working 
upon  tough  or  sticky  material.  Fig.  2. 

The  capacity  of  the  Dodge  style  ' 

of  machine  is  less  than  that  of  the  Blake.  It  is  used  largely  as  a secondary 
crusher,  or  for  crushing  comparatively  small  amounts  of  material  where  an 
approximately  sized  product  is  desired. 

The  Dodge  Crushek. 


No. 

Size  of  Jaw 
Opening. 

Diameter  of 
Pulleys. 

Width  of  Belt 
Used. 

Horsepower 

Required. 

No.  Tons  per 
Hour, Nut  Size. 

Revolutions  per 
Minute. 

Weight  Complete. 

Inches. 

Inches. 

Inches. 

1 

4X  6 

20 

4 

2 to  4 

itol 

275 

1,200 

2 

7X  9 

24 

5 

4 to  8 

1 to  3 

235 

4,300 

3 

8X12 

30 

6 

8 to  12 

2 to  5 

220 

5,600 

4 

10X16 

36 

8 

12  to  18 

5 to  8 

200 

12,000 

Roll-Jaw  Crushers.— Fig.  ~B  is  a sectional  view  of  a Sturtevant  roll-jaw 
crusher.  The  rolling  motion  of  the  jaw  subjects  the  material  to  a rolling 
and  squeezing  action,  instead  of  a direct  squeeze.  The  product  of  this 

crusher  is  approximately  sized  and 
there  is  no  greater  producer  of  sized 
output.  The  adjustment  of  the 
machine  for  fine  crushing  neces- 
sarily contracts  the  space  for  dis- 
charge, and  thereby  lessens  its 
capacity.  When  set  wide,  or  for 
material  from  1 to  inches  in  size, 
the  discharge  is  very  free  and  the 
capacity  is  claimed  to  be  greater 
than  that  of  any  other  jaw  and 
toggle  machine. 

Gyratory  Crushers. — These  crush- 
ers, Fig.  4,  are  all  large  capacity,  con- 
tinuous-action crushers,  a is  a ring 
or  hopper  against  which  the  material 
is  crushed  by  a conical  head  c,  which 
fits  on  a shaft  g,  the  bottom  of  which 
is  placed  in  an  eccentric  bearing 
so  that  the  amount  of  space  between  a and  c varies  as  the  head  rotates. 
The  material  to  be  crushed  is  dumped  into  the  receiving  hopper  h,  and  the 
machine  is  thus  automatically  fed. 


nOLLS. 


421 


The  advantages  of  this  style  are  that  the  large  pieces  of  material  are 
received  at  the  top  of  the  jaws,  where  the  motion  is  least  and  the  leverage 
or  purchase  greatest,  thus  reducing  the  work  necessary  in  this  heavy 
preliminary  crushing.  The  relative  move- 
ment betw'een  the  crushing  members  is  a 
maximum  at  the  discharge  opening,  but 
the  amount  of  this  movement  is  so  small 
that  the  product  is  approximately  sized. 
The  fact  that  the  maximum  movement  is 
at  the  point  of  discharge  assures  a free 
discharge.  There  is  practically  no  shaking 
imparted  to  the  building  by  gyratory 
crushers.  Their  capacity  is  very  great,  and 
with  a large  size,  material  may  "be  dumped 
into  the  hopper  h directly  from  the  cars. 
For  small  capacity  a gyratory  crusher  is 
more  expensive  than  a jaw  crusher. 

Frequently,  where  very  great  amounts 
of  material  are  to  be  crushed,  large  gyra- 
tory crushers  are  used  as  secondary  crush- 
ers after  jaw  crushers  of  the  Blake  pattern, 
the  discharge  from  the  jaw  crushers  ran- 
ging from  6' ' to  12"  cubes,  and  that  from  the 
gyratory  crushers  from  li"  to  cubes. 
(See  table  on  page  422). 


ROLLS. 


Cracking  Rolls.— This  is  a general  name 
applied  to  rolls  having  teeth,  which  are 
usually  made  separate  and  inserted. 
These  rolls.  Fig.  5,  are  employed  for 
Fig.  4.  breaking  coal,  phosphate  rock,  etc.,  the 

object  being  to  break  the  material  into 
angular  pieces  with  the  smallest  possible  production  of  very  fine  material. 
The  principal  field  for  cracking  rolls  is  in  the  preparation  of  anthracite 
coal,  and  the  exact  style  or  design  of  the  roll  depends  largely  on  the 
physical  condition  of  the  coal  under  treatment.  In  most  cases,  the  rolls 
are  constructed  with  an  iron  cylinder  having  steel  teeth  inserted,  the 
size,  spacing,  and  form  of  the 
teeth  depending  on  the  size 
and  physical  condition  of 
the  material  to  be  broken. 

Cracking  rolls  vary  from  12 
to  48  in.  in  diameter  and 
from  24  to  36  in.  in  face 
width.  The  teeth  of  the 
larger  sizes  are  from  3 to  3i 
in.  high,  and  of  the  smaller 
1 in.  or  less. 

The  average  practice  in 
the  anthracite  regions  of 
Pennsylvania  is  to  give  the 
points  of  the  teeth  a speed  of 
about  1,000  ft.  per  minute, 
though  the  speed  in  different 
cases  varies  from  750  to  1,200 
ft.  per  minute.  One  of  the 
largest  anthracite  companies 
has  a standard  roll  speed  of 
97.5  R.  P.  M.  for  the  main 
rolls  and  124.5  R.  P.  M.  for 
the  pony  rolls.  The  harder 
the  coal,  the  faster  the  rolls 
can  be  run.  If  run  slow  and  overcrowded,  the  rolls  will  make  more  culm 
than  when  driven  at  a proper  speed.  One  advantage  of  comparatively 
fast  driven  rolls  is  that  the  higher  speed  has  a tendency  to  free  the  rolls 
by  throwing  out,  by  centrifugal  force,  any  material  lodged  between  the 


(D 

- 

1 

^ r- 

(D 

oo 

]oo 

rir 

© © 

1 

Tgo: 

jo© 

m 

(D 

0 

ill 

Fig.  5. 


422 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


teeth.  In  one  test 
it  was  found  that 
less  fine  coal  was 
produced  at  800  ft. 
per  minute,  but 
that  the  rolls 
blocked  at  this 
speed  and  hence 
had  to  be  driven 
1,000  ft.  per  minute. 

In  one  case  a 
pair  of  main  rolls 
24  in.  in  diameter, 
36  in.  face,  running 
at  1,000  ft.  per  min- 
ute, handled  2,500 
tons  of  coal  in  24 
hours.  A pair  of 
19"  X 24"  main 
rolls  run  at  1,000  ft. 
per  minute  handled 
300  tons  mine  run 
in  10  hours. 

A well-known 
maker  of  rolls  for 
crushing  bitumi- 
nous coal  gives  a 
speed  of  100  to  150 
R.  P.  M.,  according 
to  the  output  re- 
quired, for  rolls  24 
in.  in  diameter  and 
33  in.  long.  As  a 
rule,  cracking  rolls 
are  never  run  up  to 
their  full  capacity, 
as  is  the  case  with 
crushing  rolls. 

The  /orm  of  the 
teeth  varies  greatly, 
but,  as  a rule,  the 
larger  rolls  have 
straight  pointed 
teeth  of  the  spar- 
row-bill or  some 
similar  form.  Fig.  6 
a.  The  old  curved, 
or  hawk-billed, 
teeth.  Fig.  6 b,  have 
now  gone  almost 
wholly  out  of  use. 

On  small  sized 
rolls,  rectangular 
teeth  with  a height 
equal  to  one  side  of 
the  square  base  are 
frequently  em- 
ployed, and  these 
may  be  cast  in  seg- 
ments of  manga- 
nese or  chrome 
steel. 

Corrugated  rolls 

have  teeth  or  cor- 
rugations extend- 
ing their  entire 
length.  They  were 
first  introduced  by 


Size  Engine 

Recommended  to  Drive 

Breaker,  Elevator, 

and  Screen. 

Indicated  Horsepower. 

Granite,  Ore. 

Limestone. 

Diameter 

of 

Hopper. 

Inches. 

Space  Occupied 
by  Breaker. 

Inches. 

JO  q:^Suaq 

•amujj 

JO  qipiAV 

•jaddoH 
dox  oj  auiujjj 

uio:^^og 
uiojj  jqSian 

•iCaitnj  SuiAiici 

JO  suoijniOAOH 

Dimensions  of 
Driving 
Pulley. 

Inches. 

Face. 

Diam. 

•8J0  JO  3[OOH  JO 
oj  Suipioooy  ‘JguiH  ‘ni 
SUTSSBJ  ‘-qq;  000‘S  JO  suox 
ui  ‘inoH  JOd 

2 to  4 

4 to  8 

6 to  12 
10  to  20 

15  to  30 

25  to  40 
30  to  60 

50  to  125 
100  to  150 

weight 

Breaker. 

Pounds. 

500 

3,300 

5,600 

7,800 

13.800 

21.500 

30.000 

40.500 

65.800 

89.000 

:inoqv  ‘pouiq 
-raoo  sSuTuado  Sni 
-AioooH  eojqx  JO 
suoisuaraia 

Inches. 

xxxxxxxxxx 

jnoqv 

‘Suiuodo  SuT 
-Apo8H  qo«a  JO 
suoisuaraiQ 

Inches. 

xxxxxxxxxx 

•azis 

gOrH<NCC'^u:>«Ot^QO 

ROLLS. 


423 


Mr.  E.  B.  Coxe,  at  Drifton,  Pa.,  but  they  have  not  come  into  general  use 
owing  to  the  fact  that,  while  they  break  some  coal  fairly  well,  in  most 
cases  it  has  been  found  that  a continuous  edge  causes  too  much  disinte- 
gration along  its  length,  while  a point  splits  the  coal  into  three  or  four 
pieces  only,  all  the  cracks  radiating  from  the  place  where  the  point  strikes, 
thus  producing  very  much  less  culm.  Another  advantage  possessed  by  the 
toothed  rolls  is  that  if  anything  hard  passes  through  the  corrugated  roll 
and  breaks  out  a piece  of  the  corrugation,  the  entire  roll 
is  ruined,  while,  in  the  case  of  the  toothed  rolls,  any  one 
of  the  teeth  may  be  replaced. 

Disintegrating  rolls  and  pulverizers  are  sometimes  used  to 
reduce  coking  coal  to  the  size  of  corn  or  rice  before  intro- 
ducing it  into  the  ovens.  One  roll  is  driven  at  double  the 
speed  of  the  other,  the  slower  roll  acting  as  a feed-roll,  and 
the  other  as  a disintegrator.  The  slower  roll  is  commonly 
driven  at  from  1,800  to  2,000  ft.  per  minute  peripheral 
speed,  and  the  faster  roll  at  from  3,600  to  4,000  ft.  per  mi- 
nute. The  teeth  are  always  fine,  rarely  being  over  | in. 
high.  In  some  cases,  the  inner  roll  is  provided  with  a 
series  of  saw  teeth  from  \ in.  to  f in.  high  and  having 
about  f in.  pitch,  the  individual  teeth  being  set  so  as  to  a b 

form  a slight  spiral  about  the  body  of  the  roll.  The  other  Fig.  6. 

roll  is  provided  with  teeth  having  their  greatest  dimension 
in  the  direction  of  rotation,  so  that  they  tend  to  cross  the  teeth  on  the  opposite 
roll.  These  teeth  are  also  set  so  as  to  form  a slight  spiral,  and  thus  prevent 
blocking.  In  other  cases,  the  teeth  on  both  rolls  are  set  in  the  form  of 
quite  a steep  spiral. 

Hammers. — For  the  reduction  of  coal,  crushers  employing  hammers  have 
been  used.  Fig.  7.  The  crushing  chamber  is  usually  of  a circular  or  barrel  form, 
and  the  crushing  is  done  by  means  of  hammers  pivoted  about  a central  shaft. 
These  swing  out  by  centrifugal  force  and  strike  blows  upon  the  coal  to  be 
broken.  When  it  is  reduced  sufficiently  fine,  it  is  discharged  through  bars 
or  gratings  at  the  lower  portion  of  the  machine.  This  style  of  machinery  is 
usually  employed  in  preparing  coal  for  coke  ovens,  thus  occupying  the  same 

field  as  the  disintegrating 
rolls.  A No.  3 pulverizer  of 
this  type  will  crush  50  to  75 
tons  per  hour  run  of  mine, 
down  to  i in.,  or  it  will  crush 
100  tons  per  hour  of  slack. 
Such  a machine  occupies 
about  8 sq.  ft.  of  floor  space 
and  requires  25  to  30  H.  P.  to 
run  it. 

Crushing  Rolls.— The  prin- 
cipal representative  of  this 
type  of  machine  is  the  ordi- 
nary Cornish  . roll  having  a 
fairly  wide  face  and  rather 
small  diameter.  The  diam- 
eter of  these  rolls  was  kept 
down  for  a great  many  years 
on  account  of  the  fact  that 
the  chilled  cast-iron  shells 
could  not  be  obtained  in 

large  sizes  and  were  expen- 

sive and  hard  to  handle. 
With  the  advent  of  the  rolled- 
steel  shells,  it  became  possible  to  employ  larger  diameters  and  higher 
speeds.  Rolls  of  the  Cornish  type  vary  from  4"  face  and  9"  diameter  to 

16"  face  and  42"  diameter.  The  distinctive  feature  of  the  Cornish  roll 

is  a comparatively  wide  face  compared  with  the  diameter,  and  a 
rather  slow  peripheral  speed.  Many  of  the  modern  Cornish  rolls  are 
provided  with  rolled-steel  shells,  especially  when  employed  for  very  fine 
crushing,  owing  to  the  fact  that  these  shells  are  of  a more  uniform 
texture,  work  more  evenly,  can  be  worn  much  thinner  before  being 
discarded,  and  can  be  trued  up  with  less  difficulty  than  is  the  case 
when  chilled  iron  is  employed.  To  guard  against  the  bending  of  the  roll 


424 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


shaft  or  breaking  of  the  machine  in  case  any  hard  material  (such  as  a pick 
or  hammer)  gets  between  the  rolls,  one  roll  is  mounted  in  a movable 
bearing  and  kept  in  place  by  a compressed  spring  washer.  This  washer  is 
composed  of  two  plates  between  which  are  placed  one  or  more  steel  springs. 
The  plates  are  kept  together  by  several  small  bolts,  which  are  screwed 
up  so  as  to  compress  the  springs  to  a certain  degree.  Then  the  entire 
arrangement  is  employed  as  a washer  on  the  rod  that  keeps  the  rolls 
together.  Should  the  pressure  exerted  on  the  rolls  exceed  that  already 
exerted  in  the  spring,  the  plates  would  be  brought  nearer  together  and  the 
roll  allowed  to  move  back  and  pass  the  hard  substance,  but  at  any  pressure 
below  this,  the  roll  acts  as  if  placed  in  a fixed  bearing. 

Cracking,  corrugated,  and  disintegrating  rolls  are  usually  provided  with 
breaking  pieces  back  of  one  of  the  rolls,  so  that  in  case  any  extra  hard  piece 
passes  through  the  rolls,  the  breaking  piece  will  give  way,  allowing  the 
rolls  to  move  back  and  thus  prevent  the  bending  of  the  shaft  or  breaking 
of  the  machine  itself.  Compressed  spring  washers  have  never  come  into 
general  use  in  connection  with  this  style  of  machinery. 

Amount  Crushed.— The  amount  of  material  that 
can  pass  between  any  pair  of  rolls  is  proportionate 
to  the  number  of  square  feet  of  roll  surface  passing 
per  minute;  hence,  the  capacity  may  be  increased 
by  keeping  the  face  width  the  same  and  in- 
creasing the  speed,  or  the  same  capacity  may 
be  obtained  by  reducing  the  face  and  increasing 
the  speed. 

According  to  Stutz  (A.  I.  M.  E.  IX,  page  464), 
if  the  distance  between  the  contact  points  of 
the  material  with  tlj^e  rolls  be  t,  Fig.  8,  the  dis- 
tance between  the  crushing  face  of  the  rolls  w, 
the  angle  a,  as  shown  in  the  figure,  and  R the  radius  of  the  roll,  then 
_ t — w _ t — w 
~ 2 vers,  sin  a “ 2(1  — cos  a)' 

According  to  Pernolet,  the  amount  of  material  that  may  be  crushed 
by  a pair  of  rolls  in  a given  time  is  equal  to  one-fourth  or  one-fifth  of  a 
band  or  layer  whose  length  is  the  circumference  of  the  roll  multiplied 
by  the  number  of  revolutions;  whose  width  is  the  length  of  the  rolls, 
and  whose  thickness  is  equal  to  the  space  or  distance  between  the  rolls. 

Or,  Q = — , where  d = diameter  of  rolls;  tt  = 3.14;  = number  of  revo- 

lutions in  the  given  time;  I = length  of  rolls;  w = space  between  rolls; 
and  i = coefficient,  to  allow  for  the  irregular  feeding  of  the  material  and 
the  space  between  the  pieces. 

The  Denver  Engineering  Works  gives  the  following  formulas  for  the 
capacity  of  crushing  rolls: 

T = tons  per  hour;  R = rev.  per  min.;  S = mesh  (inches). 

For  14"  X 27"  rolls.  T = 7.725  J7S. 

For  16"  X 36"  rolls,  T = 11.775  RS. 

For  12"  X 20"  rolls,  T = .327  R S. 

Speeds.— The  pressure  on  the  bearings  necessary  to  crush  ore  depends 
directly  on  the  face  width,  and  hence  if  the  capacity  can  be  kept  the  same 
and  the  face  width  decreased,  it  is  evident  that  there  will  be  less  pressure 
on  the  bearings  and  less  loss  in  friction.  The  difficulty  of  keeping  the 
bearings  cool  when  crushing  hard  rock  with  the  old  Cornish  rolls  has  led 
to  the  adoption  of  high-speed,  narrow-faced  rolls  for  certain  classes  of  work. 
One  objection  to  running  the  small  diameter  rolls  fast  is  that  the  larger 
pieces  of  ore  have  a tendency  to  dance  on  the  face  of  the  rolls  rather  than 
to  be  crushed,  while  the  bite  is  better  when  the  speed  is  slower. 

The  advantages  of  high-speed,  narrow-faced  rolls  are:  greater  capacity 
for  a given  bearing  pressure;  less  loss  of  power  from  friction;  less  dancing 
of  the  ore  on  the  roll  face,  owing  to  the  fact  that  the  angle  of  approach 
between  the  surfaces  of  large  rolls  is  more  acute  than  with  rolls  of  a small 
diameter.  High-speed,  large-diameter  rolls  will  handle  coarser  material  and 
hence  make  a greater  range  of  reduction  than  small-diameter  rolls.  The 
disadvantage  of  high-speed  rolls  is  that  they  tend  to  hammer  and  pulverize 
the  ore,  so  that  with  very  brittle  minerals  a high  speed  may  be  detrimental. 
In  general,  it  may  be  stated  that  for  crushing  to  any  definite  size  with  the 
Ipwest  possible  production  of  very  fine  material,  rolls  are  the  best  form  of 


MOLLS. 


425 


machinery  on  the  market.  For  fine  crushing  of  brittle  material,  quite  slow 
speeds  may  give  the  best  results. 

The  accompanying  table  gives  some  facts  in  regard  to  the  crushing-roll 
practice  of  several  manufacturers,  the  data  having  been  taken  from  their 
catalogues  or  other  information  furnished  by  them. 

Crushing  Rolls. 


Name. 

Size. 

Inches. 

Peripheral 
Speed  in 

Ft.  per  Min. 

Spring  Pres- 
sure in  Lb.  per 
In.  of  Face 
Width. 

Character  of 
Rolls. 

Frazer  & Chalmers... 

24X8 

36X16 

600-1,500 

4,000  for  hard 
quartz. 

Cornish. 

Frazer  & Chalmers,.. 

44X5 

56X8 

2,200-2,300 

Narrow  face, 
high  speed. 

Earle  C.  Bacon 

1,000 

Cornish. 

Sturtevant  Mill  Co. 

16X3 

27X5 

3,000 

Special  cen- 
trifugal. 

20X12 

E.  P.  Allis  Co 

26X  14 
30X14 
36X14 

800 

Cornish. 

E.  P.  Allis  Co 

20X12 

1,885 

4,000  for  hard 

Narrow  face, 
high  speed. 

Colorado  Ironworks 

27X  14 
36X16 
40X16 

600 

rock. 

4,800  for  very 
hard  rock. 

Cornish. 

Colorado  Ironworks 

36X6  ’ 

42X6 

54X8 

2,100-2,800 

Narrow  face, 
high  speed. 

Denver  Engineering 
Works  Co 

16X10 

to 

42X16 

350-100 

3,500-4,500 

Cornish. 

Gates  Iron  Works  .... 

9X4 

26X15 

36X15 

470-850 

2,266-3,333 

Cornish. 

The  Gates  Iron  Works  has  furnished  the  following  formulas  relating  to 
crushing  rolls,  in  which  D = diameter  of  roll  in  inches;  N = number  of 
R.  P.  M.;  S = maximum  size  of  ore  cube  in  inches  fed  to  the  rolls; 
S'  = maximum  size  of  cube  for  a given  diameter  of  roll. 

1 16 
qOO  e 

®'= 

It  will  be  seen  from  the  first  of  these  formulas  than  N is  an  inverse 
function  of  S,  which  agrees  with  the  results  shown  in  the  previous  diagram. 
As  a rule,  it  is  best  not  to  try  to  run  rolls  up  to  the  maximum  size  that  they 
will  crush,  but  to  feed  smaller  material  to  them. 

The  Denver  Engineering  Works  Company  has  furnished  the  diagram, 
Fig.  9,  and  formulas  relating  to  rolls.  This  diagram  serves  very  well  to 
illustrate  the  fact  that  small  rolls  do  not  grip  or  crush  large  pieces  as  well 
when  running  at  comparatively  high  peripherial  speeds  as  when  running 
at  slow  speeds.  In  the  case  of  the  10"  X 16"  roll,  a diiference  of  from 
1"  to  i"  cube  size  made  a difference  of  20  R.  P.  M.  in  order  to  obtain  the 


426 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


most  effective  crushing  speed,  and  the  difference  between  i"  and  cube 
sizes  made  a difference  almost  as  great.  It  will  also  be  noticed  that  the 
larger  diameters,  as,  for  instance,  the  42"  roll,  are  not  so  greatly  affected  by 
this  cause,  owing  to  the  fact  that  the  effective  or  crushing  angle  between  the 
rolls  is  much  more  acute  than  in  the  case  of  the  smaller  diameters. 


CRUSHING  MILLS. 

Radial  Roller  Mills.— In  this  type  of  mill,  the  crushing  is  performed  on  a 
ring  or  die  by  a series  of  heavy  rolls  pressing  on  it  by  gravity.  In  some 
cases,  the  rolls  travel  around  on  the  die  and  in  others  the  die  travels  in 
relation  to  the  rolls.  Fig.  10  represents  one  form  of  Chilian  mill  that  is  the 
leading  type  of  this  class. 

The  peculiarity  of  the  grinding  action  of  the  radial  rolling  mills  is  that  it 
is  not  a pure  crushing  action,  but  a triturating  or  grinding  action  as  well, 
owing  to  the  fact  that  while  the  different  portions  of  the  face  of  the  roll  are 
all  traveling  at  the  same  speed,  the  outer  portions  have  to  travel  over 
a greater  length  of  ring  than  the  inner  portions,  so  that  there  is  only  one 
line  along  which  true  crushing  action  occurs.  Some  manufacturers  have 
made  the  crushing  ring  and  the  rollers  both  with  coning  faces,  the  vertices 
of  both  cones  meeting  at  a common  point.  This  has  resulted  in  a true 
crushing  action,  but  for  some  classes  of  work  the  triturating  action  is  to  be 
preferred,  as,  for  instance,  in  the  grinding  of  silver  ores  for  the  patio  process 
of  amalgamation. 

Centrifugal  Roller  Mills.— In  centrifugal  roller  mills,  the  crushing  is  accom- 
plished between  rapidly  moving  rolls  and  the  inside  of  a stationary  die  or 
ring.  The  Huntington  mill.  Fig.  11,  is  one  of  the  principal  representatives 
of  this  class  of  machinery.  The  rollers  c are  supported  from  bearings  e and 
are  carried  rapidly  around  by  means  of  the  frame  a and  the  shaft  g.  The 
ore  is  crushed  against  the  ring  d.  In  order  to  prevent  the  accumulation 


CRUSHING  MILLS. 


427 


Fig.  10. 


of  ore  below  the  rollers,  and  to  throw  it  out  for  crushing,  scrapers  / are  pro- 
vided.  The  crushed  ore  discharges  through  screens,  as  shown  in  the  illus- 
tration. There  are  many  styles  of  this  class  of  machinery  having  different 
numbers  of  rollers,  varying  from  1 up,  and  some  machines  have  been  intro- 
duced combining  a portion 
of  the  action  of  radial  and 
centrifugal  machines,  the 
faces  of  the  die  or  ring  being 
at  an  angle  and  the  rollers 
being  mounted  in  inclined 
bearings  so  that  they  tend  to 
crowd  out  and  down  upon 
the  ring.  Centrifugal  roller 
mills  have  found  two  espe- 
cial fields  in  concentration 
works,  one  for  crushing  clay 
or  soft  ores  containing  free 
gold,  and  the  other  for  re- 
grinding middlings  for  fur- 
ther concentration.  Rolls  of 
this  type  are  also  extensively 
employed  in  grinding  cement 
and  phosphate  rocks. 

Ball  Mills.— There  are  two 
types  of  ball  mills;  (1)  those 
in  which  the  crushing  is  per- 
formed by  balls  traveling  in 
a fixed  path,  and  (2)  those 
in  which  the  crushing  is  per- 
formed by  a large  mass  of  balls  of  various  sizes  rolling  over  one  another. 
In  the  first  type  the  balls  travel  in  a fixed  path,  track,  or  race  that 
may  be  either  vertical  or  horizontal.  Where  it  is  vertical,  the  balls 
must  be  driven  at  such  a rapid  rate  that  their  centrifugal  force  will 
keep  them  in  contact  with  the  crushing  ring  or  track.  This  form  may  be 
likened  to  a bicycle  ball  bearing  on  a large  scale,  the  crushing  being 
accomplished  between  the  balls  and  the  race  or  track.  The  serious  objec- 
tion to  this  class  of  ball  mills  is  found  in  the  uneven  wear  of  both  the  balls 
and  the  race,  so  that  the  work  soon  becomes  unevenly  distributed,  and  also 
in  the  fact  that  the  balls  cannot  be  used  after  they  have  been  worn  to  a 
slight  extent. 

In  the  second  class  of  machines  the  balls  are  introduced  into  a large 
barrel  or  chamber,  where  they  roll  over  one  another,  the  ore  being  crushed 

between  the  different  balls  and 
between  the  balls  and  the  lin- 
ing of  the  chamber.  In  this 
style  of  machine  the  crushed 
material  may  be  discharged 
through  openings  in  the  per- 
iphery or  through  openings  in 
one  end  of  the  barrel.  One 
great  advantage  with  this  style 
of  mill  is  that  the  balls  can  be 
entirely  worn  out  and  it  is 
only  necessary  to  charge  a 
sufficient  number  of  new  balls 
with  the  ore  each  day  to  make 
up  for  the  wear  of  those  in 
the  mill. 


STAMPS. 


Fig.  11. 


Gravity  stamps  are  especially 
well  suited  for  material  the 


valuable  portion  of  which  does 
not  have  a tendency  to  slime. 
The  fact  that  these  stamps  are  very  simple  in  construction,  easy  to  transport 
and  erect,  as  well  as  to  operate,  gives  them  a decided  advantage  over  other 
forms  of  crushers.  Fig.  12  illustrates  a 10-stamp  battery  of  the  gravity  type. 


428 


ORE  DRESSING  AND  PREPARATION  OF  COAL, 


Fig.  13  is  a detail  of  the  mortar  stamp  heads  and  dies.  The  mortar  a is  placed 
on  a suitable  foundation  of  timbers  h and  the  ore  crushed  on  dies  d by  the 
stamps  s,  which  are  secured  by  means  of  tapered  joints  to  the  heads  or  bosses 
h.  The  stems  e are  attached  to  the  heads  h and  the  whole  lifted  by  the  cams 
(shown  in  detail  in  Fig.  12).  The  cams  operate  under  tappets  on  the  stems, 
as  shown  in  Fig.  12.  As  the  cam  operates  under  the  edge  of  the  tappet,  it 
not  only  lifts  the  stamp,  but  gives  a partial  rotation,  thus  equalizing  the  wear 
on  both  the  stamp  and  die.  The  ore  is  fed  in  at  the  back  of  the  mortar  and 
the  crushed  material  discharged  through  the  screen,  as  shown  in  Figs.  12  and 
13.  Usually  a single  screen  at  the  front  is  employed,  but  sometimes  two  or 
more  upon  different  sides  of  the  mortar  may  be  introduced.  For  treating 
free-milling  gold  ores  in  which  the  gold  occurs  in  rather  large  grains  free 
from  iron  pyrites,  the  California  style  of  battery  was  developed,  the  charac- 
teristics of  which  are  a small  drop  (4  in.  to  6 in.),  low  discharge  (4  in.),  a 
heavy  stamp  (750  to  1,000  lb.),  and  a high  speed  or  number  of  drops  per  min- 
ute (90  to  105).  The  advantage  of  this  style  is  rapid  crushing,  but  the 
majority  of  the  gold  had  to  be  saved  on  apron  plates  outside  the  mortar. 

For  working  ores  that  contain  large  quantities  of  iron  i)yrites  with  the 
gold  values  occurring  in  the  cleavage  planes  of  the  pyrites,  the  Gilpin 
County ^ Colo.,  style  of  battery  was  developed.  This  is  characterized  by  a 
high  drop  (18  to  20  in.),  a high  discharge 
(14  in.),  a light  stamp  (550  to  600  lb.),  and 
a comparatively  slow  rate  of  drop  (30  per 
minute) . With  this  style  of  battery,  most 
of  the  gold  was  obtained  on  amalgamated 
plates  in  the  battery,  but  its  use  was 
accompanied  by  excessive  sliming  on 


Fig.  12.  Fig.  13. 


account  of  the  fact  that  the  high  discharge  kept  the  material  in  the  mortar 
for  a long  time,  and  subjected  it  to  repeated  treatment. 

Modern  practice  tends  toward  the  use  of  rather  heavy  stamps  (about 
1,000  lb.),  quick  drop  (90  to  105  per  minute),  and  low  discharge  (4  to  6 in.). 
The  advantages  are  that  the  capacity  of  the  battery  is  very  great  and  the 
sliming  reduced  to  a minimum.  If  the  ore  contains  sulphides  carrying  gold, 
they  are  separated  by  concentration  upon  venuers  or  bumping  tables,  and 
subsequently  treated  by  chlorination  or  sm  If  the  apron  plates  do 

not  catch  the  major  portion  of  the  values,  the  “"ailings  may  be  treated  by  the 
cyanide  process.  This  last  method  is  that  employed  at  many  large  gold 
mines,  especially  those  of  the  Transvaal  in  South  Africa. 

Order  of  Drop.— There  is  much  diversity  of  practice  in  this  respect.  It  is 
desirable  to  drop  the  stamps  in  such  rotation  as  to  insure  an  even  distribu- 
tion of  the  pulp  on  the  several  dies.  Adjacent  stamps  should  not  drop  con- 
secutively, as  this  occasions  accumulation  of  the  pulp  at  one  end  of.  the 
mortar,  in  consequence  of  which  the  efficiency  of  the  stamps  at  that  end  is 
reduced  by  having  a decreased  height  of  drop  and  a cushion  that  retards  the 
pulverization  of  the  ore.  The  stamps  at  the  other  end  of  the  mortar  have 
too  little  work,  and  are  liable  to  “ pound  iron.”  The  order  of  drop  1,  4,  2,  5,  3 


STAMPS. 


429 


seems  to  best  fulfil  the  requirements.  It  gives  a good  splash  and  satisfac- 
tory results  in  other  respects.  The  order  1,  5,  2,  4,  3 is  also  extensively 
adopted.  There  are  several  other  orders  of  drops  in  use,  but  the  two  just 
mentioned  are  generally  preferred. 

In  large  mills,  the  standard  drop  is  given  as  1,  7,  3,  9,  5,  2,  8,  4,  10,  6,  with 
1,  8,  4,  10,  2,  7,  5,  9,  3,  6 as  a close  favorite;  while  1,  5,  9,  7,  3,  2,  6,  10,  8,  4 and 
1,  5,  9,  3,  7,  10,  6,  2,  8,  4 are  used. 

Speed  of  Stamps.— Heavy  stamps  and  stamps  having  high  drops  should 
have  correspondingly  low  speed.  With  900-  to  950-lb.  stamps,  having  6"  to  7" 
drop,  the  speed  should  be  from  85  to  95  drops  per  minute.  With  double- 
armed cams,  the  speed  must  not  be  great  enough  to  bring  the  cam  into 
collision  with  the  falling  tappet,  i.  e.,  the  interval  between  the  revolutions 
of  the  cam  must  be  sufficient  to  give  the  tappet  time  to  finish  its  drop. 
When  the  cam  strikes  the  descending  tappet,  a shoe,  boss,  or  tappet  is  often 
dislodged,  and  breakage  is  imminent.  A fast  drop  produces  a good  splash, 
which  is  very  desirable  for  battery  amalgamation. 

Shoes  and  Dies. — Shoes  and  dies  are  either  of  iron  or  steel.  In  most  mills, 
remote  from  foundries  where  transportation  is  an  important  item  in  the  cost 
of  shoes  and  dies,  steel  shoes  and  dies  have  replaced  those  of  iron.  Chrome 
steel  shoes  and  dies  have  been  introduced  and  have  proved  superior.  In 
some  mills,  steel  shoes  and  iron  dies  are  used.  The  iron  dies  wear  more 
evenly  with  steel  shoes  than  the  steel  dies  do.  The  life  is  about  2^  to  3 times 
that  of  iron  shoes  and  dies,  and  the  cost  about  twice  as  great  as  those  of  iron. 
The  mixture  of  steel  (from  the  old  chrome  steel  shoes  and  dies)  with  iron 
produces  shoes  and  dies  that  wear  considerably  longer  than  those  of  pure 
iron,  and  may  be  advantageously  introduced  where  there  is  no  other  dispo- 
sition possible  for  the  old  steel,  because  of  want  of  local  facilities  for  the 
utilization  of  this  residue.  In  many  districts,  the  old  iron  shoes  and  dies  are 
sold  to  local  foundries  for  from  li  to  2 cents  per  lb. 

The  weights  of  the  shoes  bear  a certain  relation  to  the  weights  of  the 
tappets,  stems,  and  bosses.  Chrome  steel  shoes  made  for  stamps  of  850  to 
950  lb.,  weigh  from  150  to  155  lb.,  and  measure  about  9 in.  in  diameter  by 
7i  to  8 in.  long.  The  neck  is  from  4i  to  5 in.  long,  with  a taper  to  correspond 
to  the  socket  of  the  boss  or  stamp  head.  Iron  shoes  are  usually  from  15  to 
20  lb.  lighter  than  the  above  weights.  The  chrome  steel  dies  weigh  from 
110  to  125  lb.,  and  measure  (where  shoes  of  the  above  dimensions  are  used) 
9 in.  in  diameter  by  4 to  4i  in.  in  height,  with  a rectangular  foot-plate  lOi  in. 
by  91  in.  by  i in.  thick.  Iron  shoes  usually  weigh  from  20  to  25  lb.  less  than 
the  above  weights  for  steel. 

Life  of  the  Shoes  and  Dies.— There  are  many  conditions  that  affect  the 
durability  of  shoes  and  dies,  as,  for  instance,  the  hardness  of  the  rock,  the 
weight,  speed,  and  hffight  of  drop  of  the  stamp,  the  manner  of  feeding 
the  ore,  etc.  Iron  shoes  of  good  quality  last  from  30  to  47  days.  Old  shoes 
wear  usually  down  to  11  in.  or  1 in.  in  thickness,  and  weigh  about  25  or  40  lb. 
Old  dies  usually  wear  down  to  about  11  in.  in  thickness,  and  weigh  from 
20  to  50  lb.  The  consumption  of  iron  or  steel  in  shoes  and  dies  depends  on 
the  character  of  the  ore  crushed.  Other  conditions  being  the  same,  it  will 
depend  on  the  coarseness  of  the  stamping  and  the  height  of  discharge. 
Dies  wear  less  rapidly  than  the  shoes,  as  they  are  protected  by  the  thickness 
and  the  pulp,  which  covers  them  to  the  depth  of  from  11  to  3 in.  But  while 
the  actual  wear  of  dies  is  less  than  that  of  the  shoes,  the  life  of  the  dies 
is  shorter  than  that  of  the  shoes,  owing  to  the  fact  that  the  shoes  have 
several  inches  greater  length  of  wearing  part  than  the  dies.  The  con- 
sumption of  iron  for  shoes  and  dies  per  ton  of  ore  crushed  is,  in  California, 
from  11  to  3 lb.  To  obtain  the  maximum  crushing  capacity  of  the 
battery,  the  dies  must  be  kept  as  high  (with  reference  to  the  lower  edge 
of  the  screens)  as  is  compatible  with  the  safety  of  the  screens  and  with 
successful  amalgamation  in  the  battery.  To  prevent  the  pounding  of  iron, 
it  is  necessary  to  preserve  more  or  less  uniformity  in  the  level  of  the  dies. 
Should  one  die  in  the  battery  project  much  above  the  others,  little  or  no 
pulp  would  remain  upon  it,  and  the  shoe  would  consequently  drop  upon 
the  naked  die. 

Cams,  Stamp  Heads,  and  Stems.— Cams  and  stamp  heads  ought  to  last 
several  years.  They  are  usually  broken  through  carelessness.  The  stems 
break  at  the  socket  of  the  stamp'  head.  Stems  are  reversible;  when  broken, 
they  may  be  swedged  or  planed  down  and  additional  lengths  welded  on 
when  necessary. 

Tappets.— When  there  is  much  grease  on  the  tappet  or  cam  or  when  the 


430 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


tappets  have  so  worn  that  the  face  of  the  cam  strikes  a grooved  instead  of  a 
level  face  on  a tappet,  the  rotary  motion  is  greatly  impaired.  Tappets  last 
for  several  years,  from  4 to  5 years  being  their  usual  life.  Sometimes  they 
are  broken  by  being  too  tightly  keyed.  When  their  faces  are  worn,  they 
are  planed  down.  They  are  reversible,  so  that  when  one  face  has  been 
worn  as  far  as  possible,  the  other  face  is  placed  downwards.  They  are 
usually  of  steel,  and  weigh  about  112  lb.  when  900-lb.  stamps  are  used. 

Battery  Water. — The  amount  of  water  fed  to  the  battery  depends  on  the 
character  of  the  ore  and  the  size  of  the  screen.  Clayey  arid  highly  sulphu- 
reted  ores  require  the  maximum  amount  of  water.  The  amount  of  water 
used  per  ton  of  ore  stamped  varies  from  1,000  to  2,400  gallons.  The  mean 
amount  used  per  ton  of  ore  stamped  is  about  1,800  gallons.  From  I to  li 
miner’s  inches  per  battery  should  be  provided.  In  winter,  when  the  battery 
water  is  chilly,  it  should,  when  possible,  be  heated  to  tepidity,  as  this  pro- 
motes amalgamation.  A high  temperature  should  be  avoided,  as  it  renders 
the  quicksilver  too  lively. 

Duty  of  Stamps.— The  capacity  of  gravity  stamps  varies  from  a little  over 
1 ton  per  stamp  for  24  hours  to  as  high  as  4 tons  per  stamp  for  24  hours, 
depending  on  the  quality  of  the  ore.  Usually,  an  average  of  from  1.7  to  2 
tons  per  stamp  for  24  hours  in  a combination  mill  would  be  good  practice, 
while  where  the  ore  is  crushed  to  a rather  coarse  screen  and  the  tailings 
treated  with  the  cyanide  process,  a larger  capacity  is  usually  obtained. 

The  number  of  tons  of  ore  crushed  per  stamp  depends  chiefly  on  the 
weight  of  the  stamp,  the  number  of  drops  per  minute,  the  height  of  drop, 
the  height  of  discharge,  the  size  of  the  screens,  the  width  of  the  mortar,  and 
chiefly  on  the  character  of  the  ore.  Hard  ores  and  ores  of  a clayey  nature 
(from  the  difficulty  experienced  in  discharging  the  clayey  pulp)  decrease 
the  duty  of  the  stamps.  About  2i  tons  per  stamp  in  24  hours  is  the  average 
duty  of  the  stamp  in  California.  The  discharging  capacity  of  a mortar 
depends  on  the  height  and  size  of  the  discharge  opening,  the  character  of 
the  screen,  and  the  width  of  the  mortar  discharge,  as  will  be  illustrated 
from  two  well-known  mills. 

The  Homestake  Mill  uses  an  850-lb.  stamp  dropped  9 in.,  85  times  per 
minute,  developing  78,030,000  ft.-lb.  in  24  hours,  and  crushing  4i  tons  of  rock, 
or  1 ton  for  every  17,340,000  ft.-lb.  developed. 

The  Caledonia  Mill  uses  an  850-lb.  stamp,  dropping  12  in.,  74  times  per 
minute,  crushing  3.3  tons,  of  rock  and  developing  90,576,000  ft.-lb.  in  24 
hours,  or  1 ton  to  every  24,447,272  ft.-lb.  developed.  Although  developing 
more  foot-pounds  in  24  hours,  and  therefore  seemingly  more  efficient,  yet  it 
crushes  less  rock  than  the  former.  The  reasons  for  this  are  (1)  that  the  rock 
is  harder  than  that  of  the  Homestake;  (2)  the  width  of  mortar  is  16  in. 
against  13i  in.;  and  (3)  the  2"  recess  for  the  8"  copper  plate  below  the  feed. 
On  the  other  hand,  the  Caledonia  has  a lower  discharge  from  the  mortar, 
using  6 in.  against  10  in.  in  the  Homestake;  but  this  advantage  is  again 
neutralized  by  a smaller  screen,  the  Caledonia  using  258  sq.  in.  against 
376  sq.  in.  of  the  Homestake. 

Horsepower  of  Stamps. — The  H.  P.  of  a stamp  battery  = 

No.  of  stamps  X wgt.  of  each  stamp  X No.  of  drops  per  min.  X drop  of  each  in  in. 

12X33,000 

The  weight  of  each  stamp  is  equal  to  the  sum  of  the  weights  of  the  stem, 
tappet,  stamp  head,  and  shoe.  To  the  nominal  H.  P.  add  25^^  for  friction  of 
machinery  in  calculating  driving  H.  P. 

Cost  of  Stamping. — The  cost  of  stamping  varies  from  a little  over  Sl.OO 
per  ton  up.  The  Montana  Co.,  Limited,  operating  a 60-stamp  combination 
mill,  in  1888  treated  40,530  tons  of  ore  at  S1.13  per  ton.  In  Australia,  stamp- 
mill  costs  have  been  reported  varying  from  $1.30  to  $2.50  per  ton  where 
fairly  favorable  conditions  for  working  could  be  obtained.  Figures  from 
other  districts  compare  favorably  with  these,  but  it  would  be  impossible  to 
give  any  absolute  rule  by  means  of  which  the  cost  can  be  determined  in 
advance,  without  an  intimate  knowledge  of  the  character  of  the  ore  and 
the  local  conditions. 

Pneumatic  Stamps.— This  is  a name  given  to  a form  of  large  capacity 
power  stamp,  the  head  of  which  is  connected  to  a piston  in  an  air  cylinder. 
The  cylinder  is  raised  and  lowered  by  power,  the  air  forming  an  elastic 
connection  by  means  of  which  the  stamp  is  operated.  They  are  quite 
extensively  employed  in  crushing  tin  ore,  but  have  never  come  into  general 
use  for  other  purposes.  The  capacity  is  as  high  as  30  tons  per  24  hours. 


SIZING  AND  CLASSIFYING  APPARATUS. 


431 


Power  Stamps.— Various  forms  of  stamps  have  been  brought  out  at  differ- 
ent times,  intended  to  operate  by  power  like  a trip  hammer,  or  in  which 
the  stamps  were  connected  directly  to  the  cranks  operating  them  by  means 
of  spring  joints.  Nearly  all  of  these  forms  have  failed  on  account  of  exces- 
sive wear,  small  capacity,  and  the  large  amount  of  power  consumed. 

Steam  Stamps. — The  large  capacity  steam  stamp,  which  was  evolved  in 
connection  with  the  concentration  of  the  Lake  Superior  copper  ores,  con- 
sists of  a steam  cylinder  in  which  operates  a piston,  to  the  stem  of  which  the 
stamp  head  is  directly  connected.  Machines  of  this  style  are  usually 
made  very  large  and  heavy,  frequently  extending  through  two  or  three 
stories  of  the  mill,  and  having  a capacity  equivalent  to  from  60  to  100  ordi- 
nary gravity  stamps.  In  most  forms,  live  steam  is  admitted  on  top  of  the 
piston  during  the  descent  of  the  stamp,  thus  increasing  the  force  of  the 
blow.  For  lifting  the  stamp,  the  steam  is  throttled  so  that  a lower  pressure 
is  employed.  The  discharge  is  usually  through  a coarse  screen,  f"  to 
mesh  not  being  uncommon.  One  interesting  fact  connected  with  the  large 
steam  stamps  is  that  their  heavy  blows  do  not  cause  as  excessive  sliming  as 
the  lighter  gravity  stamps,  and  bn  this  account  this  form  of  stamp  has  been 
introduced  in  some  cases  for  crushing  free-milling  gold  ores. 

For  prospecting  work,  for  testing  properties,  or  for  operating  small  prop- 
erties, a number  of  forms  of  portable  or  semiportable  steam  stamps  have 
come  out  during  the  last  few  years.  One  of  these  (the  Tremain)  is  illus- 
trated in  Fig.  14.  In  this  form,  two  pistons  work  in  cylin- 
ders side  by  side  and  strike  alternate  blows  in  a common 
mortar.  The  steam  is  introduced  at  full  boiler  pressure  on 
the  lower  side  of  the  cylinder,  which,  owing  to  the  large 
diameter  of  the  piston  rod,  has  a small  area.  This  high  pres- 
sure  steam  is  then  allowed  to  expand  on  to  the  top  of  the  mTTI 
piston,  thus  urging  it  down  with  greater  force  than  its  own  j 
weight  would.  These  steam  stamps  can  be  run  at  a much 
higher  speed  than  gravity  stamps,  and  hence  have  a greater  |tT|4 
capacity.  In  the  figure  shown,  three  screens  are  employed, 
one  in  front  and  one  at  each  end  of  the  mortar.  There"  are  j 

several  other  forms  of  portable  steam  stamps  manufactured. 

They  all  have  the  advantage  that  for  a small  property  they 
can  be  installed  with  much  less  trouble  than  any  other  form 
of  crusher,  owing  to  the  fact  that  no  steam  engine  is  required 
and  the  steam  necessary  to  drive  them  can  usually  be 
obtained  from  the  boiler  operating  the  hoisting  engine, 
pumps,  etc. 

Miscellaneous  Forms  of  Crushers.— Most  crushers  can  be  Fig.  14. 

classed  under  one  of  the  previous  heads,  but  there  are  some 
forms  that  depend  on  the  material  itself  to  do  the  crushing.  For  instance, 
in  the  preparation  of  coal  for  coke  ovens,  there  has  been  a combined  crusher 
and  separator  invented  that  may  be  described  as  follows:  A large  horizontal 
drum  or  cylinder,  provided  with  screen  openings  around  its  periphery,  is 
mounted  in  a horizontal  position.  The  coal  to  be  separated  is  fed  into  one 
end  and  is  caught  by  shelves  or  plates  projecting  radially  into  the  cylinder. 
These  lift  the  material  to  the  upper  side,  from  which  it  falls  by  gravity  and 
strikes  the  bottom,  thus  crushing  the  softer  parts.  The  sulphur  and  slate, 
being  harder  than  the  coal,  are  not  crushed  by  the  same  height  of  fall,  and 
hence,  by  a proper  adjustment  of  the  diameter  of  the  cylinder,  the  coal  may 
be  crushed  and  discharged  through  the  screen  while  the  slate  and  sulphur 
will  pass  out  at  the  opposite  end  of  the  cylinder. 


SIZING  AND  CLASSIFYING  APPARATUS. 

Stationary  Screens,  Grizzlies,  Head-Bars,  or  Platform  Bars.— These  are  the 
various  names  given  to  an  inclined  screen  employed  for  removing  the 
fine  material  from  the  run  of  mine  so  that  only  the  coarse  portion  will  be 
passed  to  the  crushers.  At  concentrating  works,  the  term  grizzly  is  usually 
employed,  and  a common  form  is  shown  in  Fig.  15.  This  is  composed  of  flat 
bars  held  apart  by  cast-iron  washers  through  which  the  bar  bolts  are  passed 
to  hold  the  entire  frame  together.  Grizzlies  are  usually  placed  at  an  angle 
of  from  -45°  to  55°,  and  ordinarily,  for  the  head  of  a large  concentrating 
works,  they  are  from  3 to  6 ft.  wide  and  from  8 to  12  ft.  long,  the  amount 
of  ^ace  between  the  bars  depending  on  the  size  of  the  run-of-mine  material 
and  on  its  subsequent  treatment. 


432 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


In  the  anthracite  coal  breakers,  the  terms  platform  bars  or  head-bars  are 
usually  employed,  and  these  bars  are  made  of  li"  to  2"  round  iron  placed  at 
an  inclination  of  5 in.  to  1 ft.,  the  spacing  depending  on  the  size  of  coal  it  is 
desired  to  make  in  the  breaker. 

At  ttie  present  time,  in  accordance  with  an  agreement  between  the  oper- 
ators and  the  miners’  officials,  the  standard  size  for  a bituminous  lump 
screen  (the  bars  are  called  a screen)  for  Ohio, 
Pennsylvania,  Indiana,  and  Illinois  is  12  ft. 
long  and  6 ft. wide  over  the  screen  surface.  The 
screen  consists  of  6 bearing  bars  4 in.  by  | in. 
of  soft  steel  and  39  steel  screen  bars.  Fig.  16, 
with  li  in.  clear  space  between  bars.  In  Iowa, 
the  same  sized  bar  is  used,  but  the  space  be- 
tween the  bars  is  1|  in.  In  the  other  Western 
and  Southern  States  there  is  at  present  no 
standard. 

The  standard  nut-coal  screen  for  Pennsyl- 
vania and  Ohio  is  ^ in.  space,  but  | in.  is 
sometimes  used  and  the  nut  screen  is  often 
varied  to  suit  the  special  trade.  At  present 
very  few  pea  screens  are  used,  but  if  placed  under  a nut  screen,  the 
space  is  from  f in.  to  | in.  In  the  Pittsburg  region  of  Pennsylvania,  all 
coal  passing  through  screen  is  called  slack,  while,  on  the  Monongahela 
River,  coal  passing  through  ip'  screen  is  called  slack  and.  is  used  in  stokers. 
iMany  companies  are  at  present  crushing  their  run-of-mine  coal  to  make 
slack  suitable  for  stokers. 

It  is  difficult  to  classify  bituminous  coal  by  sizes,  but  as  nearly  as  possible 
the  following  seem  to  be  the  standard:  Lump,  all  coal  passing  over  li"  screen; 
nut,  all  coal  passing  through  ip'  openings  and  over  openings;  slack,  all 
coal  passing  through  screen.  If  a pea-coal  screen  is  used,  all  coal  passing 
over  I",  i",  and  f"  would  be  pea  coal,  and  that  passing  through  or  f" 

would  be  slack. 

Adjustable  Rars.— The  top  of  the  bar  is  cylindrical  and  projects  beyond  the 
web  which  supports  it,  so  that  any  lump  which  passes  through  the  upper 
part  will  fall  freely  without  jamming.  The  two  ends  of  the  bar  are  V shaped 
and  fit  into  similarly  shaped  grooves,  so  that  the  bars  can  be  set  at  distances 
from  each  other  varying  with  the  sum  of  the  width  of  the  bases  of  the 
triangles,  the  usual  opening  being  about  4 in.  These  bars  are  generally 
4 ft.  long,  but  they  can  be  of  any  size. 

Finger  bars  are  screen  bars  that  are  fixed  at  one  end  only,  and  the  bars 
are  narrower  at  the  lower  end  than  at  the  top,  so  that  the  spaces  between 
them  are  wider  at  the  bottom  than  at  the  top,  thus  giving  less  tendency  for 
pieces  of  material  to  become  wedged  between  the  bars. 

Movable  or  oscillating  bars  are  screen  bars  that  are  attached  to  eccentrics 
at  their  lower  ends,  the  eccentrics  of  adjoining  bars  being 
placed  180°  apart.  This  movement  throws  the  material  for-  5'ijj 

wards  and  the  bars  do  not  therefore  require  nearly  the  same  i 

inclination  as  fixed  bars.  — N 

Shaking  screens  have  an  advantage  in  that  the  entire  area  ^ 
of  the  screen  is  available  for  sizing,  and  hence  a greater 
capacity  can  be  obtained  from  a given  area  of  screening 
surface.  They  also  occupy  less  vertical  height  than  a revolv- 
ing screen.  In  coal  breakers  they  are  particularly  applicable 
where  the  coal  is  wet  and  has  a tendency  to  stick  together. 

The  principal  disadvantage  of  the  shaking  screen  is  that 
the  reciprocating  motion  imparts  a vibration  to  the  framing 
of  the  building.  For  anthracite  coal,  the  screens  usually 
have  an  angle  or  pitch  of  from  i in.  to  2 in.  per  foot,  the 
average  being  about  f in.  per  foot.  These  screens  are  run  at 
from  90  to  280  shakes  per  minute,  the  average  being  about  200 
shakes  per  minute,*  or  100  revolutions  per  minute  for  the 
cam-shaft.  The  throw  of  the  eccentric  or  cam  varies  from 
’2  in.  to  5 in.  Fig.  16. 

Similar  screens  are  employed  for  sizing  salt,  but  are  usually 
placed  at  a much  steeper  incline  and  are  frequently  so  hung  that  they  have  a 
combined  rocking  and  swinging  motion.  Shaking  screens  are  rarely  employed 
in  concentrating  works  on  account  of  the  fact  that  revolving  screens  can 
be  hung  in  the  upper  part  of  the  mill  where  they  will  not  interfere  with 


SCREENS. 


433 


other  machinery,  and  hence  the  greater  space  that  they  occupy  is  not 
objectionable  while  they  do  the  sizing  satisfactorily  without  imparting  jar 
to  the  structure. 

The  capacities  of  shaking  screens  operating  on  anthracite  coal  have  been 
given  as  follows.  The  parties  giving  these  figures  advise  the  use  of  140  R.  P.  M. 
for  the  cam-shaft. 

For  broken  and  egg  coal,  i sq.  ft.  per  ton  for  10  hours. 

For  stove  and  chestnut  coal,  i sq.  ft.  per  ton  for  10  hours. 

For  pea  and  buckwheat  coal,  ^ sq.  ft.  for  10  hours. 

For  birdseye  and  rice,  li  sq.  ft.  per  ton  for  10  hours. 

For  sizing  bituminous  coal,  inclined  shaking  screens  are  extensively  used 
in  certain  sections,  particularly  in  the  Middle  Western  States.  These  screens 
are  given  a shaking  motion  by  means  of  cams  and  connecting-rods,  which 
make  from  60  to  100  strokes  per  minute,  the  speed  varying  according  to  the  ‘ 
amount  of  moisture  in  the  coal.  The  throw  of  the  eccentric  is  about  6 in. 
These  screens  are  7 ft.  wide  and  vary  in  length  according  to  the  conditions 
in  the  tipple,  no  standard  having  been  adopted.  The  average  inclination  at 
which  they  are  set  is  14°,  though  this  angle  varies  under  different  conditions 
from  12°  to  15°.  The  capacity  of  these  screens  running  under  the  conditions 
given  above  is  ^ven  by  one  maker  as  2,000  to  2,500  tons  per  day  of  8 hours. 
In  one  test  lasting  8 hours,  2,000  tons  of  coal  were  passed  over  screens  having 
perforated  plates  of  the  following  dimensions: 

56  sq.  ft:  with  perforations  for  making  slack. 

56  sq.  ft.  with  1^"  perforations  for  making  pea  coal. 

28  sq.  ft.  with  2\"  perforations  for  making  nut  coal. 

28  sq.  ft.  with  4i"  perforations  for  making  egg  coal. 

Another  maker  uses,  for  taking  pea  and  dust  from  nut,  and  nut  from 
lump,  50  to  60  sq.  ft.  of  surface  for  each  size,  and  to  handle  600  to  800  tons  in 
8 hours  he  uses  a 4i"  travel  and  120  to  130  shakes  per  minute,  with  the 
screen  at  an  inclination  of  15°.  » 

Size  of  Mesh.— The  following  perforations  have  been  adopted  by  two  of  the 
largest  anthracite  coal  companies  as  the  dimensions  for  the  holes  in  shaking 
screens  to  produce  sizes  equivalent  to  those  produced  by  revolving  screens: 

Mesh  for  Shaking  Screens. 


Kind  of  Coal. 

Lehigh  Valley 
Coal  Co. 

Phila.  & Reading 
Coal  A;  Iron  Co. 

Kind  of  Coal. 

Round. 

Round. 

Square. 

Steamboat 

5|" 

5" 

Steamboat. 

Lump 

4V' 

4i// 

4" 

Large  broken. 

Broken  

3i" 

zl" 

2r' 

Small  broken. 

Egg  

2tV' 

2" 

Egg. 

Stove  

1|" 

IF' 

If" 

Stove. 

Chestnut  

16// 

V' 

7// 

T 

r 

Chestnut. 

Pea  

tV' 

j.// 

Pea. 

Buckwheat 

H" 

tb" 

i// 

Buckwheat. 

Rice 

tV^ 

tV' 

Rice. 

Revolving  Screens,  or  Trommels.— The  screen  is  placed  about  the  periphery 
of  a cylinder  or  frustum  of  a cone.  The  material  to  be  sized  is  introduced 
at  one  end;  the  small  size  passes  through  the  screen,  and  the  other  size  is 
discharged  from  the  other  end.  If  the  form  is  cylindrical,  it  is  necessary 
to  place  the  supporting  shaft  on  an  incline  so  that  the  material  will 
advance  toward  the  discharge  end.  The  inclination  of  the  shaft  deter- 
mines the  rapidity  with  w^hich  the  material  will  be  carried  through  the 
screen.  The  advantage  of  the  conical  screen  is  that  the  shaft  is  horizontal 
and  hence  the  bearings  are  simpler.  This  a very  decided  advantage  in 
many  mills  where  the  machinery  must  of  necessity  be  crowded  into  a 
minimum  space  and  be  hard  to  get  at. 

Pentagonal  screens,  or  screens  having  some  other  number  of  flat  sides, 
are  sometimes  employed.  These  are  run  at  a very  much  more  rapid  rate 
than  circular  screens,  it  being  intended  that  the  material  shall  be  thrown 
or  dashed  against  the  screen  surfaces  to  break  it  or  to  loosen  adhering  clay 


434 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


or  dirt.  The  shaft  is  sometimes  hollow,  and  streams  of  water  from  this 
hollow  shaft  wash  the  material  as  it  is  being  screened. 

Revolving  screens  are  frequently  jacketed,  that  is,  two  or  more  screens 
are  placed  concentrically  about  the  same  shaft,  the  inmost  one  being  the 
coarsest,  and  each  succeeding  screen  serving  to  make  additional  separations. 
This  method  reduces,  the  space  necessary  for  a given  amount  of  sizing 
machinery.  In  other  cases,  a long  cylindrical  screen  has  a coarse  mesh  near 
its  discharge  end  and  finer  mesh  near  the  entrance  end,  thus  making  two  or 
more  through  products  as  well  as  the  overproduct.  The  disadvantage  of 
jacketed  screens  is  that  the  necessarily  slow  speed  of  the  inmost  screen 
reduces  the  capacity  of  the  entire  combination,  so  that  if  rapid  work  is 
essential,  it  is  better  to  use  fairly  large-diameter  screens  placed  one  after  the 
other  in  place  of  jacketed  screens.  Another  disadvantage  is  that,  to  renew 
the  inner  jackets,  it  is  often  necessary  to  remove  the  outer  ones. 

The  disadvantages  of  having  two  or  more  sizes  of  wire  cloth  on  one  screen 
are  that  the  fine-meshed  screen  near  the  head  is  worn  out  rapidly,  as  all  the 
material  both  coarse  and  fine  passes  over  it,  while,  when  separate  screens 
are  employed,  each  screen  has  to  deal  only  with  its  through  or  over  sized 
product,  all  coarser  material  having  been  removed. 

Speed.— The  periphery  of  a revolving  screen  should  travel  about  200  ft. 
per  minute.  In  the  case  of  very  fine  material,  screens  are  sometimes  run 
faster  than  this. 

The  following  have  been  adopted  as  standard  speeds  for  screens  by  one 
of  the  largest  anthracite  coal  companies: 


Speed  of  Screens. 


Rev.  per  Minute.  Rev.' per  Minute. 

Mud  screens  8.87  Big  screens 8.52 

Counter  mud  screens 15.49  Pony  screens 10.87 

Cast-iron  screens 11.25  Buckwheat  screens 15.30 

Duty  of  Anthracite  Screens.— The  following  table  gives  the  number  of 
square  feet  of  screen  surface  required  for  a given  duty  in  the  case  of 
revolving  screens  working  upon  anthracite  coal: 

Egg  coal,  1 ton  per  1 sq.  ft.  per  10  hours. 

Stove  coal.  1 ton  per  11  sq.  ft.  per  10  hours. 

Chestnut  coal,  1 ton  per  li  sq.  ft.  per  10  hours. 

Pea  coal,  1 ton  per  2 sq.  ft.  per  10  hours. 

Buckwheat  coal,  1 ton  per  21  sq.  ft.  per  10  hours. 

Rice  coal,  1 ton  per  3|  sq.  ft.  per  10  hours. 

Culm,  1 ton  per  5 sq.  ft.  per  10  hours. 


These  figures  may  be  reduced  from  20^  to  30^  for  very  dry  or  wash  coal. 

Revolving  Screen  Mesh  for  Anthracite. — A standard*  mesh  for  revolving 
screens  for  sizing  anthracite  coal  was  adopted  some  years  ago,  but  it  is  only 
approximately  adhered  to  and  a considerable  variation  from  the  standard  is 
found  throughout  the  anthracite  region. 

The  following  are  probably  as  nearly  standard  meshes  for  revolving 
screens  for  sizing  anthracite  coal  as  can  be  given: 


Mesh  for  Sizing  Coal. 

Culm  passes  through  mesh. 

Birdseye  passes  over  1"  mesh,  and  through  mesh. 

Buckwheat  passes  over  1"  mesh,  and  through  i"  mesh. 

Pea  passes  over  i"  mesh,  and  through  1"  mesh. 

Chestnut  passes  over  1"  mesh,  and  through  If"  mesh. 

Stove  passes  over  If"  mesh,  and  through  2"  mesh. 

Egg  passes  over  2"  mesh,  and  through  21"  mesh. 

* Grate  passes  over  21"  mesh,  and  out  end  of  screen. 

* Special  grate  passes  over  3"  mesh,  and  out  end  of  screen. 

* Special  steamboat  passes  over  3"  bars,  and  through  6"  bars. 

Hydraulic  Classifiers.— The  separation  of  materials  by  this  class  of 

machinery  depends  upon  the  law  of  equally  falling  bodies,  which  may  be 
stated  as  follows;  Bodies  falling  free  in  a fluid,  fall  at  a speed  proportional 
to  their  weight  divided  by  the  resistance.  From  this  it  will  be  seen  that  small 
masses  of  a heavy  mineral  will  fall  as  rapidly  as  large  masses  of  a light 
mineral,  owing  to  the  fact  that  the  weight  increases  as  the  volume  and  the 


* These  sizes  aiul  “lump”  size  are  seldom  made,  and  there  is  no  uniformity  whatever  in  the 
sizes  called  by  these  names. 


HYDRAULIC  CLASSIFIERS. 


435 


resistance  only  as  the  area,  so  that  if  a quantity  of  galena  and  quartz  of 
various  sizes  were  introduced  into  water,  it  would  settle  into  approximate 
layers,  each  composed  of  relatively  large  pieces  of  quartz  and  relatively 
small  pieces  of  galena.  This  same  action  would  be  true  in  the  case  of  any 


minerals  differing  in  specific  gravity.  The  principal  representatives  of  the 
hydraulic  classifying  machines  are  the  Spitzkasten  and  Spitzlutten. 

The  Spitzkasten  consists  of  a series  of  pyramidal  boxes,  one  of  which  is 
shown  in  Fig.  17.  The  material  enters  the  box  at  a,  passes  down  under  the 
diving  board  b,  and  discharges  into  the  next  box  through  the  trough  c.  At 
the  bottom  of  the  box,  water  is  introduced  through  the  pipe  d from  the 
launder  g in  such  quantity  as  to  more  than  supply  the  opening  or  spigot  e. 
The  heavy  particles  of  mineral  settle  against  this  rising  stream  of  water  into 
the  elbow/,  from  which  they  are  washed  out  through  e.  Each  succeeding 
box  is  made  larger  than  the  preceding,  and  the  rising  current  is  so  regulated 
that  a different  product  will  settle  out  in  each. 

The  Spitzlutten  is  a V-shaped  box,  inside  of  which  is  set  another  V having 
the  same  slope,  the  material  flowing  down  between  the  two  V’s  on  one  side 
and  up  and  out  on  the  other.  The  distance  between  the  V’s  can  be  regulated, 
as  can  also  the  rising  current  of  water,  thus  obtaining  the  separation  desired. 

Many  other  forms  of  separators,  all  depending  on  this  same  principle, 
have  been  brought  out,  some  having  a conical  form,  some  being  arranged  in 
the  form  of  troughs,  and  others  as  boxes  of  various  shapes. 

The  Calumet  classifier,  Fig.  18,  consists  of  a series  of  boxes  or  pockets  in  the 
bottom  of  a gradually  widening 
trough.  Wash  water  enters 
a pipe  a and  discharges 
against  the  discharge 
which  is  however  not 
large  enough  to  carry  all  the 
water  off  directly,  hence  it  twirls 
and  eddies  in  the  bottom  of  the 
box  so  that  only  the  heaviest 
particles  having  weight  enough 
to  settle  in  this  disturbed  water 
pass  out  through  the  spigot.  A 
shield  c reflects  upward  currents 
and  confines  the  agitation  to  the 
bottom.  The  pulp  flowing  in 
the  direction  of  the  arrows  is 
deflected  downwards  by  the 
boards  s. 

The  settling  boxes  employed  for  mills  are  really  a form  of  hydraulic  classi- 
fier. They  are  usually  very  large  V-shaped  boxes  provided  with  a diving 
board  similar  to  that  shown  at  b in  Fig.  17,  but  no  current  of  water  is 


through 
directly 
spigot  d, 


436 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


introduced.  In  some  cases  a small  stream  of  the  heavy  muds  or  concen- 
trates is  kept  continually  flowing  from  the  bottom,  while  in  others  they 
are  drawn  off  intermittently.  One  very  important  point  to  be  observed 
in  settling  boxes  is  that  the  settling  action  depends  on  the  arresting  of 
the  current,  and  with  a given  amount  of  floor  space,  very  much  more 
efficient  settling  can  be  obtained  from  two  boxes  placed  side  by  side  and 
having  half  the  material  pass  through  each  than  from  two  boxes  placed 
in  series,  and  that  the  width  of  the  box  is  of  vastly  more  importance 
than  the  length.  The  depth  is  also  fairly  important,  and  a diving  board 
mast  always  be  introduced  to  prevent  surface  currents.  If  the  boxes 
are  properly  arranged,  nearly  all  the  solid  material  will  be  settled  out  of 
the  water. 

The  Jeffrey-Robinson  coal  washer,  Fig.  19,  which  operates  on  the  principle  of 
the  Spitzkasten,  consists  of  a steel  chamber  B in  the  form  of  an  inverted 
cone,  inside  of  which  are 
projecting  arms  and  stir- 
ring plates  (7,  C revolved 
by  a driving  gear  A.  The 
water  ■ supply  enters  at 
the  bottom  from  the 
water  pipe  P through 
perforations  M.  The  coal 
is  introduced  through  a 
chute  S and  is  kept  in  a 
continual  state  of  agita- 
tion by  the  current  of 
water,  and  being  lighter 
than  the  impurities,  it 
passes  out  through  the 
overflow  K onto  the  con- 
veyors E,  F and  through 
the  chutes  X,  X,  while 
the  water  and  sludge 
drain  through  the  hop- 
per into  the  sludge  tank 
G,  whence,  if  necessary, 
the  same  water  can  be 
again  pumped  by  the  pul-  Fig.  19. 

someter  H back  into  the 

washer.  (As  mentioned  elsewhere,  it  is  poor  practice  to  use  this  w^ater  over 
again  when  it  is  desired  to  decrease  the  percentage  of  sulphur  in  the 
washed  product  as  greatly  as  possible. ) 

The  heavy  impurities  sink  to  the  bottom  into  the  chamber  J and  when 
this  is  full  the  upper  of  the  two  valves  shown  is  closed  and  the  lower  valve  is 
opened  to  discharge  the  refuse. 

The  following  data  in  regard  to  one  of  these  washers  is  given  by 
Mr.  J.  J.  Ormsbee  in  the  Transactions  of  the  A.  I.  M.  E.  These  results  were 
obtained  at  the  Pratt  Mines,  Alabama,  with  a plant  having  a nominal 
capacity  of  400  tons  per  day.  By  washing  slack  that  passed  between  screen 
bars  spaced  f in.  in  the  clear,  the  washed  coal  contained  42?^  less  ash  than 
the  unwashed  coal,  the  reduction  in  sulphur  was  15^,  while  the  volatile 
matter  was  increased  4^,  and  the  fixed  carbon  hie.  With  coal  passing  over  f" 
perforations,  the  results  were  a reduction  of  48;i  in  ash,  15^  in  sulphur,  and  a 
gain  of  hio  in  volatile  matter  and  6^^  fixed  carbon.  These  results  indicate  that 
the  washer  is  better  adapted  to  large  sizes  than  to  fines.  The  amount  of 
water  used  per  ton  of  washed  coal  ivas  35.1  gallons  and  the  cost  was 
2.25  cents  per  ton  for  washing  400  tons,  itemized  as  follows:  Labor  at  washer, 
S2.00;  labor  at  boiler,  fuel,  etc.,  ^.00;  repairs  and  supplies,  $3.00;  total,  $9.00. 

Log  Washer.— For  removing  clay  from  ores  or  other  material,  the  log 
washer  illustrated  in  Fig.  20  has  proved  itself  to  be  efficient.  Either 
single  or  double  logs  are  employed,  the  form  shown  being  the  double- 
log washer.  The  logs  work  over  troughs  which  have  a slight  inclination, 
so  that  the  water  will  flow  from  one  end  to  the  other.  Water  is  introduced 
at  the  upper  end  and  discharged  at  the  lower  end.  The  material  to  be  washed 
is  introduced  near  the  lower  end  and  is  fed  up  against  the  water  by  spiral 
arms  or  plates  fixed  about  the  logs,  as  shown  in  the  illustration.  As  the 
material  is  advanced,  the  clay  or  other  sticky  substance  is  broken  up, 
washed  away,  and  discharged  at  the  lower  end  with  the  wash  water. 


LOG  AND  TROUGH  WASHERS. 


437 


These  washers  have  been  extensively  employed  for  cleaning  iron  ores 
occurring  as  rather  hard  masses  in  clay. 

There  is  no  general  standard  size  of  these  washers,  but  most  of  the  double- 
log washers  for  both  steel  and  wood  logs  are  the  same,  except  in  length  of 
logs,  the  washer  box  being  7 ft. 

4 in.  wide,  2 ft.  deep  at  discharge 
end,  and  4 ft.  deep  at  receiving 
end.  The  length  of  logs  varies 
from  20  to  30  ft.  The  logs  are 
generally  given  an  elevation  of 
1 in.  in  1 ft.,  and  sometimes  li  in. 
in  1 ft. 

The  capacity  of  an  ore  washer 
depends  very  much  on  the 
quality  of  the  material,  avera- 
ging for  one  pair  of  logs  from  100 
tons  per  day,  when  the  matrix 
is  of  a clayey  nature,  to  350  tons 
with  loose  sandy  material.  The 
capacity  of  a washer  is  based 
on  the  amount  of  material  from 
the  mines  it  will  put  through 
more  than  the  tonnage  of  clean 
ore,  and  this  amount  varies  from 
600  to  1,000  yd.  per  10  hours.  The  amount  of  water  used  varies  from  300  to 
500  gal.  per  minute.  The  total  expense  for  labor  and  fuel,  including  the 
water  supply,  varies  from  5 cents  to  25  cents  per  ton  of  ore,  averaging 
possibly  10  cents  per  ton. 

The  Scaife  trough  washer  consists  of  a semicircular  iron  trough  2 ft. 
in  diameter  and  24  ft.  long.  Inside  is  a series  of  fixed  dams  or  partitions 
that  can  be  made  higher  or  lower,  as  required,  by  means  of  plates.  A shaft 
running  the  entire  length  of  the  trough  and  turning  in  babbitted  journals 
carries  a number  of  stirring  arms  or  forks  and  is  given  a reciprocating 
motion  by  a connecting-rod  attached  to  a driving  pulley  at  its  center.  The 
coal  is  fed  with  water  at  the  upper  end  of  the  trough,  and  by  the  action  of 
the  fiowing  water  and  the  agitation  of  the  arms,  the  slate,  pyrites,  and  other 
impurities  settle  at  the  bottom  and  are  caught  behind  the  dams,  while  the 
clean  coal  passes  over  the  dams  and  out  at  the  lower  end  of  the  trough. 
When  the  spaces  behind  the  dams  are  filled,  feeding  is  stopped  and  the 
refuse  in  the  dams  quickly  dumped.  This  form  of  washer  is  particularly 
successful  with  coal  mixed  with  fireclay.  One  washer  handles  from  75  to 
100  tons  of  coal  per  day,  and  one  man  can  attend  to  six  washers.  Each 
washer  requires  less  than  1 H.  P.  to  operate  it.  The  larger  the  coal,  the 
greater  must  be  the  slope  and  the  quantity  of  water  used. 

Jigs. — This  is  a general  term  applied  to  that  class  of  concentrating 
machines  in  which  the  separation  of  the  mineral  from  the  gangue  takes 
place  on  a screen  or  bed  of  material  and  is  effected  by  pulsating  up-and- 
down  currents  of  a fiuid  medium. 

There  are  a number  of  different  methods  in  use  for  driving  the  pistons 
that  cause  the  pulsations  of  the  water  in  jigs.  Some  of  these  use  plain 
eccentrics,  giving  the  same  time  to  both  the  up  and  the  down  strokes  of  the 
pistons,  while  others  employ  special  arrangements  of  parts,  which  give  a 
quick  dov/n  stroke  and  a slow  up  stroke,  thus  allowing  the  water  ample 
time  to  work  its  way  back  through  the  bed  without  any  sucking  action 
from  the  piston.  This  tends  to  make  a better  separation  in  some  cases  than 
the  use  of  the  plain  eccentrics. 

Stationary  Screen  Jigs.— This  class  is  illustrated  by  Fig.  21,  which  shows  a 
3-compartment  jig.  The  separation  takes  place  on  screens  supported  on 
wooden  frames  gr,  and  is  effected  by  moving  the  water  in  each  compartment 
so  that  it  ascends  through  the  screen,  lifting  the  mineral  and  allowing  it  to 
settle  again,  thus  giving  the  material  an  opportunity  to  arrange  itself  accord- 
ing to  the  law  of  equally  falling  particles.  Each  compartment  is  composed 
of  two  separate  parts,  one  containing  the  screen  on  the  support  g and  the 
other  adjoining  it  and  arranged  so  that  the  piston  in  it  may  impart  the 
necessary  pulsations  to  the  water.  These  pistons  are  usually  loose  fitting  and 
are  operated  by  the  eccentrics  e on  the  shaft  s.  Jigs  operating  on  coarse  ore 
should  be  fed  with  approximately  sized  material,  when  the  ore  will  accumu- 
late near  the  bottom  on  the  screen  and  the  barren  portion  or  gangue  will 


438 


ORE  DRESSING  AND  PREPARATION  OF  COAL, 


be  carried  over  the  discharge.  Formerly,  the  concentrates  were  discharged 
from  jigs  intermittently  by  digging  out  the  tailings  first,  then  the  middlings, 
which  are  composed  of  pieces  containing  some  ore  and  some  gangue,  and 
then  the  concentrates,  but  it  has  been  found  that  the  concentrates  will 
flow  over  the  screen  like  a liquid  of  comparatively  heavy  specific  gravity, 


Advantage  has  been  taken  of  this  fact  in  the  design  of  several  forms  of  jig 
discharges. 

The  Heberle  gate,  Fig.  22,  acts  as  follows:  a is  a U-shaped  shield  fastened 
against  the  inside  of  the  jig  and  held  in  place  by  a band  6,  the  ends  of 
which  are  drawn  down  into  the  form  of 
bolts  and  pass  through  the  sides  of  the 
jig,  where  they  are  secured  with  suitable 
nuts.  The  shield  a may  be  raised  or 
lowered  by  loosening  the  band  b.  The 
discharge  takes  place  through  the  open- 
ing ^ in  the  side  of  the  jig,  the  size  and 
position  of  the  opening  being  regulated 
by  slides  c.  The  concentrates  k rest  on 
the  screen  e supported  by  a grating  d, 
while  the  tailings  i occupy  a higher  posi- 
tion. The  shield  a prevents  the  tailings 
from  flowing  out  through  the  opening  /, 
while  the  concentrates  flow  along  the 
screen  and  rise  to  a height  somewhat 
lower  than  the  top  of  the  tailings  in  the 
jig,  when  they  are  discharged  through  the 
opening  / over  the  spout  h,  as  shown  at 
p.  The  tailings  are  usually  discharged 
over  the  dam  at  the  end  of  the  jig,  and 
in  some  cases  a third  discharge  is  provided  of  the  Heberle-gate  pattern 
and  so  arranged  that  the  middlings  will  flow  out  through  it  and  discharge 
separately  from  the  tailings  and  the  concentrates. 

In  the  case  of  jigs  handling  fine  material,  the  material  may  be  sorted  by 
hydraulic  classifiers  and  then  introduced  on  to  the  jigs.  In  this  class  the 
mineral  will  be  in  the  form  of  relatively  small  pieces,  while  the  gangue  will 
occur  as  relatively  large  pieces.  Advantage  may  be  taken  of  this  fact  by 
regulating  the  mesh  of  the  jig  screen  so  that  the  concentrates  will  pass 
through  into  the  space  below  the  screen,  commonly  called  the  hutch,  while 
the  tailings  will  pass  over  the  tailing  dam.  In  some  cases  the  gate 
discharge  is  employed  on  the  side  to  remove  the  middlings.  The  middlings 
are  recrushed  and  treated  on  other  machines.  This  form  of  concentration 
has  been  used  very  largely  in  connection  with  the  Lake  Superior  copper 
ores,  the  values  of  which  occur  as  metallic  copper  in  a relatively  light 
gangue,  and  also  in  concentrating  tin  ores  that  occur  in  the  light  gangue 
containing  considerable  mica. 


THEORY  OF  JIGGING. 


439 


Theory  of  Jigging. — By  far  the  most  exhaustive  investigations  on  the  theory 
of  jigging  carried  on  in  America  are  those  of  Prof.  Robert  H.  Richards,  of  the 
Massachusetts  Institute  of  Technology,  and  the  greater  part  of  the  following 
theoretical  discussion  is  based  on  his  several  papers  published  in  the  Trans- 
actions of  the  American  Institute  of  Mining  Engineers. 

Four  laws  of  jigging  are  given  by  the  several  authorities:  (1)  The  law  of 
equal  settling  particles,  under  free  settling  conditions;  (2)  the  law  of 
interstitial  currents,  or  settling  under  hindered  settling  conditions;  (3)  the 
law  of  acceleration;  (4)  the  law  ofisuction. 

The  first  of  these  is  the  most  important,  but  the  others  are  elements  that 
cannot  be  disregarded  in  connection  with  jigging. 

Equal  Settling  Particles.— Rittinger  gives' the  following  formulas  to  repre- 
sent the  relation  between  diameter  of  grains  and  rate  of  falling  in  water  for 
irregularly  shaped  grains:  

V = 2.73 1/ 1){8  — 1),  for  roundish  grains; 

V = 2.14^/ 1){8  — 1),  for  average  grains; 

V — 2.37 1/ D(6  — 1),  for  long  grains; 

V = 1.92 1/ D{8  — 1),  for  flat  grains, 

in  which  V — velocity  in  m-eters  per  second;  i)  = diameter  of  particles  in 
meters,  and  5 = specific  gravity  of  the  minerals. 

By  means  of  these  different  formulas,  the  ratios  of  the  diameters  of 
different  particles  that  will  be  equal  settling  in  water  can  be  computed. 
Professor  Richards  has  not  found  these  formulas  to  hold  in  all  cases  in 
practice,  and,  as  the  result  of  elaborate  experiments,  he  gives  the  following 
table: 

Equal  Settling  Factors  or  Multipliers. 

Table  of  equal  settling  factors  or  multipliers  for  obtaining  the  diameter  of 
a quartz  grain  that  will  be  equal  settling  under  free  settling  conditions  with 
the  mineral  specified. 


% 

Velocity  in  Inches  per  Second. 

OJ  02 

5 

o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

*s 

o 

ft 

m 

Author’s  Multipliers. 

g| 

Anthracite  

1.473 

.500 

.352 

.225 

.213 

.288 

Epidote 

3.380 

1.57 

1.35 

1.05 

1.13 

1.50 

1.61 

1.56 

1.56 

1.47 

1.45 

Sphalerite 

4.046 

1.46 

1.05 

1.17 

1.62 

1.64 

1.68 

1.66 

1.56 

1.85 

Pyrrhotite  

4.508 

1.73 

1.29 

1.48 

2.00 

2.22 

2.26 

2.13 

2.08 

2.14 

Chal cocite  

5.334 

1.90 

1.47 

1.62 

2.07 

2.28 

2.41 

2.44 

2.17 

2.64 

Arsenopyrite  ... 

5.627 

1.90 

1.57 

1.89 

2.42 

2.56 

2.72 

2.84 

2.94 

2.82 

Cassiterite 

6.261 

2.11 

1.79 

2.00 

2.73 

2.93 

3.03 

3.05 

3.12 

3.32 

Anitmony 

6.706 

2.71 

2.00 

2.00 

2.73 

2.93 

3.03 

2.98 

3.00 

3.48 

Wolframite 

6.937 

2.71 

1.83 

2.07 

2.86 

3.04 

3.21 

3.28 

3.26 

3.64 

Galena  

7.856 

2.71 

1.83 

2.26 

3.00 

3.42 

3.65 

3.76 

3.75 

4.01 

Copper  

Quartz  

8.479 

2.640 

2.71 

2.00 

2.36 

3.00 

3.20 

3.58 

3.76 

3.75 

4.56 

The  significance  of  the  above  table  is  as  follows:  If  a piece  of  anthracite 
of  a certain  size  falls  in  water  with  a velocity  of  4 in.  per  second,  a piece  of 
quartz  0.213  times  the  diameter  of  the  anthracite  will  fall  with  the  same 
velocity.  If  a piece  of  quartz  of  a certain  size  falls  with  a velocity  of  7 in. 
per  second,  a piece  of  copper  3.58  times  as  large  as  the  quartz  will  fall  with 
the  same  velocity. 

Interstitial  Currents,  or  Law  of  Settling  Under  Hindered  Settling  Conditions. 

If  d equals  the  diameter  of  a falling  particle,  and  D that  of  the  tube  in  which 

it  falls,  the  larger  the  fraction  — , the  greater  will  be  the  retardation  or  loss 


440  OBE  DBESSINO  AND  PBEPARATION  OP  COAL. 


of  velocity  by  the  particle.  When  this  fraction  equals  1,  the  particle  stops. 
If,  in  Fig.  23  (a),  the  larger  circles  represent  particles  of  quartz  and  the 
smaller  circles  equal  settling  particles  of  galena,  then  if  these  mixed  parti- 
cles are  settling  together  or  are  held  in  suspension  by  a rising  current  of 
water,  each  particle  may  be  considered  to  be  falling  in  a tube,  the  walls  of 
which  consist  of  the  surrounding  particles.  Substituting  a circle  in  each 


than  for  the  quartz,  and  it  will 
therefore  be  much  less  impeded  in 
its  fall  than  the  quartz;  hence,  the 
I)articles  of  galena  found  adjacent 
to  the  particles  of  quartz  will  be 


Fig.  23. 


smaller  than  the  ratio  that  the  law  of  equal  settling  particles  under 
free  settling  conditions  would  indicate.  Application  of  this  principle  is 
found  when  a mass  of  grains  is  subjected  to  a rising  current  of  sufficient 
force  to  rearrange  the  grains  according  to  their  settling  power  and  the 
grains  are  said  to  be  treated  under  hindered  settling  conditions,  as  on  the 
bed  of  a jig. 

Interstitial  factors,  or  multipliers  for  obtaining  the  diameter  of  the  particle 
of  quartz  that  under  hindered  settling  conditions  will  be  found  adjacent 
to  and  in  equilibrium  with  the  particle  of  the  mineral  specified,  are  the 
following: 

Copper 8.598  Cassiterite  4.698  Pyrrhotite 2.808 

Galena 5.842  Arsenopyrite . .3.737  Sphalerite 2.127 

Wolframite...  5.155  Chalcocite 3.115  Epidote  1.628 

Antimony  ...4.897  Magnetite 2.808  Anthracite  1782 

These  signify  that,  after  pulsion  has  done  its  work  on  a jig  bed,  for  exam- 
ple, where  quartz  and  anthracite  are  being  jigged,  the  grains  will  be  so 
arranged  that  the  grains  of  quartz  are  .1782  times  the  diameter  of  the  grains 
of  anthracite  that  are  adjacent  to  and  in  equilibrium  with  them. 

Acceleration. — A particle  of  galena  that  is  equal  settling  to  the  particle  of 
quartz  reaches  its  maximum  velocity  in  perhaps  xV  the  time  required  by  the 
quartz.  The  oft-repeated  pulsations  of  a jig,  therefore,  give  the  galena  par- 
ticles a decided  advantage  over  the  quartz,  placing  beside  the  quartz,  when 
equilibrium  is  reached,  a much  smaller  particle  of  galena  than  we  should 
expect  according  to  the  law  of  equal  settling  particles. 

Suction  acts  to  draw  down  through  the  screen  small  grains,  mainly  of  the 
heavier  mineral,  which  are  distributed  among  large  grains.  It  increases  as 
the  length  of  plunger  stroke,  with  the  difference  in  specific  gravity  of  the 
two  minerals,  and  with  the  diminishing  of  the  thinkness  of  the  bed  on  the 
sieve,  whether  of  the  heavier  mineral  only  or  of  both  minerals.  The  law 
of  suction  seems  to  be  that  jigging  is  greatly  hindered  by  strong  suction 
where  the  two  minerals  are  nearly  of  the  same  size,  the  quickest  and  best 
work  then  being  done  with  no  suction;  but  when  the  two  minerals  differ 
much  in  size  of  particles,  the  quartz  being  the  larger,  strong  suction  is  not 
only  a great  advantage,  but  may  be  necessary  to  get  any  separation  at  all. 
Experiments  have  inmcated  an  approximate  boundary  between  grains  that 
are  helped  and  those  that  are  hindered  by  suction;  namely,  if  the  diameter 
of  the  quartz  particles  is  equal  to  or  greater  than  3.52  times  the  diameter 
of  the  other  mineral  particles,  then  separation  is  helped  by  suction;  if  less, 
separation  is  hindered.  This  value  3.52  (obtained  by  dividing  .0683  by  .0195) 
is  approximate  only,  and  it  will  differ  with  the  fracture  of  the  quartz  under 
consideration;  if  the  quartz  grains,  are  much  fiattened,  it  will  have  a large 
value. 

Eccentric  jigs  invariably  spend  more  time  on  pulsion  than  accelerated 
jigs.  Is  it  not  fair  to  conclude  that  the  eccentric  jigs  are  better  adapted  for 
treating  sands  that  require  the  most  pulsion?  Such  sands  are  the  sized 
products  from  the  trommel  and  the  first  spigot  of  the  hydraulic  classifier. 
On  the  other  hand,  may  not  the  long-protracted  mild  suction  of  the  acceler- 
ated jig  be  best  adapted  to  the  treatment  of  such  products  as  require 
primary  suction  for  their  separation;  for  example,  the  second  spigot  and 


THEORY  OF  JIGGING. 


441 


the  following  spigots  of  the  hydraulic  classifier?  This  may  be  the  reason 
that  the  Collom  jig  has  found  so  great  favor  at  Lake  Superior  and  at 
Anaconda,  where  all  the  jigging  is  done  on  true  hydraulic-separator 
products,  except  the  first  sieve  of  the  first  jig.  We  should,  however,  bear 
in  mind  that  the  somewhat  harsh  suction  of  the  eccentric  jig  can  be  made 
milder  by  increasing  the  hydraulic  water.  This  will  diminish  the  harden- 
ing of  the  bed,  but  it  cannot  lengthen  the  time  of  suction,  so  as  to  secure 
the  condition  as  presented  in  this  particular  by  the  accelerated  jigs. 

Two  extreme  suggestions  arise  from  a contemplation  of  the  experiments 
we  have  carried  on:  (1)  On  closely  sized  products,  an  accelerated  jig  should 
be  run  backwards,  to  lengthen  out  the  pulsion  period,  which  is  the  only 
period  that  does  any  work;  and  (2)  the  accelerated  jig  should  be  run  for- 
wards on  the  spigot  products  of  the  hydraulic  separator,  to  increase  the 
period  of  suction. 

In  the  way  of  the  first  suggestion,  there  are  two  difficulties,  either  of 
which  may  cancel  the  advantage:  firsts  the  violent  downward  motion  of  the 
quick  return  will  tend  to,“  blind  up  ” the  sieve;  and,  second^  the  same  action 
will  tend  to  pulverize  a soft  mineral  like  galena. 

Professor  Richards  summarizes  his  experiments  in  connection  with 
jigging  as  follows:  The  two  chief  reactions  of  jigging  are  pulsion  and  suc- 
tion. The  effect  of  pulsion  depends  on  the  laws  of  interstitial  currents,  or 
of  equal  settling  particles,  under  hindered  settling  conditions.  The  chief 
function  of  pulsion  is  to  save  the  larger  grains  of  the  heavier  mineral,  or  the 
grains  that  settle  faster  and  farther  than  the  waste.  The  effect  of  suction 
depends  on  the  interstitial  factor  of  the  minerals  to  be  separated.  If  this 
factor  is  greater  than  3.70,  suction  will  be  efficient  and  rapid.  If  the  factor 
is  less  than  3.70,  suction  will  be  much  hampered  and  hindered.  The  use  of 
a long  stroke  will  help  to  overcome  this  difficulty.  The  chief  function  of 
suction  is  to  save  the  particles  that  are  too  small  to  be  saved  by  the  law 
of  interstitial  currents,  acting  through  the  pulsion  of  the  jig.  For  jigging 
mixed  sizes,  pulsion  with  full  suction  should  be  used.  For  jigging  closely 
sized  products,  pulsion  with  a minimum  of  suction  should  be  used. 

The  degree  of  sizing  needed  as  preparation  for  jigging,  if  perfect  work  is 
desired,  depends  on  the  interstitial  factor  of  the  minerals  to  be  separated. 
If  the  factor  is  above  3.70  (assuming  this  value  to  be  sufficiently  proved), 
then  sizing  is  simply  a matter  of  convenience.  The  fine  slimes  should  of 
course  be  removed;  and  if  it  is  more  convenient  to  send  egg  size,  nut  size, 
pea  size,  and  sand  size,  each  to  its  own  jig,  the  suitable  screens  should  be 
provided  for  this  purpose  and  a hydraulic  separator  for  grading  the  finest 
sizes.  But  if,  on  the  other  hand,  the  factor  is  below  3.70,  then  the  jigging  of 
mixed  sizes  cannot  give  perfectly  clean  work,  and  the  separation  will  be 
approximate  only.  To  effect  the  most  perfect  separation,  close  sizing  must 
be  adopted,  and  the  closer  the  sizes  are  to  one  another,  the  more  rapid  and 
perfect  will  the  jigging  be.  There  may  be  conditions  where  the  jigging  of 
mixed  sizes  of  this  class  will  be  considered  sufficiently  satisfactory,  as  an 
expedient,  under  the  circumstances. 

Removal  of  Sulphur  From  Coal.— The  object  of  washing  coal  is  to  remove  the 
slate  and  pyrites,  thus  reducing  the  amount  of  ash  and  sulphur.  Many  forms 
of  washers  easily  and  cheaply  reduce  the  slate  from  20^  in  the  coal  to  8^  of 
ash  in  the  coke,  but  it  is  much  more  difficult  to  reduce  4^  of  sulphur  in  the 
coal  to  lie  or  less  of  sulphur  in  the  coke.  Sulphur  occurs  in  the  coal  in 
three  forms,  as  hydrogen  sulphide,  calcium  sulphate,  and  pyrite.  The  first 
is  volatile  and  is  removed  in  coking,  the  second  cannot  usually  be  removed 
by  preliminary  treatment,  and  it  is  the  removal  of  the  third  form  with  which 
washing  has  to  do.  The  presence  of  water  in  the  coke  ovens  apparently 
assists  the  removal  of  the  sulphur;  but  wet  coals  require  a longer  time  for 
coking  than  dry,  and,  therefore,  pyrite  should  be  removed  as  far  as  practicable 
before  charging  the  coal  into  the  coke  ovens.  The  pyrite  in  coal  as  it  comes 
from  the  mine  seems  to  be  in  particles  even  finer  than  those  of  the  coal  dust. 
This  impalpable  powder  or  fiour  pyrites  fioats  in  air  or  water.  This  being 
the  case,  the  common  practice  of  using  the  water  over  and  over  again  in  a 
washery  cannot  give  the  best  results  in  the  removal  of  sulphur,  as  some 
flour  pyrites  will  be  carried  back  each  time  and  remain  with  the  washed 
coal.  Experiments  made  by  Mr.  C.  C.  Upham,  of  New  York  City,  show  that 
the  critical  size  at  which  an  almost  complete  division  of  the  coal  and  pyrites 
takes  place  varies  with  coals  from  different  districts  and  beds,  and  in  laying 
out  coal-washing  plants,  the  proper  fineness  of  crushing  should  be  deter- 
piined  beforehand  by  careful  experiment. 


442 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


Preparation  of  Anthracite.— The  method  of  preparing  anthracite  coal  is 
clearly  shown,  graphically,  by  the  diagram  below.  This  consists  in  screen- 
ing the  coal  over  bars  and  through  revolving  or  over  shaking  screens, 
together  with  breaking  it  with  rolls  to  produce  the  required  market  size. 


The  large  lumps  of  slate  and  other  impurities  are  separated  by  hand  on  the 
platform  near  the  dump,  while  the  smaller  portions  are  picked  out  by  auto- 
matic pickers  or  by  hand  by  boys  or  old  men  seated  along  the  chutes  leading 
to  the  shipping  pockets  or  bins.  The  smaller  sizes  are  cleaned  by  jigging. 


HANDLING  OF  COAL. 


44: 


HANDLING  OF  MATERIAL. 

Anthracite  Coal.— The  following  may  be  taken  as  average  figures  for  the 
angle  or  grade  of  chutes  for  anthracite  coal,  to  be  used  where  the  chutes  are 
lined  with  sheet  steel:  For  broken  or  egg  coal,  in.  per  ft.;  for  stove  or 
chestnut  coal,  in.  per  ft.;  for  pea  coal,  4i  in.  per  ft.;  for  buckwheat  coal, 
6 in.  per  ft.;  for  rice  coal,  7 in.  per  ft.;  for  culm,  8 in.  per  ft. 

If  the  coal  is  to  start  on  the  chute,  1 in.  per  ft.  should  be  added  to  each  of 
the  above  figures;  while  if  the  chutes  are  lined  with  manganese  bronze  in 
place  of  steel,  the  above  figures  can  be  reduced  1 in.  per  ft.  for  coal  in 
motion,  or  would  remain  as  in  the  table  to  start  the  coal.  When  the  run  of 
mine  is  to  be  handled,  as  in  the  main  chute,  at  the  head  of  the  breaker,  the 
angle  should  be  not  less  than  5 in.  per  ft.,  or  practically  22i°  from  the  hori- 
zontal. If  chutes  for  hard  coal  are  lined  with  glass,  the  angle  can  be 
reduced  from  SO<fo  to  50/c,  depending  somewhat  on  the  nature  of  the  coal. 
In  all  cases,  the  flatter  the  coal,  the  steeper  the  angle  must  be,  on  account  of 
the  large  friction  surfaces  exposed,  compared  with  the  weight  of  the  piece. 
If  chutes  are  lined  with  cast  iron,  the  angle  should  be  about  the  same  as 
that  employed  for  steel,  though  sometimes  a slightly  greater  angle  is  allowed. 

The  following  table  is  printed  through  the  courtesy  of  the  Link-Belt 
Engineering  Co.,  Philadelphia,  Pa.: 


Pitch  at  Which  Anthkacite  Coal  Will  Run,  in  Inches  per  Foot. 


Kind  of  Coal. 

Sheet  Iron. 

Cast 

Iron. 

Glass. 

Glass. 

Start 

on. 

Con- 

tinue 

on. 

Start 

on. 

Start 

on. 

Con- 

tinue 

on. 

Start 

on. 

Con- 

tinue 

on. 

Dry. 

Wet. 

Broken  slate 

5i 

4f 

3i 

3 

Dry  egg  slate 

5i 

4f 

5i 

3i 

3 

Dry  stove  slate 

5i 

4i 

5i 

3i 

3 

Dry  chestnut  slate 

5 

4f 

5i 

3i 

3 

Broken  coal 

21 

2i 

Egg  coal 

3| 

3 

2i 

2i 

2i 

11 

Stove  coal 

4^ 

4i 

4f 

3 

2i 

2i 

21 

Chestnut  coal 

4| 

4i 

4^ 

3 

2i 

3 

21 

Pea  coal 

5i 

5 

5^ 

2i 

3 

2t% 

Buckwheat  No.I... 

3f 

31- 

3i 

31 

Buckwheat  No.2... 

3f 

3i 

3f 

31 

Buckwheat  No.3.... 

4| 

3f 

41 

41 

Buckwheat  No.4.... 

4| 

4} 

41 

41 

Bituminous  Coal  —When  the  run  of  mine  is  to  be  handled,  the  angle  of 
the  chutes  should  be  from  35°  to  45°  from  the  horizontal,  or  from  85  in.  to 
12  in.  per  ft.  If  the  coal  is  wet,  the  angle  should  always  be  steeper,  and 
coarse  coal  will  slide  on  a flatter  angle  than  slack  or  fine  coal. 

Ore,  Rock,  Etc.— For  coarse  fairly  dry  ore,  i.  e.,  from  2 in.  or  3 in.  size  up, 
chutes  may  have  an  angle  of  45°,  or  if  the  material  is  always  to  be  in  motion, 
the  ore  will  sometimes  slide  on  40°.  For  fine  ore  or  run  of  mine,  the  chutes 
should  have  an  angle  of  50°  from  the  horizontal  or  practically  14  in.  vertical 
to  1 ft.  horizontal. 

Flumes  and  Launders.— Water  flumes  are  given  grades  varying  from  4 or  5 to 
20  or  30  ft.  per  mile,  depending  on  the  surface  of  the  ground  and  the  amount 
of  water  to  be  carried.  Practical  results  have  demonstrated  the  fact  that  in 
ordinary  ground  the  water  should  travel  at  the  rate  of  from  180  to  200  ft.  per 
minute. 

Where  rather  coarse  stuff  is  to  be  carried  through  launders  in  a mill  with 
a comparatively  small  amount  of  water,  an  angle  of  2 in.  per  ft.  should  be 
used.  With  an  excess  of  water,  1 in.  per  ft.  will  be  ample.  The  spouting  for 
vanners  or  launders  from  trommels  carrying  rather  fine  material  should 
have  a grade  of  about  2 in.  per  ft.  In  placer  mining,  the  minimum  grade 


444 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


for  the  sluice  should  not  be  less  than  i in.  per  ft.,  or  about  4|^in.  period. 
Experiments  made  in  river  gravel  have  shown  that  with  a grade  of  from  1 in 
20  to  1 in  25,  60  cu.  ft.  per  min.  will  wash  140  to  175  cu.  yd.  per  day  of  24  hours. 

No  absolutely  definite  figures  can  be  given  on  this  subject,  owing  to  the 
fact  that  the  nature  of  the  ore  plays  an  important  part,  and  while  angular 
quartzose  ore  can  be  transported  at  a comparatively  flat  angle,  it  may  be 
necessary  to  use  quite  a steep  angle  if  the  material  is  of  a clayey  nature  or 
contains  many  large  flat  plates,  exposing  large  friction  surfaces  when  com- 
pared to  the  mass  of  the  pieces. 

The  following  tables  are  printed  through  the  courtesy  of  the  Link-Belt 
Engineering  Co.,  Philadelphia,  Pa.: 

Horizontal  Pressure  Exerted  by  Bituminous  Coal  Against  Vertical 
Retaining  Walls  per  Foot  of  Length. 


Surface  hori/ontflll^^^^l  = 6.37^2 

buriace  nonzontai  | pressure  lowest  ft.  = 6.37(2  d-1) 

Surface  slonine- i pressure  = 10 d2 

buriace  sloping | pressure  lowest  ft.  = 10(2 d-1) 

Angle  of  repose  = 35° 

d = height  of  wall  in  feet  or  a 6 

a 

BITUMINOUS. 


Depth  5 a in  Ft. 

Horizontal 
Surface. 
b m. 

Sloping 

Surface. 

be. 

Depth  bain  Ft. 

Horizontal 
Surface. 
b m. 

Sloping 
Surface. 
b e. 

Total 

Pressure. 

Pressure 
Lowest  Ft. 

Total 

Pressure. 

Pressure 
Lowest  Ft. 

Total 

Pressure. 

Pressure 
Lowest  Ft. 

Total 

Pressure. 

Pressure 
Lowest  Ft. 

1 

6.4 

6.4 

10 

10 

26 

4,305 

325 

6,760 

510 

2 

25.0 

19.0 

40 

30 

27 

4,641 

338 

7,290 

530 

3 

57.0 

32.0 

90 

50 

28 

4,993 

350 

7,840 

550 

4 

102.0 

45.0 

160 

70 

29 

5,358 

363 

8,410 

570 

5 

159.0 

57.0 

250 

90 

30 

5,733 

376 

9,000 

590 

6 

229.0 

70.0 

360 

110 

31 

6,122 

389 

9,610 

610 

7 

312.0 

83.0 

490 

130 

32 

6,523 

401 

10,240 

630 

8 

407.0 

96.0 

640 

150 

33 

6,935 

414 

10,890 

650 

9 

516.0 

108.0 

810 

170 

34 

7,362 

427 

11,560 

670 

10 

637.0 

121.0 

1,000 

190 

35 

7,778 

440 

12,250 

690 

11 

770.0 

134.0 

1,210 

210 

36 

8,253 

452 

12,960 

710 

12 

917.0 

146.0 

1,440 

230 

37 

8,754 

465 

13,690 

730 

13 

1,076.0 

159.0 

1,690 

250 

38 

9,193 

478 

14,440 

750 

14 

1,248.0 

172.0 

1,960 

270 

39 

9,682 

490 

15,210 

770 

15 

1,433.0 

185.0 

2,250 

290 

40 

10,192 

503 

16,000 

790 

16 

1,630.0 

197.0 

2.560 

310 

41 

10,669 

516 

16,810 

810 

17 

1,840.0 

210.0 

2,890 

330 

42 

11,236 

529 

17,640 

830 

18 

2,063.0 

223.0 

3,240 

350 

43 

11,797 

541 

18,490 

850 

19 

2,298.0 

236.0 

3,610 

370 

44 

12,331 

554 

19,360 

870 

20 

2,548.0 

248.0 

4,000 

390 

45 

12,968 

567 

20,250 

890 

21 

2,809.0 

261.0 

4,410 

410 

46 

13,478 

580 

21,160 

910 

22 

3,083.0 

274.0 

4,840 

430 

47 

14,100 

592 

22,090 

930 

23 

3,369.0 

287.0 

5,290 

450 

48 

14,679 

605 

23,040 

950 

24 

3,669.0 

299.0 

5,760 

470 

49 

15,275 

618 

24,010 

970 

25 

3,981.0 

312.0 

6,250 

490 

50 

15,925 

631 

25,000 

990 

Weight  of  coal  = 47  lb.  per  cu.  ft. 


HANDLING  OF  COAL. 


445 


Horizontal  Pressure  Exerted  by  Anthracite  Coal  Against  Vertical 
Retaining  Walls  per  Foot  of  Length. 


■{1 


Surface  horizontal 

Surface  sloping  | 

Angle  of  repose 
d = height  of  wall  in  feet. 


total  pressure 
^ pressure  lowest  ft. 
total  pressure 
pressure  lowest  ft. 


9.78 

9.78(2  d-1) 
14.22  d2 
14.22(2d  — 1) 
27° 


ANTHRACITE. 


4^ 

a 

Horizontal 

Surface. 

bm. 

Sloping 

Surface. 

be. 

ft 

B 

Horizontal 

Surface. 

bm. 

Sloping 

Surface. 

be. 

e 

fO 

.a 

6 

1— 1 (H 

d 

•— ! ^ 

e 

rO 

6 

1— 1 u 

d 

% ^ 

ge 

ft 

ft 

"o  M 

"O  M 

QQ  CC 

0) 

Q 

o w 

- 

O) 

ft 

H 1 

gi 

ft 

ft  o 

ft 

ft  o 

1-1 

ft 

ft  O 

M 

ft 

ft  o 
ft 

1 

9.78 

9.78 

14.22 

14.22 

26 

6,611.1 

498.78 

9,612.8 

725.21 

2 

39.12 

29.34 

56.88 

42.66 

27 

7,129.5 

518.35 

10,366.0 

753.67 

3 

88.02 

48.90 

127.98 

71.10 

28 

7,667.6 

537.90 

11,149.0 

782.10 

4 

156.48 

68.46 

227.52 

99.54 

29 

8,225.0 

557.46 

11,988.0 

810.54 

5 

244.50 

88.02 

355.50 

127.98 

30 

8,802.0 

577.01 

12,797.0 

839.00 

6 

352.08 

107.58 

511.92 

156.42 

31 

9,398.5 

596.59 

13,665.0 

867.41 

7 

479.22 

127.14 

696.78 

184.86 

32 

10,015.0 

616.14 

14,561.0 

895.86 

8 

625.92 

146.70 

910.08 

213.30 

33 

10,650.0 

635.70 

15,486.0 

924.30 

9 

792.18 

166.26 

1,151.82 

241.74 

34 

11,306.0 

655.26 

16,439.0 

952.70 

10 

978.00 

185.82 

1,422.00 

270.18 

35 

11,980.0 

674.81 

17,420.0 

981.19 

11 

1,183.38 

205.38 

1,720.62 

298.62 

36 

12,675.0 

694.39 

18,429.0 

1,009.60 

12 

1,408.32 

224.94 

2,047.68 

327.06 

37 

13,389.0 

713.94 

19,467.0 

1,038.10 

13 

1,652.82 

244.50 

2,403.18 

355.50 

38 

14,123.0 

733.50 

20,533.0 

1,066.50 

14 

1,916.88 

264.06 

2,787.12 

383.94 

39 

14,875.0 

753.07 

21,629.0 

1,095.00 

15 

2,200.50 

283.62 

3,199.50 

412.38 

40 

15,648.0 

772.63 

22,752.0 

1,123.40 

16 

2,503.68 

303.18 

3,640.32 

440.82 

41 

16,440.0 

792.20 

23,904.0 

1,151.80 

17 

2,826.42 

322.74 

4,109.56 

469.26 

42 

17,252.0 

811.74 

25,084.0 

1,180.30 

18 

3,168.72 

342.30 

4,607.28 

497.70 

43 

18,083.0 

830.73 

26,293.0 

1,208.70 

19 

3,530.58 

361.86 

5,133.42 

526.14 

44 

18,934.0 

850.86 

27,530.0 

1,237.20 

20 

3,912.00 

381.42 

5,688.00 

554.58 

45 

19,804.0 

870.41 

28,793.0 

1,265.60 

21 

4,313.00 

400.98 

6,271.00 

583.26 

46 

20,695.0 

889.99 

30,090.0 

1,294.00 

22 

4,733.50 

420.54 

6,882.50 

611.46 

47 

21,605.0 

909.54 

31,412.0 

1,322.30 

23 

5,173.70 

440.10 

7,522.50 

639.90 

48 

22,533.0 

929.10 

32,763.0 

1,350.90 

24 

5,633.30 

459.67 

8,190.70 

668.35 

49 

23,482.0 

948.66 

34,143.0 

1,379.40 

25 

6,112.60 

479.22 

8,887.50 

696.79 

50 

24,450.0 

968.21 

35,550.0 

1,407.90 

Horsepowers  for  Coal  Conveyors  (Coal  Included). 

Speed,  100  ft.  per  minute.  Conveyors,  100  ft.  long.  Standard  steel  troughs. 


1 Size  of 

1 Chain. 

Size  of 
Flights. 
In. 

Horizontal. 

Inclined. 

Size  of 
Chain. 

Size  of 
Flights. 
In. 

Horizontal. 

Inclined. 

12  In. 
Between 
Flights. 

18  In. 
Between 
Flights. 

12  In. 

Between 

Flights. 

16  In. 
Between 
Flights. 

24  In. 
Between 
Flights. 

16  In. 

Between 

Flights. 

B 

4X10 

2 

3 

<D 

5X15 

4 

3i 

4i 

4X12 

3 

2^ 

be 

6X18 

5 

4 

5i 

5X  12 

3^ 

3 

4 

o 

8X  18 

7 

5 

8 

5X15 

41 

3^ 

5^ 

p 

8 X 20 

8 

6 

10 

do 

6X18 

5i 

4i 

6i 

B 

8 X 24 

n 

7 

lU 

z 

10  X 24 

12i 

8 

14 

446 


ORE  DRESSING  AND  PREPARATION  OF  COAL. 


Weights  and  Capacities  of  Standakd  Steel  Buckets. 


1 

Chain. 

Size  of  Bucket. 
In. 

Weight  of 
Bucket. 
Lb. 

Capacity  of 
Bucket. 

Lb. 

Capacity  of  Elevator.  100'  per  Min. 

Number  of 

Drawing. 

Lb.  per  Min. 

Net  Tons  per  Hr. 

bO 

t3 

12X  9xm 

181 

11 

1,100 

33.0 

5,357 

Q 

14  X 9X1U 

221 

121 

1,250 

37.5 

5,357 

a 

18  X 9X1U 

27 

■ 161 

1,650 

49.5 

5,357 

24 X 9xm 

36 

22 

2,200 

66.0 

5,357 

12  X 10  X 16i 

20 

19 

1,380 

41.4 

5,357 

18  X 10  X 161 

29 

281 

2,072 

62.2 

5,357 

-C! 

O 

24X10X161 

38 

38 

2,760 

82.8 

5,357 

Q 

30  X 10  X 161 

461 

471 

3,450 

103.5 

5,357 

a 

18  X 12  X 161 

31 

33 

2,400 

72.0 

5,357 

24  X 12  X 161 

40 

44 

3,200 

96.0 

5,357 

30  X 12  X 161 

48 

55 

4,000 

120.0 

5,357 

Buckets  taken  f full.  Buckets  continuous.  1 lb.  of  coal  = 34  cu.  in. 


Elevating  Capacities  of  Malleable  Iron  Buckets. 


Table  gives  tons  (2,000  lb.)  of  pea  coal  per  hour  at  100  ft.  per  minute. 


Buckets. 

Capacities. 

Distance  Between  Buckets  in  In. 

Size. 

Wt. 

'Cu. 

1 

In. 

Lb. 

In. 

Lb. 

8 

10 

12 

14 

16 

18 

20 

j 22 

24 

21  X 4 

0.75 

15 

0.48 

2.16 

1.73 

1.44 

1.23 

1.08 

31  X 5 

1.50 

31 

0.97 

4.36 

3.49 

2.91 

2.49 

2.18 

1.94 

4X6 

2.00 

51 

1.57 

7.06 

5.65 

4.71 

4.04 

3.53 

3.14 

2.83 

41  X 7 

2.56 

75 

2.33 

10.38 

8.39 

6.99 

5.99 

5.19 

4.66 

4.19 

3.81 

5X8 

3.56 

102 

3.15 

11.34 

9.45 

8.10 

7.09 

6.30 

5.67 

5.15 

4.72 

6 XIO 

5.47 

185 

5.73 

17.19 

14.73 

12.88 

11.46 

10.31 

9.38 

8.59 

7 X12 

8.97 

287 

8.90 

22.88 

20.02 

17.80 

16.02  14.56 

13.35 

7 X14 

11.41 

295 

9.14 

20.56 

18.28 

16.45  14.95 

13.71 

10  X18 

t 

Weight  of  1 cu.  ft.  of  pea  coal  = 53.5  lb.  32.3  cu.  in.,  or  .0187  cu.  ft.  = 1 lb. 


Conveying  Capacities  of  Plights  at  100  Ft.  Per  Minute. 


(Tons  of  Pea  Coal  per  Hour.) 


Size 

of 

Flight. 

In. 

Horizontal. 

Inclined. 

10° 

20° 

30° 

Every 
16  In. 

Every 
18  In. 

Every 
24  In. 

Lb.  Coal 
per 

Flight. 

Every 
24  In. 

Every 
24  In. 

/ 

Every 
24  In. 

4X  10 

33.75 

30 

22.5 

15 

18.0 

14.25 

10.5 

4X12 

42.75 

38 

28.5 

19 

24.0 

18.00 

13.5 

5 X 12 

51.75 

46 

34.5 

23 

28.5 

22.50 

16.5 

5 X 15 

69.75 

62 

46.5 

31 

40.5 

31.50 

22.5 

6 X 18 

80 

60.0 

40 

49.5 

40.50 

31.5 

8 X 18 

120 

90.0 

60 

72.0 

57.00 

48.0 

8X  20 

105.0 

70 

84.0 

66.50 

56.0 

8 X 24 

135.0 

90 

120.0 

96.00 

72.0 

10X24 

172.5 

115 

150.0 

120.00 

90.0 

Note. — These  ratings  are  for  continuous  feed.  2,000  lb,  = 1 ton. 


HANDLING  OF  COAL. 


447 


Horsepower  for  Bucket  Elevators. 
H.P.= 

N = number  taken  from  table; 

H = height  of  elevator  in  feet; 

(0  = weight  of  material  in  one  bucket; 
d = distance  apart  of  buckets,  in  inches. 


Revolu- 

tions 

per 

Minute. 

Diameter  of  Head-Wheels. 

Revolu- 

tions 

per 

Minute. 

22  In. 

24  In. 

26  In. 

28  In. 

30  In. 

32  In. 

10 

.064 

.070 

.075 

.080 

.087 

.093 

10 

12 

.077 

.083 

.090 

.097 

.104 

.111 

12 

14 

.089 

.096 

.106 

.114 

.121 

.130 

14 

16 

.102 

.111 

.121 

.130 

.140 

.148 

16 

18 

.115 

.125 

.136 

.146 

.157 

.167 

18 

20 

.128 

.139 

.151 

.162 

.174 

.186 

20 

22 

.140 

.153 

.166 

.179 

.191 

.204 

22 

24 

.153 

.167 

.181 

.195 

.209 

.223 

24 

26 

.166 

.181 

.196 

.211 

.226 

.242 

26 

28 

.179 

.195 

.211 

.227 

.244 

.260 

28 

30 

.191 

.209 

.226 

.244 

.261 

.279 

30 

32 

.204 

.223 

.241 

.260 

.278 

.297 

32 

34 

.217 

.237 

.256 

.276 

.296 

.316 

34 

36 

.230 

.251 

.271 

.292 

.313 

.334 

36 

38 

.242 

.265 

.287 

.309 

.331 

.353 

38 

40 

.255 

.279 

.302 

.325 

.348 

.372 

40 

COST  OF  UNLOADING  COAL. 

Coal  is  generally  unloaded  from  railroad  cars  into  the  hold  of  a vessel  by 
some  form  of  unloader,  which  usually  raises  the  car  bodily  and  dumps  it 
directly  into  the  hold  of  the  vessel.  In  this  way  the  cost  of  unloading  has 
been  reduced  to  a very  small  figure,  and  the  speed  of  unloading  greatly 
increased.  The  cost  of  unloading  is  given  by  the  makers  of  the  Brown  hoist 
as  varying  from  2i  cents  per  ton  up  to  41  cents  per  ton;  deducting  in  each 
case  2 cents  for  trimming  the  coal  in  the  vessel,  the  actual  cost  of  loading 
varies  from  i cent  to  2i  cents  per  ton,  depending  on  the  conditions.  Along 
the  Lakes  it  is  customary  to  pay  a premium  of  i cent  per  ton  to  all  connected 
with  the  loading,  for  all  coal  loaded  in  excess  of  2,500  tons  per  day  and  1,800 
tons  per  night.  The  Brown  hoist  has  a guaranteed  capacity  of  at  least  300 
tons  per  hour,  but  this  has  been  greatly  exceeded  in  practice.  The  McMyler 
end  dump  has  a record  of  4.65  tons  per  minute,  and  the  McMyler  side  dump 
of  8.41  tons  per  minute.  These  figures  apply  to  the  lake  cities  of  the  United 
States.  (See  “ Mines  and  Minerals,”  May,  1898,  for  complete  description  of 
coal-unloading  machines.) 

The  C.  W.  Hunt  Co.,  West  New  Brighton,  New  York,  gives  the  following 
figures  for  handling  coal  along  the  Atlantic  seaboard:  The  cost  of  shoveling 
coal  by  hand  in  the  hold  of  the  vessel  into  ordinary  iron  buckets  is  about  G 
to  7 cents  per  ton  of  2,000  lb.;  the  cost  for  iron  ore,  phosphate  rock,  or  sand, 
about  10^  less.  The  cost  of  shoveling  coal  and  hoisting  it  out  of  vessel  to  the 
wharf  with  an  ordinary  hoist  with  manila  rope  is  12  to  13  cents  per  ton,  so 
that  the  hoisting  costs  about  the  same  as  the  shoveling.  The  cost  for  both 
shoveling  and  hoisting  with  a steam  engine  is  10  to  11  cents  per  ton.  The 
cost  when  using  a steam  shovel  or  grab  bucket  for  taking  up  coal  out  of  the 
vessel  varies  greatly  in  different  classes  of  vessels,  but  usually  runs  from 
about  li  to  5 cents  per  ton,  averaging  about  3 cents.  After  the  coal  is 
hoisted,  it  can  be  carried  into  storage  with  an  automatic  railway  or  other 
efficient  plant,  at  a cost  of  about  1 to  li  cents  per  ton.  In  places  where  the 
distance  is  great,  a cable  railway  or  a conveyor  can  be  used,  which  handles 
the  material  about  as  cheaply  as  for  short  distances,  but  the  cost  of  the  plant 
is  greatly  increased. 


448 


BEIQUETINO. 


The  cost  of  stocking  and  unloading  anthracite  by  the  Dodge  system  is 
given  by  Mr.  Piez,  “ Mines  and  Minerals,”  June,  1898,  page  488,  as  follows: 


Year. 

Engine  Service, 
Stocking  and 
f Lifting,  per  Ton. 

Cents. 

Office  Expense, 

per  Ton.  Cents. 

Steam,  Wages 

and  Fuel,  per 

Ton.  Cents. 

Labor,  Dumping 

and  Lifting,  per 

Ton.  Cents. 

Repairs,  per 

Ton.  Cents. 

Supplies,  per 

Ton.  Cents. 

Total,  per  Ton. 

Cents. 

1895 

.87 

.29 

.97 

2.67 

.78 

.25 

5.83 

1896  

.78 

.30 

.82 

2.19 

.90 

.27 

5.26 

1897  

.69 

.32 

.62 

1.88 

.97 

.16 

4.64 

BRIQUETING. 

Machines  Employed.— Fuel,  fuel  dust,  and  other  products  may  be  briqueted 
by  a number  of  different  styles  of  machines,  but  all  these  may  be  divided 
into  two  classes,  briquet  and  eggette  machines.  The  eggette  machines  have 
a pair  of  rollers,  the  faces  of  which  are  provided  with  semispherical  or  semi- 
ovoid  openings.  The  material  that  is  fed  between  these  rolls  crowds  into 
the  openings  of  the  two  rolls,  thus  forming  small  spheres.  The  material  is 
mixed  with  a suitable  bond  before  being  fed  to  the  rolls,  and  the  eggettes  are 
received  on  any  suitable  form  of  traveling  belt  or  chute  and  removed  for 
drying  or  storage.  This  style  of  machine  has  not  been  used  to  any  great 
extent  in  this  country.  The  briqueting  machines  all  act  more  or  less  on  the 
principle  of  the  brick  machine,  having  some  kind  of  a die  or  mold  into 
which  the  material  is  crowded.  The  material  is  either  pressed  as  it  is  being 
fed  into  the  mold  or  subsequently  by  some  form  of  plunger.  For  some 
materials,  common  brick  machines,  such  as  are  used  in  the  manu- 
facture of  building  brick,  are  employed,  while  in  others  special  forms  are 
necessary. 

Briqueting  of  Fuel. — Fuel  briquets  have  not  come  into  general  use  in  the 
United  States  for  two  reasons:  (1)  on  account  of  the  great  amount  of  cheap 
fuel  available,  which  has  prevented  the  utilization  of  culm,  coal  dust,  etc. ; 
and  (2)  on  account  of  the  lack  of  or  high  price  of  suitable  bonding  material. 
This  latter  condition  is  now  being  removed  by  the  introduction  of  by-product 
coke  ovens,  from  which  supplies  of  coal  tar  can  be  obtained.  Aside  from  peat 
and  certain  kinds  of  brown  coal,  and  possibly  some  caking  coals,  it  is  neces- 
sary to  employ  a bond  in  the  making  of  any  fuel  briquets.  This  is  especially 
true  in  the  case  of  anthracite  coal  The  present  tendency  is  to  employ  no 
inorganic  bonding  materials,  as  they  increase  the  ash.  The  material  to  be 
briqueted  should  be  as  clean  and  free  from  dirt  or  slate  as  possible,  and  the 
particles  should  be  of  practically  uniform  size,  the  most  satisfactory  product 
being  from  coal  crushed  to  about  }in.  cube  size.  The  coal  must  be  thor- 
oughly mixed  with  bonding  material  and  then  subjected  to  a heavy  pressure. 
One  advantage  claimed  for  briquets  is  that  they  can  be  made  of  such  a form 
as  to  occupy  less  space  than  the  original  fuel.  The  French  navy  has  found 
it  possible  to  store  10^  more  briquets  than  coal  in  a given  space,  and  also 
that  the  loss  by  breakage  and  pulverization  is  very  much  less.  Under  favor- 
able conditions,  fuel  can  be  briqueted  for  20  cents  per  ton,  and  the  following 
are  some  of  the  advantages  claimed  for  these  briquets:  They  are  sound 
throughout  and  will  not  decrepitate  while  burning,  thus  reducing  the 
loss  by  fine  material  working  through  the  grates.  The  bond,  if  properly 
selected,  renders  the  briquets  practically  waterproof,  so  that  they  are  not 
injured  if  kept  in  storage,  do  not  evolve  combustible  gases,  nor  ignite  from 
spontaneous  combustion.  There  is  no  fine  material  mixed  with  the  briquets, 
and  hence  a more  uniform  fire  can  be  maintained  with  them. 

Briqueting  of  Flue  Dust. — Flue  dust  from  iron  blast  furnaces  has  been  suc- 
cessfully briqueted  in  a number  of  instances.  One  firm  employs  a common 
brick  machine,  making  bricks  2i  in.  X 4^^  in.  X 9 in.  With  this  machine, 
they  mix  the  flue  dust  with  3^  of  lime  and  of  cement,  the  lime  acting  as 
a flux  in  the  furnace.  These  machines  work  with  comparatively  light  pres- 
sure. When  regular  briqueting  machines,  producing  round  bricks  and 


TREATMENT  OF  INJURED  PERSONS, 


449 


employing  high  pressures  are  employed,  no  cement  need  be  used,  the  flue  dust 
being  mixed  with  4^  to  6^  lime.  The  flue  dust  is  first  carefully  screened  from 
hard  lumps  and  then  mixed  warm  with  milk  of  lime  in  a mixer,  after 
which  it  is  put  through  the  press,  and  the  briquets  are  then  placed  in  drying 
ovens  and  subjected  to  heat  from  the  gases  of  a boiler  or  furnace  plant, 
the  temperature  not  to  exceed  300°  F.  For  moderate  sized  briquets,  about 
6 hours’  drying  is  sufficient.  Just  before  the  briquets  are  quite  dry,  they 
are  loaded  into  barrels  and  taken  direct  to  the  blast  furnace,  with  as 
little  handling  as  possible.  The  results  have  been  very  satisfactory  com- 
pared with  the  ore  replaced.  The  flue  dust  itself  frequently  contains  30^  to  40^ 
metallic  iron  and  more  or  less  carbonaceous  matter.  It  is  also  stated  that  at 
a large  furnace  plant  the  cost  of  making  and  handling  should  not  exceed 
^1  per  ton. 

Another  firm,  figuring  on  a basis  of  130  tons  per  24  hours,  and  using  3^ 


lime  in  the  solution,  gave  the  following  figures: 

4 tons  lime,  S3.00  per  ton $12.00 

2 machine  tenders  (day  and  night),  12  hours,  at  $2.50 5.00 

2 laborers  (day  and  night),  12  hours,  at  $1.75 3.50 

Oil  and  waste  2.00 

Wear  on  machinery 1.50 

Interest  on  cost  of  plant 1.00  $25.00 


This  is  less  than  20  cents  per  ton.  This  estimate  does  not  take  into  con- 
sideration the  cost  of  power,  which  would  be  about  35  H.  P.,  nor  does  it  take 
into  consideration  hauling  of  material  to  plant  and  removing  of  briquets. 


Cubic  Feet  Occupied  by  2,000  Pounds  of  Various  Coals. 


{Link-Belt  Engineering  Co.,  Philadelphia,  Pa.) 


Varieties. 

Broken. 

Egg. 

Stove. 

Chestnut. 

Pea. 

Lackawanna,  anthracite 

37:i0  ' 

36.65 

34.90 

34.35 

37.25 

Garfield  red  ash,  anthracite 

37.30 

36.95 

36.35 

36.35 

37.50 

Lykens  Valley,  anthracite 

37.55 

37.25 

37.55 

37.25 

38.50 

Shamokin,  anthracite  

38.05 

37.70 

37.25 

37.25 

38.50 

Plymouth  red  ash,  anthracite 

34.90 

34.85 

34.75 

34.70 

36.90 

Wilkes-Barre,  anthracite 

34.95 

34.35 

33.75 

34.00 

36.90 

Lehigh,  anthracite 

33.30 

33.80 

33.55 

32.55 

33.05 

Lorberry,  anthracite 

34.65 

34.20 

33.80 

33.55 

35.20 

Scranton,  anthracite 

35.35 

35.20 

34.60 

33.30 

34.95 

Pittston,  anthracite  

35.45 

34.95 

34.35 

33.70 

35.50 

Cumberland,  bituminous. 
Clearfield,  bituminous  .... 
New  River,  bituminous..... 


36.65 

33.55 

40.15 


Pocahontas,  bituminous 

American  cannel,  bituminous 
English  cannel,  bituminous.. 


34.00 

41.50 

42.30 


TREATMENT  OF  INJURED  PERSONS. 

The  dangers  to  be  feared  in  case  of  wounds,  are:  shock  or  collapse,  loss  of 
blood,  and  unnecessary  suffering  in  the  moving  of  the  patient. 

In  shock,  the  injured  person  lies  pale,  faint,  and  cold,  sometimes  insen- 
sible, with  feeble  pulse  and  superficial  breathing.  The  cause  of  death  in 
case  of  a shock  is  arrest  of  heart  action,  produced  by  the  suspension  of  the 
functions  of  the  brain  and  spinal  cord.  In  treatment,  the  two  most  import- 
ant parts  are:  (1)  the  position  of  the  injured  person;  (2)  the  application  of 
external  warmth. 

The  injured  person  should  at  once  be  placed  in  a recumbent  position,  his 
head  resting  on  a plane  lower  than  that  of  his  trunk,  legs,  and  feet.  He 
should  be  well  wrapped  up  and  protected  from  the  chilling  influences  of 
external  air.  When  there  is  danger  of  immediate  death,  stimulants  should 
be  given;  in  all  other  conditions  of  shock,  stimulants  are  injurious. 

Loss  of  Blood. — In  case  of  loss  of  blood,  two  conditions  present  themselves: 
(1)  The  bleeding  is  arrested  spontaneously  or  otherwise,  but  the  injured 
person  presents  all  the  symptoms  of  loss  of  blood;  (2)  the  injured  person  is 
actually  bleeding,  and  he  is,  or  is  not,  suffering  from  loss  of  blood. 

In  the  first  condition,  life  is  threatened  by  anemia  oi  brain  and  spinal 
cord,  and  all  the  efforts  of  treatment  are  to  direct  the  flow  of  whatever 


45d 


TREATMENT  OF  INJURED  PERSONS. 


a'liiiitity  of  blood  may  still  remain  in  the  body  to  the  vital  centers  in  the 
Main  and  spinal  cord.  This  is  most  efficiently  done  by  placing  the  injured 
person  in  a recumbent  position,  with  his  head  resting  on  a plane  somewhat 


Fig.  1. 


Fig.  2. 


lower  than  that  of  his  trunk  and  legs.  In  graver  cases,  constricting  bands 
should  be  applied  to  both  arms,  as  near  the  shoulders  as  possible,  and  to 
both  thighs,  as  near  the  abdomen  as  possible.  This  last  maneuver  directs 
the  entire  quantity  of  blood  in  the  body  to  the  suffering  centers,  the  centers 
of  life  itself.  Stimulants  may  be  sparingly  administered. 

If  there  is  bleeding,  do  not  try  to  stop  it  by  binding  up  the  wound.  The 
current  of  blood  to  the  part  must  be  checked.  To  do  this,  find  the  artery,  by  its 
beating;  lay  a firm  and  even  compress  or  pad  (made  of  cloth  or  rags  rolled 
up,  or  a round  stone  or  piece  of  wood  well  wrapped)  over  the  artery 
( Fig.  1 ) . Tie  a handkerchief  around  the  limb  and  compress ; put  a 
bit  of  stick  through  the  handkerchief  and  twist  the  latter  up 
until  it  is  just  tight  enough  to  stop  the  bleed- 
ing; then  put  one  end  of  the  stick  under 
the  handkerchief,  to  prevent  untwisting, 
as  in  Fig.  2. 

The  artery  in  the  thigh  runs  along  the 
inner  side  of  the  muscle  in  front  near  the 
bone,  as  shown  by  dotted  line  in  Fig.  3. 

A little  above  the  knee  it  passes  to  the 
back  of  the  bone.  In  injuries  at  or  above 
the  knee,  apply  the  compress  higher  up, 
on  the  inner  side  of  the  thigh,  at  the  point 
P,  Fig.  3,  with  the  knot  on  the  outside  of 
the  thigh. 

When  the  leg  is  injured  below  the 
knee,  apply  the  compress  at  the  back  of 
the  thigh,  just  above  the  knee,  at  P,  Fig.  4, 
and  the  knot  in  front,  as  in  Figs.  1 and  2. 

The  artery  in  the  arm  runs  down  the  inner  side  of  the  large  muscle  in 
front,  quite  close  to  the  bone,  as  shown  by  dotted  line;  low  down  it  is  further 
forwards,  towards  the  bend  of  the  elbow.  It  is  most  easily  compressed  a 
little  above  the  middle,  at  P,  Fig.  5.  Care  should  be  taken  to  examine  the 
limb  from  time  to  time,  and  to  lessen  the  compression  if  it  becomes  cold 
or  purple;  tighten  up  the  handkerchief 
again  if  the  bleeding  begins  afresh. 

To  Transport  a Wounded  Person  Comfortably. 

Make  a soft  and  even  bed  for  the  injured 
part,  of  straw,  folded  blankets,  quilts,  or 


Fig.  3. 


Fig.  4. 


Fig.  5. 


Fig.  6. 


gillows,  laid  on  a board  with  side  pieces  of  board  nailed  on,  when  this  can 
e done.  If  possible,  let  the  patient  be  laid  on  a door,  shutter,  settee,  or 
some  firm  support,  properly  covered.  Have  sufficient  force  to  lift  him 
steadily,  and  let  those  that  bear  him  not  keep  step. 

Should  any  important  arteries  be  opened,  apply  the  handkerchief,  as 
recommended.  Secure  the  vessel  by  a surgeon’s  dressing  forceps,  or  by  a 


TREATMENT  OF  PERSONS  OVERCOME  BY  OAS. 


451 


■hook,  then  have  a silk  ligature  put  around  the  vessel,  and  tighten.  Should 
the  bleeding  be  from  arterial  vessels  of  small  size,  apply  persulphate  0/  iron, 
either  in  tincture  or  in  powder,  by  wetting  a piece  of  lint  or  sponge  with  the 
solution;  then,  after  bleeding  ceases,  apply  a compress  against  the  parts,  to 
susijaln  them  during  the  application  of  the  persulphate  of  iron,  and  to  pre- 
further  bleeding,  should  it  occur.  The  persulphate  of  iron  should  be 
ikept  in  or  about  all  working  places. 

Bleeding  From  Scalp  Wounds.— A pad  or  compress  is  placed  immediately 
before  the  ear,  over  the  region  marked  by  a dotted  line.  Fig.  6.  The  com- 
press is  firmly  secured  by  a handkerchief.  If  this  does  not  arrest  bleeding,  a 
similar  compress  on  the  opposite  side  should  be  applied.  Should  the  bleed- 
ing issue  from  a wound  of  the  posterior  or  back  part  of  the  head,  a compress 
should  be  placed  behind  the  ear,  over  the  region  marked  by  the  dotted  line, 
Fig.  6,  and  firmly  secured  by  a handkerchief  or  bandage. 


TREATMENT  OF  PERSONS  OVERCOME  BY  GAS. 

Miners  are  exposed  to  asphyxia  when  the  circulation  of  the  air  is  not  suf- 
ficiently active,  when  the  mine  exhales  a quantity  of  deleterious  gas,  when 
they  imprudently  penetrate  into  old  and  abandoned  workings,  and  when 
there  is  an  explosion. 

The  symptoms  of  asphyxia  are  sudden  cessation  of  the  respiration,  of  the 
pulsations  of  the  heart,  and  of  the  action  of  the  senses;  the  countenance  is 
swollen  and  marked  with  reddish  spots,  the  eyes  are  protruded,  the  features 
are  distorted,  and  the  face  is  often  livid,  etc. 

The  best  and  first  remedy  to  employ,  and  in  which  the  greatest  confidence 
(ought  to  be  placed,  is  the  renewal  of  the  air  necessary  for  respiration. 
Proceed  as  follows; 

1.  Promptly  withdraw  the  asphyxiated  person  from  the  deleterious  place 
and  expose  him  to  pure  air. 

2.  Loosen  the  clothes  round  the  neck  and  chest,  and  dash  cold  water 
in  the  face  and  on  the  chest. 

3.  Attempts  should  be  made  to  irritate  the  mucous  membrane  with  the 
feathered  end  of  a quill,  which  should  be  gently  moved  in  the  nostrils  of  the 
insensible  person,  or  to  stimulate  it  with  a bottle  of  volatile  alkali  placed 
under  the  nose. 

4.  Keep  up  the  warmth  of  the  body,  and  apply  mustard  plasters  over  the 
heart  and  around  the  ankles. 

5.  If  these  means  fail  to  produce  respiration.  Doctor  Sylvester’s  method 
of  producing  artificial  respiration  should  be  tried  as  follows: 

Place  the  patient  on  the  back  on  a flat  surface,  inclined  a little  upwards 
from  the  feet;  raise  and  support  the  head  and  shoulders  on  a small  firm 
(Cushion  or  folded  article  of  dress  placed  under  the  shoulder  blades.  Draw 
forwards  the  patient’s  tongue  and  keep  it  projecting  beyond  the  lips;  an 
(elastic  band  over  the  tongue  and  under  the  chin  will  answer  this  purpose,  or 
a piece  of  string  or  tape  may  be  tied  around  them,  or  by  raising  the  lower 
jaw  the  teeth  may  be  made  to  retain  the  tongue  in  that  position.  Remove 
all  tight  clothing  from  about  the  neck  and  chest,  especially  the  suspenders. 
Then  standing  at  the  patient’s  head,  grasp  the  arms  just  above  the  elbows, 
and  draw  the  arms  gently  and  steadily  upwar(is  above  the  head,  and  keep 
them  stretched  upwards  for  2 seconds  (by  this  means  air  is  drawn  into  the 
lungs).  Then  turn  down  the  patient’s  arms  and  press  them  gently  and 
firmly  for  2 seconds  against  the  sides  of  the  chest  (by  this  means  air  is  pressed 
out  of  the  lungs).  Repeat  these  measures  alternately,  deliberately,  and  per- 
severingly  about  15  times  in  a minute,  until  a spontaneous  effort  to  respire 
is  perceived,  immediately  upon  which  cease  to  imitate  the  movements  of 
breathing,  and  proceed  to  induce  circulation  and  warmth. 

6.  To  promote  warmth  and  circulation,  rub  the  limbs  upwards  with  firm, 

f rasping  pressure  and  energy,  using  handkerchiefs,  flannels,  etc.  Apply  hot 
annels,  bottles  of  hot  water,  heated  bricks,  etc.  to  the  pit  of  the  stomach, 
the  arm  pits,  between  the  thighs,  and  to  the  soles  of  the  feet. 

7.  On  the  restoration  of  life,  a teaspoonful  of  warm  water  should  be  given, 
and  then,  if  the  power  of  swallowing  has  returned,  small  quantities  of  wine, 
warm  brandy  and  water,  or  coffee  should  be  administered. 

8.  These  remedies  should  be  promptly  applied,  and  as  death  does  not 
certainly  appear  for  a long  time,  they  ought  only  to  be  discontinued  when  it 
is  clearly  confirmed.  Absence  of  the  pulsation  of  the  heart  is  not  a sure  sign 
of  death,  neither  is  the  want  of  respiration. 


452 


COAL  DEALERS  TABLE. 


Coal  Dealers’  Computing  Table,  for  Ascertaining  the  Price  of  Any 
Number  of  Pounds,  at  a Given  Price  per  Ton  of  2,000  Pounds. 


Lb. 

«0.76 

$1.00 

$1.25 

$1.50 

$1.75 

$2.00 

$2.25 

$2.50 

$2.75 

10 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

20 

.01 

.01 

.01 

.02 

.02 

.02 

.02 

.03 

.03 

30 

.01 

.02 

.02 

.02 

.03 

.03 

.03 

.04 

.04 

40 

.02 

.02 

.03 

.03 

.04 

.04 

.04 

.05 

.06 

50 

.02 

.02 

.03 

.04 

.04 

.05 

.06 

.06 

.07 

60 

.02 

.03 

.04 

.05 

.05 

.06 

.07 

.08 

.08 

70 

.03 

.03 

.04 

.05 

.06 

.07 

.08 

.09 

.10 

80 

.03 

.04 

.05 

.06 

.07 

.08 

.09 

.10 

.11 

90 

.03 

.04 

.06 

.07 

.08 

.09 

.10 

.11 

.12 

100 

.04 

.05 

.06 

.08 

.09 

.10 

.11 

.13 

.14 

200 

.08 

.10 

.13 

.15 

.17 

.20 

.23 

.25 

.28 

300 

.11 

.15 

.19 

.23 

.26 

.30 

.34 

.38 

.41 

400 

.15 

.20 

.25 

.30 

.35 

.40 

.45 

.50 

.55 

500 

.19 

.25 

.31 

.38 

.44 

.50 

.56 

.63 

.69 

600 

.23 

.30 

.37 

.45 

.53 

.60 

.68 

.75 

.83 

700 

.26 

.35 

.44 

.53 

.61 

.70 

.77 

.88 

.96 

800 

.30 

.40 

.50 

.60 

.70 

.80 

.90 

1.00 

1.10 

900 

.34 

.45 

.56 

.68 

.79 

.90 

1.01 

1.13 

1.24 

1,000 

.38 

.50 

.63 

.75 

.88 

1.00 

1.13 

1.25 

1.38 

1,100 

.41 

.55 

.69 

.83 

.96 

1.10 

1.24 

1.38 

1.51 

1,200 

.45 

.60 

.75 

.90 

1.05 

1.20 

1.35 

1.50 

1.65 

1,300 

.49 

.65 

.81 

.98 

1.14 

1.30 

1.46 

1.63 

1.79 

1,400 

.52 

.70 

.88 

1.05 

1.22 

1.40 

1.58 

1.75 

1.93 

1,500 

.56 

.75 

.94 

1.13 

1.31 

1.50 

1.69 

1.88 

2.06 

1,600 

.60 

.80 

1.00 

1.20 

1.40 

1.60 

1.80 

2.00 

2.20 

1,700 

.64 

.85 

1.06 

1.28 

1.49 

1.70 

1.91 

2.13 

2.34 

1,800 

.68 

.90 

1.13 

1.35 

1.58 

1.80 

2.03 

2.25 

2.48 

1,900 

.71 

.95 

1.19 

1.43 

1.66 

1.90 

2.14 

2.38 

2.61 

Lb. 

$3.00 

$3.25 

$3.50 

$3.75 

$4.00 

$4.25 

$4.50 

$4.75 

$5.00 

10 

.02 

.02 

.02 

.02 

.02 

.02 

.03 

.03 

.03 

20 

.03 

.03 

.04 

.04 

.04 

.05 

.05 

.05 

.05 

30 

.05 

.05 

.05 

.06 

.06 

.07 

.07 

.07 

.08 

40 

.06 

.07 

.07 

.08 

.08 

.09 

.09 

.10 

.10 

50 

.08 

.08 

.09 

.09 

.10 

.11 

.12 

.12 

.13 

60 

.09 

.10 

.11 

.11 

.12 

.13 

.14 

.15 

.15 

70 

.11 

.11 

.12 

.13 

.14 

.15 

.16 

.17 

.18 

80 

.12 

.13 

.14 

.15 

.16 

.17 

.18 

.19 

.20 

90 

.14 

.15 

.16 

.17 

.18 

.19 

.20 

.22 

.23 

100 

.15 

.16 

.18 

.19 

.20 

.22 

.23 

.24 

.25 

200 

.30 

.33 

.35 

.38 

.40 

.43 

.45 

.48 

.50 

300 

.45 

.49 

.53 

.56 

.60 

.64 

.68 

.72 

.75 

400 

.60 

.65 

.70 

.75 

.80 

.85 

.90 

.95 

1.00 

500 

.75 

.81 

.88 

.94 

1.00 

1.07 

1.13 

1.19 

1.25 

600 

.90 

.98 

im 

1.13 

1.20 

1.28 

1.35 

1.43 

1.50 

700 

1.05 

1.14 

1.23 

1.31 

1.40 

1.49 

1.58 

1.67 

1.75 

800 

1.20 

1.30 

1.40 

1.50 

1.60 

1.70 

1.80 

1.90 

2.00 

900 

1.35 

1.46 

1.58 

1.69 

1.80 

1.92 

2.03 

2.14 

2.25 

1,000 

1.50 

1.63 

1.75 

1.88 

2.00 

2.13 

2.25 

2.38 

2.50 

1,100 

1.65 

1.79 

1.93 

2.06 

2.20 

2.34 

2.48 

2.62 

2.75 

1,200 

1.80 

1.95 

2.10 

2.25 

2.40 

2.55 

2.70 

2.85 

3.00 

1,300 

1.95 

2.11 

2.28 

2.44 

2.60 

2.77 

2.93 

3.09 

3.25 

1,400 

2.10 

2.28 

2.45 

2.63 

2.80 

2.98 

3.15 

3.33 

3.50 

1,500 

2.25 

2.44 

2.63 

2.81 

3.00 

3.19 

3.38 

3.57 

3.75 

1,600 

2.40 

2.60 

2.80 

3.00 

3.20 

3.40 

3.60 

3.80 

4.00 

1,700 

2.55 

2.76 

2.98 

3.19 

3.40 

3.62 

3.83 

4.04 

4.25 

1,800 

2.70 

2.93 

3.15 

3.38 

3.60 

3.83 

4.05 

4.28 

4.50 

1,900 

2.85 

3.09 

3.33 

3.56 

3.80 

4.04 

4.28 

4.52 

4.75 

NATURAL  SINES  AND  COSINES, 


453 


TABLE  OF  NATURAL  SINES,  COSINES, 
TANGENTS,  AND  COTANGENTS. 


EXPLANATION. 

Given  an  angle,  to  find  its  sine,  cosine,  tangent,  and  cotangent: 

Example.— Find  the  sine,  cosine,  tangent,  and  cotangent  of  37°  24'. 

Look  in  the  table  of  natural  sines  along  the  tops  of  the  pages,  and  find  37°. 
Glancing  down  the  left-hand  column  marked  ('),  until  24  is  found,  find 
opposite  this  24  in  the  column  marked  sine  and  headed  37°,  the  number 
.60738;  then  .60738  = sin  37°  24'.  Similarly,  find  in  the  column  marked 
cosine  and  headed  37°,  the  number  .79441,  which  corresponds  to  cos  37°  24'. 
So,  also,  find  in  the  column  marked  tangent  and  headed  37°,  and  opposite  24', 
the  number  .76456;  and  in  the  column  marked  cotangent  and  headed  37°,  and 
opposite  24',  the  number  1.30795. 

In  most  of  the  tables  published,  the  angles  run  only  from  0°  to  45°  at  the 
heads  of  the  columns;  to  find  an  angle  greater  than  45°,  look  at  the  bottom  of 
the  page  and  glance  upwards,  using  the  extreme  right-hand  column  to  find 
minutes,  which  begin  with  0 at  the  bottom  and  run  upwards,  1,  2,  3,  etc, 
up  to  60. 

Example.— Find  the  sine  of  77°  43'. 

Look  along  the  bottom  of  the  tables  until  the  column  marked  sine  and 
marked  77°  is  found.  Glancing  up  the  column  of  minutes  on  the  right  until 
43'  is  found,  find  opposite  43'  in  the  column  marked  sine  at  the  bottom  and 
marked  77°,  the  number  .97711;  this  is  the  sine  of  77°  43'.  Similarly,  the 
cosine,  tangent,  and  cotangent  may  be  found. 

To  find  the  sine,  cosine,  tangent,  or  cotangent  of  an  angle  whose  exact 
value  is  not  given  in  the  table: 

Rule. — Find  in  the  table  the  sine,  cosine,  tangent,  or  cotangent  corresponding 
to  the  degrees  and  minutes  of  the  angle. 

For  the  seconds,  find  the  difference  of  the  values  of  the  sine,  cosine,  tangent,  or 
cotangent  taken  from  the  table  between  which  the  seconds  of  the  angle  fall;  multiply 
this  difference  by  a fraction  whose  numerator  is  the  number  of  seconds  in  the  given 
angle  and  whose  denominator  is  60. 

If  sine  or  tangent,  add  this  correction  to  the  value  first  found;  if  cosine  or 
cotangent,  subtract  the  correction. 

Example.— Find  the  sine,  cosine,  tangent,  and  cotangent  of  56°  43'  17". 

Sin  56°  43'  = .83597.  Sin  56°  44'  = .83613.  Since  56°  43'  17"  is  greater  than 
,56°  43'  and  less  than  56°  44',  the  value  of  the  sine  of  the  angle  lies  between 
.83597  and  .83613;  the  difference  equals  .83613  — .83597  = .00016;  multiplying 
this  by  the  fraction  H,  .00016  X H = .00005,  nearly,  which  is  to  be  added 
to  .83597,  the  value  first  found,  or  .83597  + .00005  = .83602.  Hence,  sin 
56°  43'  17"  = .83602. 

Cos  56°  43'  = .54878;  cos  56°  44'  = .54854;  the  difference  equals  .54878 
— .54854  = .00024,  and  .00024  X = .00007,  nearly.  Now,  since  the  cosine  is 
desired,  we  must  subtract  this  correction  from  cos  56°  43',  or  .54878;  subtract- 
ing, .54878  - .00007  = .54871.  Hence,  cos  56°  43'  17"  = .54871. 

Given  the  sine,  cosine,  tangent,  or  cotangent,  to  find  the  angle  corresponding: 

Example.— The  sine  of  an  angle  is  .47486;  what  is  the  angle? 

Consulting  the  table  of  natural  sines,  glance  down  the  columns  marked 
sine  until  .47486  is  found,  opposite  21'  in  the  left-hand  column  and  under  the 
column  headed  28°.  Therefore,  the  angle  whose  sine  = .47486  is  28°  21',  or 
sin  28°  21'  = .47486. 

To  find  the  angle  corresponding  to  a given  sine,  cosine,  tangent,  or 
cotangent  whose  exact  value  is  not  contained  in  the  table: 

Rule. — Find  the  difference  of  the  two  numbers  in  the  table  between  which  the 
given  sine,  cosine,  tangent,  or  cotangent  falls,  and  use  the  number  of  parts  in  thi9 
difference  as  the  denominator  of  a fraction. 


454 


NATVRAL  SINES  AND  COSINES. 


Find  the  difference  between  the  number  belonging  to  the  smaller  angle  and  the 
given  sine,  cosine,  tangent,  or  cotangent,  and  use  the  number  of  parts  in  the  dif- 
ference just  found  as  the  numerator  of  the  fraction  mentioned  above.  Multiply 
this  fraction  by  60,  and  the  result  will  he  the  number  of  seconds  to  be  added  to  the 
smaller  angle. 

Example.— Find  the  angle  whose  sine  equals  .57698. 

Looking  in  the  table  of  natural  sines,  in  the  column  marked  sine,  it  is 
found  between  .57691  = sin  35°  14'  and  .57715  = 35°  15'.  The  difference 
between  them  is  .57715  — .57691  = .00024,  or  24  parts.  The  difference  between 
the  sine  of  the  smaller  angle,  or  sin  35°  14'  = .57691,  and  the  given  sine,  or 
.57698,  is  .57698  — .57691  = .00007,  or  7 parts. 

Then,  X 60  = 17.5",  and  the  angle  = 35°  14'  17.5",  or  sin  35°  14'  17.5" 
= .57698. 

The  cosecant  of  an  angle  is  equal  to  the  reciprocal  of  its  sine,  and  the 
secant  is  equal  to  the  reciprocal  of  its  cosine.  Hence,  to  multiply  a quantity 
by  the  cosecant,  divide  it  by  the  sine;  or,  to  divide  it  by  the  cosecant, 
multiply  it  by  the  sine.  Similarly,  to  multiply  a quantity  by  the  secant  of 
an  angle,  divide  it  by  the  cosine;  or,  to  divide  it  by  the  secant,  multiply  it 
by  the  cosine. 


NATURAL  SINES  AND  COSINES. 


455 


0° 

1°  l 

20 

3° 

40 

/ 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.00000 

1. 

.01745 

.99985 

.03490 

.99939 

.05234 

.99863 

.06976 

.99756 

60 

1 

.00029 

1. 

.01774 

.99984 

.03519 

.99938 

.05263 

.99861 

.07005 

.99754 

59 

2 

.00058 

1. 

.01803 

.99984 

.03548 

.99937 

.05292 

.99860 

.07034 

.99752 

58 

3 

.00087 

1. 

.01832 

.99983 

.03577 

.99936 

.05321 

.99858 

.07063 

.99750 

57 

4 

.00116 

1. 

.01862 

.99983 

.03606 

.99935 

.05350 

.99857 

.07092 

.99748 

56 

5 

.00145 

1. 

.01891 

.99982 

.03635 

.99934 

.05379 

.99855 

.07121 

.99746 

55 

6 

.00175 

1. 

.01920 

.99982 

.03664 

.99933 

.05408 

.99854 

.07150 

.99744 

54 

7 

.00204 

1. 

.01949 

.99981 

.03693 

.99932 

.05437 

.99852 

.07179 

.99742 

53 

8 

.00233 

1. 

.01978 

.99980 

.03723 

.99931 

.05466 

.99851 

.07208 

.99740 

52 

9 

.00262 

1. 

.02007 

.99980 

.03752 

.99930 

.05495 

.99849 

.07237 

.99738 

51 

10 

.00291 

1. 

.02036 

.99979 

.03781 

.99929 

.05524 

.99847 

.07266 

.99736 

50 

11 

.00320 

.99999 

.02065 

.99979 

.03810 

.99927 

.05553 

.99846 

.07295 

.99734 

49 

12 

.00349 

.99999 

.02094 

.99978 

.03839 

.99926 

.05582 

.99844 

.07324 

.99731 

48 

13 

.00378 

.99999 

.02123 

.99977 

.03868 

.99925 

.05611 

.99842 

.07353 

.99729 

47 

14 

.00407 

.99999 

.02152 

.99977 

.03897 

.99924 

.05640 

.99841 

.07382 

.99727 

46 

15 

.00436 

.99999 

.02181 

.99976 

.03926 

.99923 

.05669 

.99839 

.07411 

.99725 

45 

16 

.00465 

.99999 

.02211 

.99976 

.03955 

.99922 

.05698 

•99838 

.07440 

.99723 

44 

17 

.00495 

.99999 

.02240 

.99975 

.03984 

.99921 

.05727 

.99836 

.07469 

.99721 

43 

18 

.00524 

.99999 

.02269 

.99974 

.04013 

.99919 

.05756 

.99834 

.07498 

.99719 

42 

19 

.00553 

.99998 

.02298 

.99974 

.04042 

.99918 

.05785 

.99833 

.07527 

.99716 

41 

20 

.00582 

.99998 

.02327 

.99973 

.04071 

.99917 

.05814 

.99831 

.07556 

.99714 

40 

21 

.00611 

.99998 

.02356 

.99972 

.04100 

.99916 

.05844 

.99829 

.07585 

.99712 

39 

22 

.00640 

.99998 

.02385 

.99972 

.04129 

.99915 

.05873 

.99827 

.07614 

.99710 

38 

23 

.00669 

.99998 

.02414 

.99971 

.04159 

.99913 

.05902 

.99826 

.07643 

.99708 

37 

24 

.00698 

.99998 

.02443 

.99970 

.04188 

.99912 

.05931 

.99824 

.07672 

.99705 

36 

25 

.00727 

.99997 

.02472 

.99969 

.04217 

.99911 

.05960 

.99822 

.07701 

.99703 

35 

26 

.00756 

.99997 

.02501 

.99969 

.04246 

.99910 

.05989 

.99821 

.07730 

.99701 

34 

27 

.00785 

.99997 

.02530 

.99968 

.04275 

.99909 

.06018 

.99819 

.07759 

.99699 

33 

28 

.00814 

.99997 

.02560 

.99967 

.04304 

.99907 

.06047 

.99817 

.07788 

.99696 

32 

29 

.00844 

.99996 

.02589 

.99966 

.04333 

.99906 

.06076 

.99815 

.07817 

.99694 

31 

30 

.00873 

.99996 

.02618 

.99966 

.04362 

.99905 

.06105 

.99813 

.07846 

.99692 

30 

31 

.00902 

.99996 

.02647 

.99965 

.04391 

.99904 

.06134 

.99812 

.07875 

.99689 

29 

32 

.00931 

.99996 

.02676 

.99964 

.04420 

.99902 

.06163 

.99810 

.07904 

.99687 

28 

33 

.00960 

.99995 

.02705 

.99963 

.04449 

.99901 

.06192 

.99808 

.07933 

.99685 

27 

34 

.00989 

.99995 

.02734 

.99963 

.04478 

.99900 

.06221 

.99806 

.07962 

.99683 

26 

35 

.01018 

.99995 

.02763 

.99962 

.04507 

.99898 

.06250 

.99804 

.07991 

.99680 

25 

36 

.01047 

.99995 

.02792 

.99961 

.04536 

.99897 

.06279 

.99803 

.08020 

.99678 

24 

37 

.01076 

.99994 

.02821 

.99960 

.04565 

.99896 

.06308 

.99801 

.08049 

.99676 

23 

38 

.01105 

.99994 

.02850 

.99959 

.04594 

.99894 

.06337 

.99799 

.08078 

.99673 

22 

39 

.01134 

.99994 

.02879 

.99959 

.04623 

.99893 

.06366 

.99797 

.08107 

.99671 

21 

40 

.01164 

.99993 

.02908 

.99958 

.04653 

.99892 

.06395 

.99795 

.08136 

.99668 

20 

41 

.01193 

.99993 

.02938 

.99957 

.04682 

.99890 

.06424 

.99793 

.08165 

.99666 

19 

42 

.01222 

.99993 

.02967 

.99956 

.04711 

.99889 

.06453 

.99792 

.08194 

.99664 

18 

43 

.01251 

.99992 

.02996 

.99955 

.04740 

.99888 

.06482 

.99790 

.08223 

.99661 

17 

44 

.01280 

.99992 

.03025 

.99954 

.04769 

.99886 

.06511 

.99788 

.08252 

.99659 

16 

45 

.01309 

.99991 

.03054 

.99953 

.04798 

.99885 

.06540 

.99786 

.08281 

.99657 

15 

46 

.01338 

.99991 

.03083 

.99952 

.04827 

.99883 

.06569 

.99784 

.08310 

.99654 

14 

47 

.01367 

.99991 

.03112 

.99952 

.04856 

.99882 

.06598 

.99782 

.08339 

.99652 

13 

48 

.01396 

.99990 

.03141 

.99951 

.04885 

.99881 

.06627 

.99780 

.08368 

.99649 

12 

49 

.01425 

.99990 

.03170 

.99950 

.04914 

.99879 

.06656 

.99778 

.08397 

.99647 

11 

50 

.01454 

.99989 

.03199 

.99949 

.04943 

.99878 

.06685 

.99776 

.08426 

.99644 

10 

51 

.01483 

.99989 

.03228 

.99948 

.04972 

.99876 

.06714 

.99774 

.08455 

.99642 

9 

52 

.01513 

.99989 

.03257 

.99947 

.05001 

.99875 

.06743 

.99772 

.08484 

.99639 

8 

53 

.01542 

.99988 

.03286 

.99946 

.05030 

.99873 

.06773 

.99770 

.08513 

.99637 

7 

54 

.01571 

.99988 

.03316 

.99945 

.05059 

.99872 

.06802 

.99768 

.08542 

.99635 

6 

55 

.01600 

.99987 

.03345 

.99944 

.05088 

.99870 

.06831 

.99766 

.08571 

.99632 

5 

56 

.01629 

.99987 

.03374 

.99943 

.05117 

.99869 

.06860 

.99764 

.08600 

.99630 

4 

57 

.01658 

.99986 

.03403 

.99942 

.05146 

.99867 

.06889 

.99762 

.08629 

.99627 

3 

58 

.01687 

.99986 

.03432 

.99941 

.05175 

.99866 

.06918 

.99760 

.08658 

.99625 

2 

59 

.01716 

.99985 

.03461 

.99940 

.05205 

.99864 

.06947 

.99758 

.08687 

.99622 

1 

60 

.01745 

.99985 

.03490 

.99939 

.05234 

.99863 

.06976 

.99756 

.08716 

.99619 

0 

/ 

Cosine 

Sine- 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

/ 

89° 

88° 

87° 

86° 

85° 

466 


NATURAL  SINES  AND  COSINES. 


50 

60 

70 

8° 

9° 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.08716 

.99619 

.10453 

.99452 

.12187 

.99255 

.13917 

.99027 

.15643 

.98769 

60 

1 

.08745 

.99617 

.10482 

.99499 

.12216 

.99251 

.13946 

.99023 

.15672 

.98764 

59 

2 

.08774 

.99614 

.10511 

.99446 

.12245 

.99248 

.13975 

.99019 

.15701 

.98760 

58 

3 

.08803 

.99612 

.10540 

.99443 

.12274 

.99244 

.14004 

.99015 

.15730 

.98755 

57 

4 

.08831 

.99609 

.10569 

.99440 

.12302 

.99240 

.14033 

.99011 

.15758 

.98751 

56 

5 

.08860 

.99607 

.10597 

.99437 

.12331 

.99237 

.14061 

.99006 

.15787 

.98746 

55 

6 

.08889 

.99604 

.10626 

.99434 

.12360 

.99233 

.14090 

.99002 

.15816 

.98741 

54 

7 

.08918 

.99602 

.10655 

.99431 

.12389 

.99230 

.14119 

.98998 

.15845 

.98737 

53 

8 

.08947 

.99599 

.10684 

.99428 

.12418 

.99226 

.14148 

.98994 

.15873 

.98732 

52 

9 

.08976 

.99596 

.10713 

.99424 

.12447 

.99222 

.14177 

.98990 

.15902 

.98728 

51 

10 

.09005 

.99594 

.10742 

.99421 

.12476 

.99219 

.14205 

.98986 

.15931 

.98723 

50 

11 

.09034 

.99591 

.10771 

.99418 

.12504 

.99215 

.14234 

.98982 

.15959 

.98718 

49 

12 

.09063 

.99588 

.10800 

.99415 

.12533 

.99211 

.14263 

.98978 

.15988 

.98714 

48 

13 

.09092 

.99586 

.10829 

.99412 

.12562 

.99208 

.14292 

.98973 

.16017 

.98709 

47 

14 

.09121 

.99583 

.10858 

.99409 

.12591 

.99204 

.14320 

.98969 

.16046 

.98704 

46 

15 

.09150 

.99580 

.10887 

.99406 

.12620 

.99200 

.14349 

.98965 

.16074 

.98700 

45 

16 

.09179 

.99578 

.10916 

.99402 

.12649 

.99197 

.14378 

.98961 

.16103 

.98695 

44 

17 

.09208 

.99575 

.10945 

.99399 

.12678 

.99193 

.14407 

.98957 

.16132 

.98690 

43 

18 

.09237 

.99572 

.10973 

.99396 

.12706 

.99189 

.14436 

.98953 

.16160 

.98686 

42 

19 

.09266 

.99570 

.11002 

.99393 

.12735 

.99186 

.14464 

.98948 

.16189 

.98681 

41 

20 

.09295 

.99567 

.11031 

.99390 

.12764 

.99182 

.14493 

.98944 

.16218 

.98676 

40 

21 

.09324 

.99564 

.11060 

.99386 

.12793 

.99178 

.14522 

.98940 

.16246 

.98671 

39 

22 

.09353 

.99562 

.11089 

.99383 

.12822 

.99175 

.14551 

.98936 

.16275 

.98667 

38 

23 

.09382 

.99559 

.11118 

.99380 

.12851 

.99171 

.14580 

.98931 

.16304 

.98662 

37 

24 

.09411 

.99556 

.11147 

.99377 

.12880 

.99167 

.14608 

.98927 

.16333 

.98657 

36 

25 

.09440 

.99553 

.11176 

.99374 

.12908 

.99163 

.14637 

.98923 

.16361 

.98652 

35 

26 

.09469 

.99551 

.11205 

.99370 

.12937 

.99160 

.14666 

.98919 

.16390 

.98648 

34 

27 

.09498 

.99548 

.11234 

.99367 

.12966 

.99156 

.14695 

.98914 

.16419 

.98643 

33 

28 

.09527 

.99545 

.11263 

.99364 

.12995 

.99152 

.14723 

.98910 

.16447 

.98638 

32 

29 

.09556 

.99542 

.11291 

.99360 

.13024 

.99148 

.14752 

.98906 

.16476 

.98633 

31. 

30 

.09585 

.99540 

.11320 

.99357 

.13053 

.99144 

.14781 

.98902 

.16505 

.98629 

30 

31 

.09614 

.99537 

.11349 

.99354 

.13081 

.99141 

.14810 

.98897 

.16533 

.98624 

29 

32 

.09642 

.99534 

.11378 

.99351 

.13110 

.99137 

.14838 

.98893 

.16562 

.98619 

28 

33 

.09671 

.99531 

.11407 

.99347 

.13139 

.99133 

.14867 

.98889 

.16591 

.98614 

27 

34 

.09700 

.99528 

.11436 

.99344 

.13168 

.99129 

.14896 

.98884 

.16620 

.98609 

26 

35 

.09729 

.99526 

.11465 

.99341 

.13197 

.99125 

.14925 

.98880 

.16648 

.98604 

25 

36 

.09758 

.99523 

.11494 

.99337 

.13226 

.99122 

.14954 

.98876 

.16677 

.98600 

24 

37 

.09787 

.99520 

.11523 

.99334 

.13254 

.99118 

.14982 

.98871 

.16706 

.98595 

23 

38 

.09816 

.99517 

.11552 

.99331 

.13283 

.99114 

.15011 

.98867 

.16734 

.98590 

22 

39 

.09845 

.99514 

.11580 

.99327 

.13312 

.99110 

.15040 

.98863 

.16763 

.98585 

21 

40 

.09874 

.99511 

.11609 

.99324 

.13341 

.99106 

.15069 

.98858 

.16792 

.98580 

20 

41 

.09903 

.99508 

.11638 

.99320 

.13370 

.99102 

.15097 

.98854 

.16820 

.98575 

19 

42 

.09932 

.99506 

.11667 

.99317 

.13399 

.99098 

.15126 

.98849 

.16849 

.98570 

18 

43 

.09961 

.99503 

.11696 

.99314 

.13427 

.99094 

.15155 

.98845 

.16878 

.98565 

17 

44 

.09990 

.99500 

.11725 

.99310 

.13456 

.99091 

.15184 

.98841 

.16906 

.98561 

' 16 

45 

.10019 

.99497 

.11754 

.99307 

.13485 

.99087 

.15212 

.98836 

.16935 

.98556 

15 

46 

.10048 

.99494 

.11783 

.99303 

.13514 

.99083 

.15241 

.98832 

.16964 

.98551 

14 

47 

.10077 

.99491 

.11812 

.99300 

.13543 

.99079 

.15270 

.98827 

.16992 

.98546 

13. 

48 

.10106 

.99488 

.11840 

.99297 

.13572 

.99075 

.15299 

.98823 

.17021 

.98541 

12 

49 

.10135 

.99485 

.11869 

.99293 

.13600 

.99071 

.15327 

.98818 

.17050 

.98536 

11 

50 

.10164 

.99482 

.11898 

.99290 

.13629 

.99067 

.15356 

.98814 

.17078 

.98531 

10 

51 

.10192 

.99479 

.11927 

.99286 

.13658 

.99063 

.15385 

.98809 

.17107 

.98526 

9 

52 

.10221 

.99476 

.11956 

.99283 

.13687 

.99059 

.15414 

.98805 

.17186 

.98521 

8 

53 

.10250 

.99473 

.11985 

.99279 

.13716 

.99055 

.15442 

.98800 

.17164 

.98516 

7 

54 

.10279 

.99470 

.12014 

.99276 

.13744 

.99051 

.15471 

.98796 

.17193 

.98511 

6 

55 

.103C8 

.99467 

.12043 

.99272 

.13773 

.99047 

.15500 

.98791 

.17222 

.98506 

5 

56 

.10337 

.99464 

.12071 

.99269 

.13802 

.99043 

.15529 

.98787 

.17250 

.98501 

4 

57 

.10366 

.99461 

.12100 

.99265 

.13831 

.99039 

.15557 

.98782 

.17279 

.98496 

3 

58 

.10395 

.99458 

.12129 

.99262 

.13860 

.99035 

.15586 

.98778 

.17308 

.98491 

2 

59 

.10424 

.99455 

.12158 

.99258 

.13889 

.99031 

.15615 

.98773 

.17336 

.98486 

1 

60 

.10453 

.99452 

.12187 

.99255 

.13917 

.99027 

.15643 

.98769 

.17365 

.98481 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

r 

84° 

83° 

82° 

81° 

80° 

NATVRAL  SINES  AND  COSINES. 


45' 


10° 

IP 

12° 

130 

IP 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.17365 

.98481 

.19081 

.98163 

.20791 

.97815 

.22495 

.97437 

.24192 

.97030 

60 

1 

.17393 

.98476 

.19109 

.98157 

.20820 

.97809 

.22523 

.97430 

.24220 

.97023 

59 

2 

.17422 

.98471 

.19138 

.98152 

.20848 

.97803 

.22552 

.97424 

.24249 

.97015 

58 

3 

.17451 

.98466 

.19167 

.98146 

.20877 

.97797 

.22580 

.97417 

.24277 

.97008 

57 

4 

.17479 

.98461 

.19195 

.98140 

.20905 

.97791 

.22608 

.97411 

.24305 

.97001 

56 

5 

.17508 

.98455 

.19224 

.98135 

.20933 

.97784 

.22637 

.97404 

.24333 

.96994 

55 

6 

.17537 

.98450 

.19252 

.98129 

.20962 

.97778 

.22665 

.97398 

.24362 

.96987 

54 

7 

.17565 

.98445 

.19281 

.98124 

.20990 

.97772 

.22693 

.97391 

.24390 

.96980 

53 

8 

.17594 

.98440 

.19309 

.98118 

.21019 

.97766 

.22722 

.97384 

.24418 

.96973 

52 

9 

.17623 

.98435 

.19338 

.98112 

.21047 

.97760 

.22750 

.97378 

.24446 

.96966 

51 

10 

.17651 

.98430 

.19366 

.98107 

.21076 

.97754 

.22778 

.97371 

.24474 

.96959 

50 

11 

.17680 

.98425 

.19395 

.98101 

.21104 

.97748 

.22807 

.97365 

.24503 

.96952 

49 

12 

.17708 

.98420 

.19423 

.98096 

.21132 

.97742 

.22835 

.97358 

.24531 

.96945 

48 

13 

.17737 

.98414 

.19452 

.98090 

.21161 

.97735 

.22863 

.97351 

.24559 

.96937 

47 

14 

.17766 

.98409 

.19481 

.98084 

.21189 

.97729 

.22892 

.97345 

.24587 

.96930 

46 

15 

.17794 

.98404 

.19509 

.98079 

.21218 

.97723 

.22920 

.97338 

.24615 

.96923 

45 

16 

.17823 

.98399 

.19538 

.98073 

.21246 

.97717 

.22948 

.97331 

.24644 

.96916 

44 

17 

.17852 

.98394 

.19566 

.98067 

.21275 

.97711 

.22977 

.97325 

.24672 

.96909 

43 

18 

.17880 

.98389 

.19595 

.98061 

.21303 

.97705 

.23005 

.97318 

.24700 

.96902 

42 

19 

.17909 

.98383 

.19623 

.98056 

.21331 

.97698 

.23033 

.97311 

.24728 

.96894 

41 

20 

.17937 

.98378 

.19652 

.98050 

.21360 

.97692 

.23062 

.97304 

.24756 

.96887 

40 

21 

.17966 

.98373 

.19680 

.98044 

.21388 

.97686 

.23090 

.97298 

.24784 

.96880 

39 

22 

.17995 

.98368 

.19709 

.98039 

.21417 

.97680 

.23118 

.97291 

.24813 

.96873 

38 

23 

.18023 

.98362 

.19737 

.98033 

.21445 

.97673 

.23146 

.97284 

.24841 

.96866 

37 

24 

.18052 

.98357 

.19766 

.98027 

.21474 

.97667 

.23175 

.97278 

.24869 

.96858 

36 

25 

.18081 

.98352 

.19794 

.98021 

.21502 

.97661 

.23203 

.97271 

.24897 

.96851 

35 

26 

.18109 

.98347 

.19823 

.98016 

.21530 

.97655 

.23231 

.97264 

.24925 

.96844 

34 

27 

.18138 

.98341 

.19851 

.98010 

.21559 

.97648 

.23260 

.97257 

.24954 

.96837 

33 

28 

.18166 

.98336 

.19880 

.98004 

.21587 

.97642 

.23288 

.97251 

.24982 

.96829 

32 

29 

.18195 

.98331 

.19908 

.97998 

.21616 

.97636 

.23316 

.97244 

.25010 

.96822 

31 

30 

.18224 

.98325 

.19937 

.97992 

.21644 

.97630 

.23345 

.97237 

.25038 

.96815 

30 

31 

.18252 

.98320 

.19965 

.97987 

.21672 

.97623 

.23373 

.97230 

.25066 

.96807 

29 

32 

.18281 

.98315 

.19994 

.97981 

.21701 

.97617 

.23401 

.97223 

.25094 

.96800 

28 

33 

.18309 

.98310 

.20022 

.97975 

.21729 

.97611 

.23429 

.97217 

.25122 

.96793 

27 

34 

.18338 

.98304 

.20051 

.97969 

.21758 

.97604 

.23458 

.97210 

.25151 

.96786 

26 

35 

.18367 

.98299 

.20079 

.97963 

.21786 

.97598 

.23486 

.97203 

.25179 

.96778 

25 

36 

.18395 

.98294 

.20108 

.97958 

.21814 

.97592 

.23514 

.97196 

.25207 

.96771 

24 

37 

.18424 

.98288 

.20136 

.97952 

.21843 

.97585 

.23542 

.97189 

.25235 

.96764 

23 

38 

.18452 

.98283 

.20165 

.97946 

.21871 

.97579 

.23571 

.97182 

.25263 

.96756 

22 

39 

.18481 

.98277 

.20193 

.97940 

.21899 

.97573 

.23599 

.97176 

.25291 

.96749 

21 

40 

.18509 

.98272 

.20222 

.97934 

.21928 

.97566 

.23627 

.97169 

.25320 

.96742 

20 

41 

.18538 

.98267 

.20250 

.97928 

.21956 

.97560 

.23656 

.97162 

.25348 

.96734 

19 

42 

.18567 

.98261 

.20279 

.97922 

.21985 

.97553 

.23684 

.97155 

.25376 

.96727 

18 

43 

.18595 

.98256 

.20307 

.97916 

.22013 

.97547 

.23712 

.97148 

.25404 

.96719 

17 

44 

.18624 

.98250 

.20336 

.97910 

.22041 

.97541 

.23740 

.97141 

.25432 

.96712 

16 

45 

.18652 

.98245 

.20364 

.97905 

.22070 

.97534 

.23769 

.97134 

.25460 

.96705 

15 

46 

.18681 

.98240 

.20393 

.97899 

.22098 

.97528 

.23797 

.97127 

.25488 

.96697 

14 

47 

.18710 

.98234 

.20421 

.97893 

.22126 

.97521 

.23825 

.97120 

.25516 

.96690 

13 

48 

.18738 

.98229 

.20450 

.97887 

.22155 

.97515 

.23853 

.97113 

.25545 

.96682 

12 

49 

.18767 

.98223 

.20478 

.97881 

.22183 

.97508 

.23882 

.97106 

.25573 

.96675 

11 

50 

.18795 

.98218 

.20507 

.97875 

.22212 

.97502 

.23910 

.97100 

.25601 

.96667 

10 

51 

.18824 

.98212 

.20535 

.97869 

.22240 

.97496 

.23938 

.97093 

.25629 

.96660 

9 

52 

.18852 

.98207 

.20563 

.97863 

.22268 

.97489 

.23966 

.97086 

.25657 

.96653 

8 

53 

.18881 

.98201 

.20592 

.97857 

.22297 

.97483 

.2.3995 

.97079 

.25685 

.96645 

7 

54 

.18910 

.98196 

.20620 

.97851 

.22325 

.97476 

.24023 

.97072 

.25713 

.96638 

6 

55 

.18938 

.98190 

.20649 

.97845 

.22353 

.97470 

.24051 

.97065 

.25741 

.96630 

5 

56 

.18967 

.98185 

.20677 

.97839 

.22382 

.97463 

.24079 

.97058 

.25769 

.96623 

4 

57 

.18995 

.98179 

.20706 

.97833 

.22410 

.97457 

.24108 

.97051 

.25798 

.96615 

3 

58 

.19024 

.98174 

.20734 

.97827 

.22438 

.97450 

.24136 

.97044 

.25826 

.96608 

2 

59 

.19052 

.98168 

.20763 

.97821 

.22467 

.97444 

.24164 

.97037 

.25854 

.96600 

1 

60 

.19081 

.98163 

.20791 

.97815 

.22495 

.97437 

.24192 

.97030 

.25882 

.96593 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

79° 

78° 

770 

76« 

750 

t 

458 


NATVRAL  SINES  AND  COSINES, 


150 

16° 

170 

18^ 

19° 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.25882 

.96593 

.27564 

.96126 

.29237 

.95630 

.30902 

.95106 

.32557 

.94552 

60 

1 

.25910 

.96585 

.27592 

.96118 

.29265 

.95622 

.30929 

.95097 

.32584 

.94542 

59 

2 

.25938 

.96578 

.27620 

.96110 

.29293 

.95613 

.30957 

.95088 

.32612 

.94533 

58 

3 

.25966 

.96570 

.27648 

.96102 

.29321 

.9.5605 

.30985 

.95079 

.32639 

.94523 

57 

4 

.25994 

.96562 

.27676 

.96094 

.29348 

.95596 

.31012 

.95070 

.32667 

.94514 

56 

5 

.26022 

.96555 

.27704 

.96086 

.29376 

.95588 

.31040 

.95061 

.32694 

.94504 

55 

6 

.26050 

.96547 

.27731 

.96078 

.29404 

.95579 

.31068 

.95052 

.32722 

.94495 

54 

7 

.26079 

.96540 

.27759 

.96070 

.29432 

.95571 

.31095 

.95043 

.32749 

.94485 

53 

8 

.26107 

.96532 

.27787 

.96062 

.29460 

.95562 

.31123 

.95033 

.32777 

.94476 

52 

9 

.26135 

.96524 

.27815 

.96054 

.29487 

.95554 

.31151 

.95024 

.32804 

.94466 

51 

10 

.26163 

.96517 

.27843 

.96046 

. .29515 

.95545 

.31178 

.95015 

.32832 

.94457 

50 

11 

.26191 

.96509 

.27871 

.96037 

.29543 

.95536 

.31206 

.95006 

.32859 

.94447 

49 

12 

.26219 

.96502 

.27899 

.96029 

.29571 

.95528 

.31233 

.94997 

.32887 

.94438 

48 

13 

.26247 

.96494 

.27927 

.96021 

.29599 

.95519 

.31261 

.94988 

.32914 

.94428 

47 

14 

.26275 

.96486 

.27955 

.96013 

.29626 

.95511 

.31289 

.94979 

.32942 

.94418 

46 

15 

.26303 

.96479 

.27983 

.96005 

.29654 

.95502 

.31316 

.91970 

.32969 

.94409 

45 

16 

.26331 

.96471 

.28011 

.95997 

.29682 

.95493 

.31344 

.94961 

.32997 

.94399 

44 

17 

.26359 

.96463 

.28039 

.95989 

.29710 

.95485 

.31372 

.94952 

.33024 

.94390 

43 

18 

.26387 

.96456 

.28067 

.95981 

.29737 

.95476 

.31399 

.94943 

.33051 

.94380 

42 

19 

.26415 

.96448 

.28095 

.95972 

.29765 

.95467 

.31427 

.94933 

.33079 

.94370 

41 

20 

.26443 

.96440 

.28123 

.95964 

.29793 

.95459 

.31454 

.94924 

.33106 

.94361 

40 

21 

.26471 

.96433 

.28150 

.95956 

.29821 

.95450 

.31482 

.94915 

.33134 

.94351 

39 

22 

.26500 

.96425 

.28178 

.95948 

.29849 

.95441 

.31510 

.94906 

.33161 

.94342 

38 

23 

.26528 

.96417 

.28206 

.95940 

.29876 

.95433 

.31537 

.94897 

.33189 

.94332 

37 

24 

.26556 

.96410 

.28234 

.95931 

.29904 

.95424 

.31565 

.94888 

.33216 

.94322 

36 

25 

.26584 

.96402 

.28262 

.95923 

.29932 

.95415 

.31593 

.94878 

.33244 

.94313 

35 

26 

.26612 

.96394 

.28290 

.95915 

.29960 

.95407 

.31620 

.94869 

.33271 

.94303 

34 

27 

.26640 

.96386 

.28318 

.95907 

.29987 

.95398 

.31648 

.94860 

.33298 

.94293 

33 

28 

.26668 

.96379 

.28346 

.95898 

.30015 

.95389 

.31675 

.94851 

.33326 

.94284 

32 

29 

.26696 

.96371 

.28374 

.95890 

.30043 

.95380 

.31703 

.94842 

.33353 

.94274 

31 

30 

.26724 

.96363 

28402 

.95882 

.30071 

.95372 

.31730 

.94832 

.33381 

.94264 

30 

31 

.26752 

.96355 

.28429 

.95874 

.30098 

.95363 

.31758 

.94823 

.33408 

.94254 

29 

32 

.26780 

.96347 

.28457 

.95865 

.30126 

.95354 

.31786 

.94814 

.33436 

.94245 

28 

33 

.26808 

.96340 

.28485 

.95857 

.30154 

.95345 

.31813 

.94805 

.33463 

.94235 

27 

34 

.26836 

.96332 

.28513 

.95849 

.30182 

.95337 

.31841 

.94795 

.33490 

.94225 

26 

35 

.26864 

.96324 

.28541 

.95841 

.30209 

.95328 

.31868 

.94786 

.33518 

.94215 

25 

36 

.26892 

.96316 

.28569 

.95832 

.30237 

.95319 

.31896 

.94777 

.33545 

.94206 

24 

37 

.26920 

.96308 

- .28597 

.95824 

.30265 

.95310 

.31923 

.94768 

.33573 

.94196 

23 

38 

.26948 

.96301 

.28625 

.95816 

.30292 

.95301 

.31951 

.94758 

.33600 

.94186 

22 

39 

.26976 

.96293 

.28652 

.95807 

.30320 

.95293 

.31979 

.94749 

.33627 

.94176 

21 

40 

.27004 

.96285 

.28680 

.95799 

.30348 

.95284 

.32006 

.94740 

.33655 

.94167 

20 

41 

.27032 

.96277 

.28708 

.95791 

.30376 

.95275 

.32034 

.94730 

.33682 

.94157 

19 

42 

.27060 

.96269 

.28736 

.95782 

.30403 

.95266 

.32061 

.94721 

.33710 

.94147 

18 

43 

.27088 

.96261 

.28764 

.95774 

.30431 

.95257 

.32089 

.94712 

.33737 

.94137 

17 

44 

.27116 

.96253 

.28792 

.95766 

.30459 

.95248 

.32116 

.94702 

.33764 

.94127 

16 

45 

.27144 

.96246 

.28820 

.95757 

.30486 

.95240 

.32144 

.94693 

.33792 

.94118 

15 

46 

.27172 

.96238 

.28847 

.95749 

.30514 

.95231 

.32171 

.94684 

.33819 

.94108 

14 

47 

.27200 

.96230 

.28875 

.95740 

.30542 

.95222 

.32199 

.94674 

.33846 

.94098 

13 

48 

.27228 

.96222 

.28903 

.95732 

.30570 

.95213 

.32227 

.94665 

.33874 

.94088 

12 

49 

.27256 

.96214 

.28931 

.95724 

.30597 

.95204 

.32254 

.94656 

.33901 

.94078 

11 

50 

.27284 

.96206 

.28959 

.95715 

.30625 

.95195 

.32282 

.94646 

.33929 

.94068 

10 

51 

.27312 

.96198 

.28987 

.95707 

.30653 

.95186 

.32309 

.94637 

.33956 

.94058 

9 

52 

.27340 

.96190 

.29015 

.95698 

.30680 

.95177 

.32337 

.94627 

.33983 

.94049 

8 

63 

.27368 

.96182 

.29042 

.95690 

.30708 

.95168 

.32364 

.94618 

.34011 

.94039 

7 

54 

.27396 

.96174 

.29070 

.95681 

.30736 

.95159 

.32392 

.94609 

.34038 

.94029 

6 

55 

.27424 

.96166 

.29098 

.95673 

.30763 

.95150 

.32419 

.94599 

.34065 

.94019 

5 

56 

.27452 

.96158 

.29126 

.95664 

.30791 

.95142 

.32447 

.94590 

.34093 

.94009 

4 

57 

.27480 

.96150 

.29154 

.95656 

.30819 

.95133 

.32474 

.94580 

.34120 

.93999 

3 

58 

.27508 

.96142 

.29182 

.95647 

.30846 

.95124 

.32502 

.94571 

.34147 

.93989 

2 

59 

.27536 

.96134 

.29209 

.95639 

.30874 

.95115 

.32529 

.94561 

.34175 

.93979 

1 

60 

.27564 

.96126 

.29237 

.95630 

.30902 

.95106 

.32557 

.94552 

.34202 

.93969 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

f 

740 

730 

72° 

710 

70° 

f 

NATVRAL  SINES  AND  COSINES. 


459 


20° 

21° 

22°  ' 

23° 

24° 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.34202 

.93969 

.35837 

.93358 

.37461 

.92718 

.39073 

.92050 

.40674 

.91355 

60 

1 

.34229 

.93959 

.35864 

.93348 

.37488 

.92707 

.39100 

.92039 

.40700 

.91343 

59 

2 

.34257 

.93949 

.35891 

.93337 

.37515 

.92697 

.39127 

.92028 

.40727 

.91331 

58 

3 

.34284 

.93939 

.35918 

.93327 

.37542 

.92686 

.39153 

.92016 

.40753 

.91319 

57 

4 

.34311 

.93929 

.35945 

.93316 

.37569 

.92675 

.39180 

.92005 

.40780 

.91307 

56 

5 

.34339 

.93919 

.35973 

.93306 

.37595 

.92664 

.39207 

.91994 

.40806 

.91295 

55 

6 

.34366 

.93909 

.36000 

.93295 

.37622 

.92653 

.39234 

.91982 

.40833 

.91283 

54 

7 

.34393 

.93899 

.36027 

.93285 

.37649 

.92642 

.39260 

.91971 

.40860 

.91272 

53 

8 

.34421 

.93889 

.36054 

.93274 

.37676 

.92631 

.39287 

.91959 

.40886 

.91260 

52 

9 

.34448 

.93879 

.36081 

.93264 

.37703 

.92620 

.39314 

.91948 

.40913 

.91248 

51 

10 

.34475 

.93869 

.36108 

.93253 

.37730 

.92609 

.39341 

.91936 

.40939 

.91236 

50 

11 

.34503 

.93859 

.36135 

.93243 

.37757 

.92598 

.39367 

.91925 

.40966 

.91224 

49 

12 

.34530 

.93849 

.36162 

.93232 

.37784 

.92.587 

.39394 

.91914 

.40992 

.91212 

48 

13 

.34557 

.93839 

.36190 

.93222 

.37811 

.92576 

.39421 

.91902 

.41019 

.91200 

47 

14 

.34584 

.93829 

.36217 

.93211 

.37838 

.92565 

.39448 

.91891 

.41045 

.91188 

46 

15 

.34612 

.93819 

.36244 

.93201 

.37865 

.92554 

.39474 

.91879 

.41072 

.91176 

45 

16 

.34639 

.93809 

.36271 

.93190 

.37892 

.92543 

.39501 

.91868 

.41098 

.91164 

44 

17 

.34666 

.93799 

.36298 

.93180 

.37919 

.92532 

.39528 

.91856 

.41125 

.91152 

43 

18 

.34694 

.93789 

.36325 

.93169 

.37946 

.92521 

.39555 

.91845 

.41151 

.91140 

42 

19 

.34721 

.93779 

.36352 

.93159 

.37973 

.92510 

.39581 

.91833 

.41178 

.91128 

41 

20 

.34748 

.93769 

.36379 

.93148 

.37999 

.92499 

.39608 

.91822 

.41204 

.91116 

40 

21 

.34775 

.93759 

.36406 

.93137 

.38026 

.92488 

.39635 

.91810 

.41231 

.91104 

39 

22 

.34803 

.93748 

.36434 

.93127 

.38053 

.92477 

.39661 

.91799 

.41257 

.91092 

38 

23 

.34830 

.93738 

.36461 

.93116 

.38080 

.92466 

.39688 

.91787 

.41284 

.91080 

37 

24 

.34857 

.93728 

.36488 

.93106 

.38107 

.92455 

.39715 

.91775 

.41310 

.91068 

36 

25 

.34884 

.93718 

.36515 

.93095 

.38134 

.92444 

.39741 

.91764 

.41337 

.91056 

35 

26 

.34912 

.93708 

.36542 

.93084 

.38161 

.92432 

.39768 

.91752 

.41363 

.91044 

34 

27 

.34939 

.93698 

.36569 

.93074 

.38188 

.92421 

.39795 

.91741 

.41390 

.91032 

33 

28 

.34966 

.93688 

.36596 

.93063 

.38215 

.92410 

.39822 

.91729 

.41416 

.91020 

32 

29 

.34993 

.93677 

.36623 

.93052 

.38241 

.92399 

.39848 

.91718 

.41443 

.91008 

31 

30 

.35021 

.93667 

.36650 

.93042 

.38268 

.92388 

.39875 

.91706 

.41469 

.90996 

30 

31 

.35048 

.93657 

.36677 

.93031 

.38295 

.92377 

.39902 

.91694 

.41496 

.90984 

29 

32 

.35075 

.93647 

.36704 

.93020 

.38322 

.92366 

.39928 

.91683 

.41522 

.90972 

28 

33 

.35102 

.93637 

.36731 

.93010 

.38349 

.92355 

.39955 

.91671 

.41549 

.90960 

27 

34 

.35130 

.93626 

.36758 

.92999 

.38376 

.92343 

.39982 

.91660 

.41575 

.90948 

26 

35 

.35157 

.93616 

.36785 

.92988 

.38403 

.92332 

.40008 

.91648 

.41602 

.90936 

25 

36 

.35184 

.93606 

.36812 

.92978 

.38430 

.92321 

.40035 

.91636 

.41628 

.90924 

24 

37 

.35211 

.93596 

.36839 

.92967 

.38456 

.92310 

.40062 

.91625 

.41655 

.90911 

23 

38 

.35239 

.93585 

.36867 

.92950 

.38483 

.92299 

.40088 

.91613 

.41681 

.90899 

22 

39 

.35266 

.93575 

.36894 

.92945 

.38510 

.92287 

.40115 

.91601 

.41707 

.90887 

21 

40 

.35293 

.93565 

.36921 

.92935 

.38537 

.92276 

.40141 

.91590 

.41734 

.90875 

20 

41 

.35320 

.93555 

.36948 

.92924 

.38564 

.92265 

.40168 

.91578 

.41760 

.90863 

19 

42 

.35347 

.93544 

.36975 

.92913 

.38591 

.92254 

.40195 

.91566 

.41787 

.90851 

18 

43 

.35375 

.93534 

.37002 

.92902 

.38617 

.92243 

.40221 

.91555 

.41813 

.90839 

17 

44 

.35402 

.93524 

.37029 

.92892 

.38644 

.92231 

.40248 

.91543 

.41840 

.90826 

16 

45 

.35429 

.93514 

.37056 

.92881 

.38671 

.92220 

.40275 

.91531 

.41866 

.90814 

15 

46 

.35456 

.93502 

.37083 

.92870 

.38698 

.92209 

.40301 

.91519 

.41892 

.90802 

14 

47 

.35484 

.93493 

.37110 

.92859 

.38725 

.92198 

.40328 

.91508 

.41919 

.90790 

13 

48 

.35511 

.93483 

.37137 

.92849 

.38752 

.92186 

.40355 

.91496 

.41945 

.90778 

12 

49 

.35538 

.93472 

.37164 

.92838 

.38778 

.92175 

.40381 

.91484 

.41972 

.90766 

11 

50 

.35565 

.93462 

.37191 

.92827 

.38805 

.92164 

.40408 

.91472 

.41998 

.90753 

10 

51 

.35592 

.93452 

.37218 

.92816 

.38832 

.92152 

.40434 

.91461 

.42024 

.90741 

9 

52 

.35619 

.93441 

.37245 

.92805 

.38859 

.92141 

.40461 

.91449 

.42051 

.90729 

8 

53 

.35647 

.93431 

.37272 

.92794 

.38886 

.92130 

.40488 

.91437 

.42077 

.90717 

7 

54 

.35674 

.93420 

.37299 

.92784 

.38912 

.92119 

.40514 

.91425 

.42104 

.90704 

6 

55 

.35701 

.93410 

.37326 

.92773 

.38939 

.92107 

.40541 

.91414 

.42130 

.S0692 

5 

56 

.35728 

.93400 

.37353 

.92762 

.38966 

.92096 

.40567 

.91402 

.42156 

.90680 

4 

57 

.35755 

.93389 

.37380 

.92751 

.38993 

.92085 

.40594 

.91390 

.42183 

.90668 

3 

58 

.35782 

.93379 

.37407 

.92740 

.39020 

.92073 

.40621 

.91378 

.42209 

.90655 

2 

59 

.35810 

.93368 

.37434 

.92729 

.39046 

.92062 

.40647 

.91366 

.42235 

.90643 

1 

60 

.35837 

.93358 

.37461 

.92718 

.39073 

.92050 

.40674 

.91355 

.42262 

.90631 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

/ 

69"^ 

68° 

1 

O 

6G° 

65° 

/ 

460 


NATURAL' SINES  AND  COSINES. 


25° 

26° 

27° 

28° 

29° 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.42262 

.90631 

.43837 

.89879 

.45399 

.89101 

.46947 

.88295 

.48481 

.87462 

60 

1 

.42288 

.90618 

.43863 

.89867 

.45425 

.89087 

.46973 

.88281 

.48506 

.87448 

59 

2 

.42315 

.90606 

.43889 

.89854 

.45451 

.89074 

.46999 

.88267 

.48532 

.87434 

58 

3 

.42341 

.90594 

.43916 

.89841 

.45477 

.89061 

.47024 

.88254 

.48557 

.87420 

57 

4 

.42367 

.90582 

.43942 

.89828 

.45503 

.89048 

.47050 

.88240 

.48583 

.87406 

56 

5 

.42394 

.90569 

.43968 

.89816 

.45529 

.89035 

.47076 

.88226 

.48608 

.87391 

55 

6 

.42420 

.90557 

.43994 

.89803 

.45554 

.89021 

.47101 

.88213 

.48634 

.87377 

54 

7 

.42446 

.90545 

.44020 

.89790 

.45580 

.89008 

.47127 

.88199 

.48659 

.87363 

53 

8 

.42473 

.90532 

.44046 

.89777 

.45606 

.88995 

.47153 

.88185 

.48684 

.87349 

52 

9 

.42499 

.90520 

.44072 

.89764 

.45632 

.88981 

.47178 

.88172 

.48710 

.87335 

51 

10 

.42525 

.90507 

.44098 

.89752 

.45658 

.88968 

.47204 

.88158 

.48735 

.87321 

50 

11 

.42552 

.90495 

.44124 

.89739 

.45684 

.88955 

.47229 

.88144 

.48761 

.87306 

49 

12 

.42578 

.90483 

.44151 . 

.89726 

.45710 

.88942 

.47255 

.88130 

.48786 

.87292 

48 

13 

.42604 

.90470 

.44177 

.89713 

.45736 

.88928 

.47281 

.88117 

.48811 

.87278 

47 

14 

.42631 

.90458 

.44203 

.89700 

.45762 

.88915 

.47306 

.88103 

.48837 

.87264 

46 

15 

.42657 

.90446 

.44229 

.89687 

.45787 

.88902 

.47332 

.88089 

.48862 

.87250 

45 

16 

.42683 

.90433 

.44255 

.89674 

.45813 

.88888 

.47358 

.88075 

.48888 

.87235 

44 

17 

.42709 

.90421 

.44281 

.89662 

.45839 

.88875 

.47383 

.88062 

.48913 

.87221 

43 

18 

.42736 

.90408 

.44307 

.89649 

.45865 

.88862 

.47409 

.88048 

.48938 

.87207 

42 

19 

.42762 

.90396 

.44333 

.89636 

.45891 

.88848 

.47434 

.88034 

.48964 

.87193 

41 

20 

.42788 

.90383 

.44359 

.89623 

.45917 

.88835 

.47460 

.88020 

.48989 

.87178 

40 

21 

.42815 

.90321 

.44385 

.89610 

.45942 

.88822 

.47486 

.88006 

.49014 

.87164 

39 

22 

.42841 

.90358 

.44411 

.89597 

.45968 

.88808 

.47511 

.87993 

.49040 

.87150 

38 

23 

.42867 

.90346 

.44437 

.89584 

.45994 

.88795 

.47537 

.87979 

.49065 

.87136 

37 

24 

.42894 

.90334 

.44464 

.89571 

.46020 

.88782 

.47562 

.87965 

.49090 

.87121 

36 

25 

.42920 

.90321 

.44490 

.89558 

.46046 

.88768 

.47588 

.87951 

.49116 

.87107 

35 

26 

.42946 

.90309 

.44516 

.89545 

.46072 

.88755 

.47614 

.87937 

.49141 

.87093 

34 

27 

.42972 

.90296 

.44542 

.89532 

.46097 

.88741 

.47639 

.87923 

.49166 

.87079 

33 

28 

.42999 

.90284 

.44568 

.89519 

.46123 

.88728 

.47665 

.87909 

.49192 

.87064 

32 

29 

.43025 

.90271 

.44594 

.89506 

.46149 

.88715 

.47690 

.87896 

.49217 

.87050 

31 

30 

.43051 

.90259 

.44620 

.89493 

.46175 

.88701 

.47716 

.87882 

.49242 

.87036 

30 

31 

.43077 

.90246 

.44646 

.89480 

.46201 

.88688 

.47741 

.87868 

.49268 

.87021 

29 

32 

.43104 

.90233 

.44672 

.89467 

.46226 

.88674 

.47767 

.87854 

.49293 

.87007 

28 

33 

.43130 

.90221 

.44698 

.89454 

.46252 

.88661 

.47793 

.87840 

.49318 

.86993 

27 

34 

.43156 

.90208 

.44724 

.89441 

.46278 

.88647 

.47818 

.87826 

.49344 

.86978 

26 

35 

.43182 

.90196 

.44750 

.89428 

.46304 

.88634 

.47844 

.87812 

.49369 

.86964 

25 

36 

.43209 

.90183 

.44776 

.89415 

.46330 

.88620 

.47869 

.87798 

.49394 

.86949 

24 

37 

.43235 

.90171 

.44802 

.89402 

.46355 

.88607 

.47895 

.87784 

.49419 

.86935 

23 

38 

.43261 

.90158 

.44828 

.89389' 

.46381 

.88593 

.47920 

.87770 

.49445 

.86921 

22 

39 

.43287 

.90146 

.44854 

.89376 

.46407 

.88580 

.47946 

.87756 

.49470 

.86906 

21 

40 

.43313 

.90133 

.44880 

.89363 

.46433 

.88566 

.47971 

.87743 

.49495 

.86892 

20 

41 

.43340 

.90120 

.44906 

.89350 

.46458 

.88553 

.47997 

.87729 

.49521 

.86878 

19 

42 

.43366 

.90108 

.44932 

.89337 

.46484 

.88539 

.48022 

.87715 

.49546 

.86863 

18 

43 

.43392 

.90095 

.44958 

.89324 

.46510 

.88526 

.48048 

.87701 

.49571 

.86849 

17 

44 

.43418 

.90082 

.44984 

.89311 

.46536 

.88512 

.48073 

.87687 

.49596 

.86834 

16 

45 

.43445 

.90070 

.45010 

.89298 

.46561 

.88499 

.48099 

.87673 

.49622 

.86820 

15 

46 

.43471 

.90057 

.45036 

.89285 

.46587 

.88485 

.48124 

.87659 

.49647 

.86805 

14 

47 

.43497 

.90045 

.45062 

.89272 

.46613 

.88472 

.48150 

.87645 

.49672 

.86791 

13 

48. 

.43523 

.90032 

.45088 

.89259 

.46639 

.88458 

.48175 

.87631 

.49697 

.86777 

12 

49 

.43549 

.90019 

.45114 

.89245 

.46664 

.88445 

.48201 

.87617 

.49723 

.86762 

11 

50 

.43575 

.90007 

.45140 

.89232 

.46690 

.88431 

.48226 

.87603 

.49748 

.86748 

10 

51 

.43602 

.89994 

.45166 

.89219 

.46716 

.88417 

.48252 

.87589 

.49773 

.86733 

9 

52 

.43628 

.89981 

.45192 

.89206 

.46742 

.88404 

.48277 

.87575 

.49798 

.86719 

8 

53 

.43654 

.89968 

.45218 

.89193 

.46767 

.88390 

.48303 

.87561 

.49824 

.86704 

7 

54 

.43680 

.89956 

.45243 

.89180 

.46793 

.88377 

.48328 

.87546 

.49849 

.86690 

6 

55 

.43706 

.89943 

.45269 

.89167 

.46819 

.88363 

.48354 

.87532 

.49874 

.86675 

5 

56 

.43733 

.89930 

.45295 

.89153 

.46844 

.88349 

.48379 

.87518 

.49899 

.86661 

4 

57 

.43759 

.89918 

.45321 

.89140 

.46870 

.88336 

.48405 

.87504 

.49924 

.86646 

3 

58 

.43785 

.89905 

.45347 

.89127 

.46896 

.88322 

.48430 

.87490 

.49950 

.86632 

2 

59 

.43811 

.89892 

.45373 

.89114 

.46921 

.88308 

.48456 

.87476 

.49975 

.86617 

1 

60 

.43837 

.89879 

.45399 

.89101 

.46947 

.88295 

.48481 

.87462 

.50000 

.86603 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

/ 

64° 

63° 

62° 

61° 

60° 

/ 

KATUHAL  SINES  AND  COSINES. 


461 


30° 

31° 

32° 

33° 

I 34° 

t 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.50000 

.86603 

.51504 

.85717 

.52992 

.84805 

.54464 

.83867 

.55919 

.82904 

60 

1 

.50025 

.86588 

.51529 

.85702 

.53017 

.84789 

.54488 

.83851 

.55943 

.82887 

59 

2 

.50050 

.86573 

.51554 

.85687 

.53041 

.84774 

.54513 

.83835 

.55968 

.82871 

58 

3 

.50076 

.86559 

.51579 

.85672 

.53066 

.84759 

.54537 

.83819 

.55992 

.82855 

57 

4 

.50101 

.86544 

.51604 

.85657 

.53091 

.84743 

.54561 

.83804 

.56016 

.82839 

56 

5 

.50126 

.86530 

.51628 

.85642 

.53115 

.84728 

.54586 

.83788 

.56040 

.82822 

55 

6 

.50151 

.86515 

.51653 

.85627 

.53140 

.84712 

.54610 

.83772 

.56064 

.82806 

54 

7 

.50176 

.86501 

.51678 

.85612 

.53164 

.84697 

.54635 

.83756 

.56088 

.82790 

53 

8 

.50201 

.86486 

.51703 

.85597 

.53189 

.84681 

.54659 

.83740 

.56112 

.82773 

52 

9 

.50227 

.86471 

.51728 

.85582 

.53214 

.84666 

.54683 

.83724 

.56136 

.82757 

51 

10 

.50252 

.86457 

.51753 

.85567 

.53238 

.84650 

.54708 

.83708 

.56160 

.82741 

50 

11 

.50277 

.86442 

.51778 

.85551 

.53263 

.84635 

.54732 

.83692 

.56184 

.82724  * 

49 

12 

.50302 

.86427 

.51803 

.85536 

.53288 

.84619 

.54756 

.83676 

.56208 

.82708 

48 

13 

.50327 

.86413 

.51828 

.85521 

.53312 

.84604 

.54781 

.83660 

.56232 

.82692 

47 

14 

.50352 

.86398 

.51852 

.85506 

.53337 

.84588 

.54805 

.83645 

.56256 

.82675 

46 

15 

.50377 

.86384 

.51877 

.85491 

.53361 

.84573 

.54829 

.83629 

.56280 

.82659 

45 

16 

.50403 

.86369 

.51902 

.85476 

.53386 

.84557 

.54854 

.83613 

.56305 

.82643 

44 

17 

.50428 

.86354 

.51927 

.85461 

.53411 

.84542 

.54878 

.83597 

.56329 

.82626 

43 

18 

.50453 

.86340 

.51952 

.85446 

.53435 

.84526 

.54902 

.83581 

.56353 

.82610 

42 

19 

.50478 

.86325 

.51977 

.85431 

.53460 

.84511 

.54927 

.83565 

.56377 

.82593 

41 

20 

.50503 

.86310 

.52002 

.85416 

.53484 

.84495 

.54951 

.83549 

.56401 

.82577 

40 

21 

.50528 

.86295 

.52026 

.85401 

.53509 

.84480 

.54975 

.83533 

.56425 

.82561 

39 

22 

.50553 

.86281 

.52051 

.85385 

.53534 

.84464 

.54999 

.83517 

.56449 

.82544 

38 

23 

.50578 

.86266 

.52076 

.85370 

.53558 

.84448 

.55024 

.83501 

.56473 

.82528 

37 

24 

.50603 

.86251 

.52101 

.85355 

.53583 

.84433 

.55048 

.83485 

.56497 

.82511 

36 

25 

.50628 

.86237 

.52126 

.85340 

.53607 

.84417 

.55072 

.83469 

.56521 

.82495 

35 

26 

.50654 

.86222 

.52151 

.85325 

.53632 

.84402 

.55097 

.83453 

.56545 

.82478 

34 

27 

.50679 

.86207 

.52175 

.85310 

.53656 

.84386 

.55121 

.83437 

.56569 

.82462 

33 

28 

.50704 

.86192 

.52200 

.85294 

.53681 

.84370 

.55145 

.83421 

.56593 

.82446 

32 

29 

.50729 

.86178 

.52225 

.85279 

.53705 

.84355 

.55169 

.83405 

.56617 

.82429 

31 

30 

.50754 

.86163 

.52250 

.85264 

.53730 

.84339 

.55194 

.83389 

.56641 

.82413 

30 

31 

.50779 

.86148 

.52275 

.85249 

.53754 

.84324 

.55218 

.83373 

.56665 

.82396 

29 

32 

.50804 

.86133 

.52299 

.85234 

.53779 

.84308 

.55242 

.83356 

.56689 

.82380 

28 

33 

.50829 

.86119 

.52324 

.85218 

.53804 

.84292 

.55266 

.83340 

.56713 

.82363 

27 

34 

.50854 

.86104 

.52349 

.85203 

.53828 

.84277 

.55291 

.83324 

.56736 

.82347 

26 

35 

.50879 

.86089 

.52374 

.85188 

.53853 

.84261 

.55315 

.83308 

.56760 

.82330 

25 

36 

.50904 

.86074 

.52399 

.85173 

.53877 

.84245 

.55339 

.83292 

.56784 

.82314 

24 

37 

.50929 

.86059 

.52423 

.85157 

.53902 

.84230 

.55363 

.83276 

.56808 

.82297 

23 

38 

.50954 

.86045 

.52448 

.85142 

.53926 

.84214 

.55388 

.83260 

.56832 

.82281 

22 

39 

.50979 

.86030 

.52473 

.85127 

.53951 

.84198 

.55412 

.83244 

.56856 

.82264 

21 

40 

.51004 

.86015 

.52498 

.85112 

.53975 

.84182 

.55436 

.83228 

.56880 

.82248 

20 

41 

.51029 

.86000 

.52522 

.85096 

.54000 

.84167 

.55460 

.83212 

.56904 

.82231 

19 

42 

.51054 

.85985 

.52547 

.85081 

.54024 

.84151 

.55484 

.83195 

.56928 

.82214 

18 

43 

.51079 

.85970 

.52572 

.85066 

.54049 

.84135 

.55509 

.83179 

.56952 

.82198 

17 

44 

.51104 

.85956 

.52597 

.85051 

.54073 

.84120 

.55533 

.83163 

.56976 

.82181 

16 

45 

.51129 

.85941 

.52621 

.85035 

.54097 

.84104 

.55557 

.83147 

.57000 

.82165 

15 

46 

.51154 

.85926' 

.52646 

.85020 

.54122 

.84088 

.55581 

.83131 

.57024 

.82148 

14 

47 

.51179 

.85911 

.52671 

.85005 

.54146 

.84072 

.55605 

.83115 

.57047 

.82132 

13 

48 

.51204 

.85896 

.52696 

.84989 

.54171 

.84057 

.55630 

.83098 

.57071 

.82115 

12 

49 

.51229 

.85881 

.52720 

.84974 

.54195 

.84041 

.55654 

.83082 

.57095 

.82098 

n 

50 

.51254 

.85866 

.52745 

.84959 

.54220 

.84025 

.55678 

.83066 

.57119 

.82082 

10 

51 

.51279 

.85851 

.52770 

.84943 

.54244 

.84009 

.55702 

.83050 

.57143 

.82065 

9 

52 

.51304 

.85836 

.52794 

.84928 

.54269 

.83994 

.55726 

.83034 

.57167 

.82048 

8 

53 

.51329 

.85821 

.52819 

.84913 

.54293 

.83978 

.55750 

.83017 

.57191 

.82032 

7 

54 

.51354 

.85806 

.52844 

.84897 

.54317 

.83962 

.55775 

.83001 

.57215 

.82015 

6 

55 

.51379 

.85792 

.52869 

.84882 

.54342 

.83946 

.55799 

.82985 

.57238 

.81999 

5 

56 

.61404 

.85777 

.52893 

.84866 

.54366 

.83930 

.55823 

.82969 

.57262 

.81982 

4 

57 

.51429 

.85762 

.52918 

.84851 

.54391 

.83915 

.55847 

.82953 

.57286 

.81965 

3 

58 

.51454 

.85747 

.52943 

.84836 

.54415 

.83899 

.55871 

.82936 

.57310 

.81949 

2 

59 

.51479 

.85732 

.52967 

.84820 

.54440 

.83883 

.55895 

.82920 

.57334 

.81932 

1 

60 

.51504 

.85717 

.52992 

.84805 

.54464 

.83867 

.55919 

.82904 

.57358 

.81915 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

f 

69° 

58° 

57° 

56° 

55° 

t 

m 


NATURAL  SINES  AND  COSINES. 


35° 

36*^ 

37° 

38° 

39° 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.57358 

.81915 

.58779 

.80902 

.60182 

.79864 

.61566 

.78801 

.62932 

.77715 

60 

1 

.57381 

.81899 

.58802 

.80885 

.60205 

.79846 

.61589 

.78783 

.62955 

.77696 

59 

2 

.57405 

.81882 

.58826 

.80867 

.60228 

.79829 

.61612 

.78765 

.62977 

.77678 

58 

3 

.57429 

.81865 

.58849 

.80850 

.60251 

.79811 

.61635 

.78747 

.63000 

.77660 

57 

4 

.57453 

.81848 

.58873 

.80833 

.60274 

.79793 

.61658 

.78729 

.63022 

.77641 

56 

5 

.57477 

.81832 

.58896 

.80816 

.60298 

.79776 

.61681 

.78711 

.63045 

.77623 

55 

6 

.57501 

.81815 

.58920 

.80799 

.60321 

.79758 

.61704 

.78694 

.63068 

.77605 

54 

7 

.57524 

.81798 

.58943 

.80782 

.60344 

.79741 

.61726 

.78676 

.63090 

.77586 

53 

8 

.57548 

.81782 

.58967 

.80765 

.60367 

.79723 

.61749 

.78658 

.63113 

.77568 

52 

9 

.57572 

.81765 

.58990 

.80748 

.60390 

.79706 

.61772 

.78640 

.63135 

.77550 

51 

10 

.57596 

.81748 

.59014 

.80730 

.60414 

.79688 

.61795 

.78622 

.63158 

.77531 

50 

11 

.57619 

-.81731 

.59037 

.80713 

.60437 

.79671 

.61818 

.78604 

.63180 

.77513 

49 

12 

.57643 

.81714 

.59061 

.80696 

.60460 

.79653 

.61841 

.78586 

.63203 

.77494 

48 

13 

.57667 

.81698 

.59084 

.80679 

.60483 

.79635 

.61864 

.78568 

.63225 

.77476 

47 

14 

.57691 

.81681 

.59108 

.80662 

.60506 

.79618 

.61887 

.78550 

.63248 

.77458 

46 

15 

.57715 

.81664 

.59131 

.80644 

.60529 

.79600 

.61909 

.78532 

.63271 

.77439 

45 

16 

.57738 

.81647 

.59154 

.80627 

.60553 

.79583 

.61932 

.78514 

.63293 

.77421 

44 

17 

.57762 

.81631 

.59178 

.80610 

.60576 

.79565 

.61955 

.78496 

.63316 

.77402 

43 

18 

.57786 

.81614 

.59201 

.80593 

.60599 

.79547 

.61978 

.78478 

.63338 

.77384 

42 

19 

.57810 

.81597 

.59225 

.80576 

.60622 

.79530 

.62001 

.78460 

.63361 

.77366 

41 

20 

.57833 

.81580 

.59248 

.80558 

.60645 

.79512 

.62024 

.78442 

.63383 

.77347 

40 

21 

.57857 

.81563 

.59272 

.80541 

.60668 

.79494 

.«2046 

.78424 

.63406 

.77329 

39 

22 

.57881 

.81546 

.59295 

.80524 

.60691 

.79477 

.62069 

.78405 

.63428 

.77310 

38 

23 

.57904 

.81530 

.59318 

.80507 

.60714 

.79459 

.62092 

.78387 

.63451 

.77292 

37 

24 

.57928 

.81513 

.59342 

.80489 

.60738 

.79441 

.62115 

.78369 

.63473 

.77273 

36 

25 

.57952 

.81496 

.59365 

.80472 

.60761 

.79424 

.62138 

.78351 

.63496 

.77255 

35 

26 

.57976 

.81479 

.59389 

.80455 

.60784 

.79406 

.62160 

.78333 

.63518 

.77236 

34 

27 

.57999 

.81462 

.59412 

.80438 

.60807 

.79388 

.62183 

.78315 

.63540 

.77218 

33 

28 

.58023 

.81445 

.59436 

.80420 

.60830 

.79371 

.62206 

.78297 

.63563 

.77199 

32 

29 

.58047 

.81428 

.59459 

.80403 

.60853 

.79353 

.62229 

.78279 

.63585 

.77181 

31 

30 

.58070 

.81412 

.59482 

.80386 

.60876 

.79335 

.62251 

.78261 

.63608 

.77162 

30 

31 

.58094 

.81395 

.59506 

.80368 

.60899 

.79318 

.62274 

.78243 

.63630 

.77144 

29 

32 

.58118 

.81378 

.59529 

.80351 

.60922 

.79300 

.62297 

.78225 

.63653 

.77125 

28 

33 

.58141 

.81361 

.59552 

.80334 

.60945 

.79282 

.62320 

.78206 

.63675 

.77107 

27 

34 

.58165 

.81344 

.59576 

.80316 

.60968 

.79264 

.62342 

.78188 

.63698 

.77088 

26 

35 

.58189 

.81327 

.59599 

.80299 

.60991 

.79247 

.62365 

.78170 

.63720 

.77070 

25 

36 

.58212 

.81310 

.59622 

.80282 

.61015 

.79229 

.62388 

.78152 

.63742 

.77051 

24 

37 

.58236 

.81293 

.59646 

.80264 

.61038 

.79211 

.62411 

.78134 

.63765 

.77033 

23 

38 

.58260 

.81276 

.59669 

.80247 

.61061 

.79193 

.62433 

.78116 

.63787 

.77014 

22 

39 

.58283 

.81259 

.59693 

.802^0 

.61084 

.79176 

.62456 

.78098 

.63810 

.76996 

21 

40 

.58307 

.81242 

.59716 

.80212 

.61107 

.79158 

.62479 

.78079 

.63832 

.76977 

20 

41 

.58330 

.81225 

.59739 

.80195 

.61130 

.79140 

.62502 

.78061 

.63854 

.76959 

19 

42 

.58354 

.81208 

.59763 

.80178 

.61153 

.79122 

.62524 

.78043 

.63877 

.76940 

18 

43 

.58378 

.81191 

.59786 

.80160 

.61176 

.79105 

.62547 

.78025 

.63899 

.76921 

17 

44 

.58401 

.81174 

.59809 

.80143 

.61199 

.79087 

.62570 

.78007 

.63922 

.76903 

16 

45 

.58425 

.81157 

.59832 

.80125 

161222 

.79069 

.62592 

.77988 

.63944 

.76884 

15 

46 

.58449 

.81140 

.59856 

.80108 

.61245 

.79051 

.62615 

.77970 

.63966 

.76866 

14 

47 

.58472 

.81123 

.59879 

.80091 

.61268 

.79033 

.62638 

.77952 

.63989 

.76847 

13 

48 

.58496 

.81106 

.59902 

.80073 

.61291 

.79016 

.62660 

.77934 

.64011 

.76828 

12 

49 

.58519 

.81089 

.59926 

.80056 

.61314 

.78998 

.62683 

.77916 

.64033 

.76810 

11 

50 

.58543 

.81072 

.59949 

.80038 

.61337 

.78980 

.62706 

.77897 

.64056 

.76791 

10 

51 

.58567 

.81055 

.59972 

.80021 

.61360 

.78962 

.62728 

.77879 

.64078 

.76772 

9 

52 

.58590 

.81038 

.59995 

.80003 

.61383 

.78944 

.62751 

.77861 

.64100 

.76754 

8 

53 

.58614 

.81021 

.60019 

.79986 

.61406 

.78926 

.62774 

.77843 

.64123 

.76735 

7 

54 

.58637 

.81004 

.60042 

.79968 

.61429 

.78908 

.62796 

.77824 

.64145 

.76717 

6 

55 

.58661 

.80978 

.60065 

.79951 

.61451 

.78891 

.62819 

.77806 

.64167 

.76698 

5 

56 

.58684 

.80970 

.60089 

.79934 

.61474 

.78873 

.62842 

.77788 

.64190 

.76679 

4 

57 

.58708 

.80953 

.60112 

.79916 

.61497 

.78855 

.62864 

.77769 

.64212 

.76661 

3 

58 

.58731 

.80936 

.60135 

.79899 

.61520 

.78837 

.62887 

.77751 

.64234 

.76642 

2 

59 

.58755 

.80919 

.60158 

.79881 

.61543 

.78819 

.62909 

.77733 

.64256 

.76623 

1 

60 

.58779 

.80902 

.60182 

.79864 

.61566 

.78801 

.62932 

.77715 

.64279 

.76604 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

t 

54° 

53° 

52° 

51° 

50° 

/ 

NATURAL  SINES  AND  COSINES. 


463 


40® 

41® 

42® 

43® 

44® 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.64279 

.76604 

.65606 

.75471 

.66913 

.74314 

.68200 

.73135 

.69466 

.71934 

60 

1 

.64301 

.76586 

.65628 

.75452 

.66935 

.74295 

.68221 

.73116 

.69487 

.71914 

59 

2 

.64323 

.76567 

.65650 

.75433 

.66956 

.74276 

.68242 

.73096 

.69508 

.71894 

58 

3 

.64346 

.76548 

.65672 

.75414 

.66978 

.74256 

.68264 

.73076 

.69529 

.71873 

57 

4 

.64368 

.76530 

.65694 

.75395 

.66999 

.74237 

.68285 

.73056 

.69549 

.71853 

56 

5 

.64390 

.76511 

.65716 

.75375 

.67021 

.74217 

.68306 

.73036 

.69570 

.71833 

55 

6 

.64412 

.76492 

.65738 

.75356 

.67043 

.74198 

.68327 

.73016 

.69591 

.71813 

54 

7 

.64435 

.76473 

.65759 

.75337 

.67064 

.74178 

.68349 

.72996 

.69612 

.71792 

53 

8 

.64457 

.76455 

.65781 

.75318 

.67086 

.74159 

.68370 

.72976 

.69633 

.71772 

52 

9 

.64479 

.76436 

.65803 

.75299 

.67107 

.74139 

.68391 

.72957 

.69654 

.71752 

51 

10 

.64501 

.76417 

.65825 

.75280 

.67129 

.74120 

.68412 

.72937 

.69675 

.71732 

50 

11 

.64524 

.76398 

.65847 

.75261 

.67151 

.74100 

.68434 

.72917 

.69696 

.71711 

49 

12 

.64546 

.76380 

.65869 

.75241 

.67172 

.74080 

.68455 

.72897 

.69717 

.71691 

48 

13 

.64568 

.76361 

.65891 

.75222 

.67194 

.74061 

.68476 

.72877 

.69737 

.71671 

47 

14 

.64590 

.76342 

.65913 

.7.5203 

.67215 

.74041 

.68497 

.72857 

.69758 

.71650 

46 

15 

.64612 

.76323 

.65935 

.75184 

.67237 

.74022 

.68518 

.72837 

.69779 

.71630 

45 

16 

.64635 

.76304 

.65956 

.75165 

.67258 

.74002 

.68539 

.72817 

.69800 

.71610 

44 

17 

.64657 

.76286 

.65978 

.75146 

.67280 

.73983 

.68561 

.72797 

.69821 

.71590 

43 

18 

.64679 

.76267 

.66000 

.75126 

.67301 

.73963 

.68582 

.72777 

.69842 

.71569 

42 

19 

.64701 

.76248 

.66022 

.75107 

.67323 

.73944 

.68603 

.72757 

.69862 

.71549 

41 

20 

.64723 

.76229 

.66044 

.75088 

.67344 

.73924 

.68624 

.72737 

.69883 

.71529 

40 

21 

.64746 

.76210 

.66066 

.75069 

.67366 ■ 

.73904 

.68645 

.72717 

.69904 

.71508 

39 

22 

.64768 

.76192 

.66088 

.75050 

.67387 

.73885 

.68666 

.72697 

.69925 

.71488 

38 

23 

.64790 

.76173 

.66109 

.75030 

.67409 

.73865 

.68688 

72677 

.69946 

.71468 

37 

24 

.64812 

.76154 

.66131 

.75011 

.67430 

.73846 

.68709 

.72657 

.69966 

.71447 

36 

25 

.64834 

.76135 

.66153 

.74992 

.67452 

.73826 

.68730 

.72637 

.69987 

.71427 

35 

26 

.64856 

.76116 

.66175 

.74973 

.67473 

.73806 

.68751 

.72617 

.70008 

.71407 

34 

27 

.64878 

.76097 

.66197 

.74953 

.67495 

.73787 

.68772 

.72597 

.70029 

.71386 

33 

28 

.64901 

.76078 

.66218 

.74934 

.67516 

.73767 

.68793 

.72577 

.70049 

.71366 

32 

29 

.64923 

.76059 

.66240 

.74915 

.67538 

.73747 

.68814 

.72557 

.70070 

.71345 

31 

30 

.64945 

.76041 

.66262 

.74896 

.67559 

.73728 

.68835 

.72537 

.70091 

.71325 

30 

31 

.64967 

.76022 

.66284 

.74876 

.67580 

.73708 

.68857 

.72517 

.70112 

.71305 

29 

32 

.64989 

.76003 

.66306 

.74857 

.67602 

.73688 

.68878 

.72497 

.70132 

.71284 

28 

33 

.65011 

.75984 

.66327 

.74838 

.67623 

.73669 

.68899 

.72477 

.70153 

.71264 

27 

34 

.65033 

.75965 

.66349 

.74818 

.67645 

.73649 

.68920 

.72457 

.70174 

.71243 

26 

35 

.65055 

.75946 

.66371 

.74799 

.67666 

.73629 

.68941 

.72437 

.70195 

.71223 

25 

36 

.65077 

.75927 

.66393 

.74780 

.67688 

.73610 

.68962 

.72417 

.70215 

.71203 

24 

37 

.65100 

.75908 

.66414 

.74760 

.67709 

.73590 

.68983 

.72397 

.70236 

.71182 

23 

38 

.65122 

.75889 

.66436 

.74741 

.67730 

.73570 

.69004 

.72377 

.70257 

.71162 

22 

39 

.65144 

.75870 

.66458 

.74722 

.67752 

.73551 

.69025 

.72357 

.70277 

.71141 

21 

40 

.65166 

.75851 

.66480 

.74703 

.67773 

.73531 

.69046 

.72337 

.70298 

.71121 

20 

41 

.65188 

.75832 

.66501 

.74683 

.67795 

.73511 

.69067 

.72317 

.70319 

.71100 

19 

42 

.65210 

.75813 

.66523 

.74664 

.67816 

.73491 

.69088 

.72297 

.70339 

.71080 

18 

43 

.65232 

.75794 

.66545 

.74644 

.67837 

.73472 

.69109 

.72277 

.70360 

.71059 

17 

44 

.65254 

.75775 

.66566 

.74625 

.67859 

.73452 

.69130 

.72257 

.70381 

.71039 

16 

45 

.65276 

.75756 

.66588 

.74606 

.67880 

.-73432 

.69151 

.72236 

.70401 

.71019 

15 

46 

.65298 

.75738 

.66610 

.74586 

.67901 

.73413 

.69172 

.72216 

.70422 

.70998 

14 

47 

.65320 

.75719 

.66632 

.74567 

.67923 

.73393 

.69193 

.72196 

.70443 

.70978 

13 

48 

.65342 

.75700 

.66653 

.74548 

.67944 

.73373 

.69214 

.72176 

.70463 

.70957 

12 

49 

.65364 

.75680 

.66675 

.74528 

.67965 

.73353 

.69235 

.72156 

.70484 

.70937 

11 

50 

.65386 

.75661 

.66697 

.74509 

.67987 

.73333 

.69256 

.72136 

.70505 

.70916 

10 

51 

.65408 

.75642 

.66718 

.74489 

.68008 

.73314 

.69277 

.72116 

.70525 

.70896 

9 

52 

.65430 

.75623 

.66740 

.74470 

.68029 

.73294 

.69298 

.72095 

.70546 

.70875 

8 

53 

.65452 

.75604 

.66762 

.74451 

.68051 

.73274 

.69319 

.72075 

.70567 

.70855 

7 

54 

.65474 

.75585 

.66783 

.74431 

.68072 

.73254 

.69340 

.72055 

.70587 

.70834 

6 

55 

.65496 

.75.566 

.66805 

.74412 

.68093 

.73234 

.69361 

.72035 

.70608 

.70813 

5 

56 

.65518 

.75547 

.66827 

.74392 

.68115 

.73215 

.69382 

.72015 

.70628 

.70793 

4 

57 

.65540 

.75528 

.66848 

.74373 

. .68136 

.73195 

.69403 

.71995 

.70649 

.70772 

3 

58 

.65562 

.75509 

.66870 

.74353 

.68157 

.73175 

.69424 

.71974 

.70670 

.70752 

2 

59 

.65584 

.75490 

.66891 

.74334 

.68179 

.73155 

.69445 

.71954 

.70690 

.70731 

1 

60 

.65606 

.75471 

.66913 

.74314 

.68200 

.73135 

.69466 

.71934 

.70711 

.70711 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

49® 

48® 

47® 

46® 

45® 

/ 

464 


NATURAL  TANGENTS  AND  COTANGENTS. 


0° 

1° 

2° 

3° 

4° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.00000 

Infin. 

.01746 

57.2900 

.03492 

28.6363 

,05241 

19.0811 

.06993 

14.3007 

60 

1 

.00029 

3437.75 

.01775 

56.3506 

.03521 

28.3994 

.05270 

18.9755 

.07022 

14.2411 

59 

2 

.00058 

1718.87 

.01804 

55.4415 

.03550 

28.1664 

.05299 

18.8711 

.07051 

14.1821 

58 

3 

.00087 

1145.92 

.01833 

54.5613 

.03579 

27.9372 

.05328 

18.7678 

.07080 

14.1235 

57 

4 

.00116 

859.436 

.01862 

53.7086 

.03609 

27.7117 

.05357 

18.6656 

.07110 

14.0655 

56 

5 

.00145 

687.549 

.01891 

52.8821 

.03638 

27.4899 

.05387 

18.5645 

.07139 

14.0079 

55 

6 

.00175 

572.957 

.01920 

52.0807 

.03667 

27.2715 

.05416 

18.4645 

.07168 

13.9507 

54 

7 

.00204 

491.106 

.01949 

51.3032 

.03696 

27.0566 

.05445 

18.3655 

.07197 

13.8940 

53 

8 

.00233 

429.718 

.01978 

50.5485 

.03725 

26.8450 

.05474 

18.2677 

.07227 

13.8378 

52 

9 

.00262 

381.971 

.02007 

49.8157 

.03754 

26.6367 

.05503 

18.1708 

.07256 

13.7821 

51 

10 

.00291 

343.774 

.02036 

49.1039 

.03783 

26.4316 

.05533 

18.0750 

.07285 

13.7267 

50 

11 

.00320 

312.521 

.02066 

48.41*21 

.03812 

26.2296 

.05562 

17.9802 

.07314 

13.6719 

49 

12 

.00349 

286.478 

.02095 

47.7395 

.03842 

26.0307 

.05591 

17.8863 

.07344 

13.6174 

48 

13 

.00378 

264.441 

.02124 

47.0853 

.03871 

25.8348 

.05620 

17.7934 

,07373 

13.5634 

47 

14 

.00407 

245.552 

.02153 

46.4489 

.03900 

25.6418 

.05649 

17.7015 

.07402 

13.5098 

46 

15 

.00436 

229.182 

.02182 

45.8294 

.03929 

25.4517 

.05678 

17.6106 

.07431 

13.4566 

45 

16 

.00465 

214.858 

.02211 

45.2261 

.03958 

25.2644 

.05708 

17.5205 

.07461 

13.4039 

44 

17 

.00495 

202.219 

.02240 

44.6386 

.03987 

25.0798 

.05737 

17.4314 

.07490 

13.3515 

43 

18 

.00524 

190.984 

.02269 

44.0661 

.04016 

24.8978 

.05766 

17.3432 

.07519 

13.2996 

42 

19 

.00553 

180.932 

.02298 

43.5081 

.04046 

24-.7185 

.05795 

17.2558 

.07548 

13.2480 

41 

20 

.00582 

171.885 

.02328 

42.9641 

.04075 

24.5418 

.05824 

17.1693 

.07578 

13.1969 

40 

21 

.00611 

163.700 

.02357 

42.4335 

.04104 

24.3675 

.05854 

17.0837 

.07607 

13.1461 

39 

22 

.00640 

156.259 

.02386 

41.9158 

.04133 

24.1957 

.05883 

16.9990 

.07636 

13.0958 

38 

23 

.00669 

149.465 

.02415 

41.4106 

.04162 

24.0263 

.05912 

16.9150 

.07665 

13.0458 

37 

24 

.00698 

143.237 

.02444 

40.9174 

.04191 

23.8593 

.05941 

16.8319 

.07695 

12.9962 

36 

25 

.00727 

137.507 

.02473 

40.4358 

.04220 

23.6945 

.05970 

16.7496 

.07724 

12.9469 

35 

26 

.00756 

132.219 

.02502 

39.9655 

.04250 

23.5321 

.05999 

16.6681 

.07753 

12.8981 

34 

27 

.00785 

127.321 

.02531 

39.5059 

.04279 

23.3718 

.06029 

16.5874 

.07782 

12.8496 

33 

28 

.00815 

122.774 

.02560 

39.0568 

.04308 

23.2137 

.06058 

16.5075 

.07812 

12.8014 

32 

29 

.00844 

118.540 

.02589 

38.6177 

.04337 

23.0577 

.06087 

16.4283 

.07841 

12.7536 

31 

30 

.00873 

114.589 

.02619 

38.1885 

.04366 

22.9038 

.06116 

16.3499 

.07870 

12.7062 

30 

31 

.00902 

110.892 

.02648 

37.7686 

.04395 

22.7519 

.06145 

16.2722 

.07899 

12.6591 

29 

32 

.00931 

107.426 

.02677 

37.3579 

.04424 

22.6020 

.06175 

16.1952 

.07929 

12.6124 

28 

33 

.00960 

104.171 

.02706 

36.9560 

.04454 

22.4541 

.06204 

16.1190 

.07958 

12.5660 

27 

34 

.00989 

101.107 

.02735 

36.5627 

.04483 

22.3081 

.06233 

16.0435 

.07987 

12.5199 

26 

35 

.01018 

98.2179 

.02764 

36.1776 

.04512 

22.1640 

.06262 

15.9687 

.08017 

12.4742 

25 

36 

.01047 

95.4895 

.02793 

35.8006 

.04541 

22.0217 

.06291 

15.8945 

.08046 

12.4288 

24 

37 

.01076 

92.9085 

.02822 

35.4313 

.04570 

21.8813 

.06321 

15.8211 

.08075 

12.3838 

23 

38 

1 .01105 

90.4633 

.02851 

35.0695 

.04599 

21.7426 

.06350 

15.7483 

.08104 

12.3390 

22 

39 

.01135 

88.1436 

.02881 

34.7151 

.04628 

21.6056 

.06379 

15.6762 

,08134 

12.2946 

21 

40 

.01164 

85.9398 

,02910 

34.3678 

.04658 

21.4704 

.06408 

15.6048 

.08163 

12.2505 

20 

41 

.01193 

83.8435 

.02939 

34.0273 

.04687 

21.3369 

.06437 

15.5340 

.08192 

12.2067 

19 

42 

.01222 

81.8470 

.02968 

33.6935 

.04716 

21.2049 

.06467 

15.4638 

.08221 

12.1632 

18 

43 

.01251 

79.9434 

.02997 

33.3662 

.04745 

21.0747 

.06496 

15.3943 

.08251 

12.1201 

17 

44 

.01280 

78.1263 

.03026 

33.0452 

.04774 

20.9460 

.06525 

15.3254 

.08280 

12.0772 

16 

45 

.01309 

76.3900 

.03055 

32.7303 

.04803 

20.8188 

.06554 

15.2571 

.08309 

12.0346 

15 

46 

.01338 

74.7292 

.03084 

32.4213 

.04833 

20.6932 

.06584 

15.1893 

.08339 

11.9923 

14 

47 

.01367 

73.1390 

.03114 

32.1181 

.04862 

20.5691 

.06613 

15.1222 

.08368 

11.9504 

13 

48 

.01396 

71.6151 

.03143 

31.8205 

.04891 

20.4465 

.06642 

15.0557 

.08397 

11.9087 

12 

49 

.01425 

70.1533 

.03172 

31.5284 

.04920 

20.3253 

.06671 

14.9898 

.08427 

11.8673 

11 

50 

.01455 

68.7501 

.03201' 

31.2416 

.04949 

20.2056 

.06700 

14.9244 

.08456 

11.8262 

10 

51 

.01484 

67.4019 

.03230 

30.9599 

.04978 

20.0872 

.06730 

14.8596 

.08485 

11.7853 

9 

52 

.01513 

66.1055 

.03259 

30.6833 

.05007 

19.9702 

.06759 

14.7954 

.08514 

11.7448 

8 

53 

.01542 

64.8580 

.03288 

30.4116 

.05037 

19.8546 

.06788 

14.7317 

.08544 

11.7045 

7 

54 

.01571 

63.6567 

.03317 

30.1446 

.05066 

19.7403 

.06817 

14.6685 

.08573 

11.6645 

6 

55 

.01600 

62.4992 

.03346 

29.8823 

.05095 

19.6273 

.06847 

14.6059 

.08602 

11.6248 

5 

56 

.01629 

61.3829 

.03376 

29.6245 

.05124 

19.5156 

.06876 

14.5438 

.08632 

11.5853 

4 

57 

.01658 

60.3058 

.03405 

29.3711 

.05153 

19.4051 

.06905 

14.4823 

.08661 

11.5461 

3 

58 

.01687 

59.2659 

.03434 

29.1220 

.05182 

19.2959 

.06934 

14.4212 

.08690 

11.5072 

2 

59 

.01716 

58.2612 

.03463 

28.8771 

.05212 

19.1879 

.06963 

14.3607 

.08720 

11.4685 

1 

60 

.01746 

57.2900 

.03492 

28.6363 

.05241 

19.0811 

.06993 

14.3007 

.08749 

11.4301 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

89° 

88° 

87° 

86° 

85° 

NATURAL  TANGENTS  AND  COTANGENTS. 


465 


5° 

6° 

7° 

8° 

9° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.08749 

11.4301 

.10510 

9.51436 

.12278 

8.14435 

.14054 

7.11537 

.15838 

6.31375 

60 

1 

.08778 

11.3919 

.10540 

9.48781 

.12308 

8.12481 

.14084 

7.10038 

.15868 

6.30189 

59 

2 

.08807 

11.3540 

.10569 

9.46141 

.12338 

8.10536 

.14113 

7.08546 

.15898 

6.29007 

58 

3 

.08837 

11.3163 

.10599 

9.43515 

.12367 

8.08600 

.14143 

7.07059 

.15928 

6.27829 

57 

4 

.08866 

11.2789 

.10628 

9.40904 

.12397 

8.06674 

.14173 

7.05579 

.15958 

6.26655 

56 

5 

.08895 

11.2417 

.10657 

9.38307 

.12426 

8.04756 

.14202 

7.04105 

.15988 

6.25486 

55 

6 

.08925 

11.2048 

.10687 

9.35724 

.12456 

8.02848 

.14232 

7.02637 

.16017 

6.24321 

54 

7 

.08954 

11.1681 

.10716 

9.33155 

.12485 

8.00948 

.14262 

7.01174 

.16047 

6.23160 

53 

8 

.08983 

11.1316 

.10746 

9.30599 

.12515 

7.99058 

.14291 

6.99718 

.16077 

6.22003 

52 

9 

.09013 

11.0954 

.10775 

9.28058 

.12544 

7.97176 

.14321 

6.98268 

.16107 

6.20851 

51 

10 

.09042 

11.0594 

.10805 

9.25530 

.12574 

7.95302 

.14351 

6.96823 

.16137 

6.19703 

50 

11 

.09071 

11.0237 

.10834 

9.23016 

.12603 

7.93438 

.14381 

6.95385 

.16167 

6.185.59 

49 

12 

.09101 

10.9882 

.10863 

9.20516 

.12633 

7.91582 

.14410 

6.93952 

.16196 

6.17419 

48 

13 

.09130 

10.9529 

.10893 

9.18028 

.12662 

7.89734 

.14440 

6.92525 

.16226 

6.16283 

47 

14 

.09159 

10.9178 

.10922 

9.15554 

.12692 

7.87895 

.14470 

6.91104 

.16256 

6.15151 

46 

15 

.09189 

10.8829 

.10952 

9.13093 

.12722 

7.86064 

.14499 

6.89688 

.16286 

6.14023 

45 

16 

.09218 

10.8483 

.10981 

9.10646 

.12751 

7.84242 

.14529 

6.88278 

.16316 

6.12899 

44 

17 

.09247 

10.8139 

.11011 

9.08211 

.12781 

7.82428 

.14559 

6.86874 

.16346 

6.11779 

43 

18 

.09277 

10.7797 

.11040 

9.05789 

.12810 

7.80622 

.14588 

6.85475 

.16376 

6.10664 

42 

19 

.09306 

10.7457 

.11070 

9.03379 

.12840 

7.78825 

.14618 

6.84082 

.16405 

6.09552 

41 

20 

.09335 

10.7119 

.11099 

9.00983 

.12869 

7.77035 

.14648 

6.82694 

.16435 

6.08444 

40 

21 

.09365 

10.6783 

.11128 

8.98598 

.12899 

7.75254 

.14678 

6.81812 

.16465 

6.07340 

39 

22 

.09394 

10.6450 

.11158 

8.96227 

.12929 

7.73480 

.14707 

6.79936 

.16495 

6.06240 

38 

23 

.09423 

10.6118 

.11187 

8.93867 

.12958 

7.71715 

.14737 

6.78564 

.16525 

6.05143 

37 

24 

.09453 

10.5789 

.11217 

8.91520 

.12988 

7.69957 

.14767 

6.77199 

.16555 

6.04051 

36 

25 

.09482 

10.5462 

.11246 

8.89185 

.13017 

7.68208 

.14796 

6.75838 

.16585 

6.02962 

35 

26 

.09511 

10.5136 

.11276 

8.86862 

.13047 

7.66466 

.14826 

6.74483 

.16615 

6.01878 

34 

27 

.09541 

10.4813 

.11305 

8.84551 

.13076 

7.64732 

.14856 

6.73133 

.16645 

6.00797 

33 

28 

.09570 

10.4491 

.11335 

8.82252 

.13106 

7.63005 

.14886 

6.71789 

.16674 

5.99720 

32 

29 

.09600 

10.4172 

.11364 

8.79964 

.13136 

7.61287 

.14915 

6.70450 

.16704 

5.98646 

31 

30 

.09629 

10.3854 

.11394 

8.77689 

.13165 

7.59575 

.14945 

6.69116 

.16734 

5.97576 

30 

31 

.09658 

10.3538 

.11423 

8.75425 

.13195 

7.57872 

.14975 

6.67787 

.16764 

5.96510 

29 

32 

.09688 

10.3224 

.11452 

8.73172 

.13224 

7.56176 

.15005 

6 66463 

.16794 

5.95448 

28 

33 

.09717 

10.2913 

.11482 

8.70931 

.13254 

7.54487 

.15034 

6.65144 

.16824 

5.94390 

27 

34 

.09746 

10.2602 

.11511 

8.68701 

.13284 

7.52806 

.15064 

6.63831 

.16854 

5.93335 

26 

35 

.09776 

10.2294 

.11541 

8 66482 

.13313 

7.51132 

.15094 

6.62523 

.16884 

5.92283 

25 

36 

.09805 

10.1988 

.11570 

8.64275 

.13343 

7.49465 

.15124 

6.61219 

.16914 

5.91236 

24 

37 

.09834 

10.1683 

.11600 

8.62078 

.13372 

7.47806 

.15153 

6.59921 

.16944 

5.90191 

23 

38 

.09864 

10.1381 

.11629 

8.59893 

.13402 

7.46154 

.15183 

6.58627 

.16974 

5.89151 

22 

39 

.09893 

10.1080 

.11659 

8.57718 

.13432 

7.44509 

.15213 

6.57339 

.17004 

5.88114 

21 

40 

.09923 

10.0780 

.11688 

8.55555 

.13461 

7.42871 

.15243 

6.56055 

.17033 

5.87080 

20 

41 

.09952 

10.0483 

.11718 

8.53402 

.13491 

7.41240 

.15272 

6.54777 

.17063 

5.86051 

19 

42 

.09981 

10.0187 

.11747 

8.51259 

.13521 

7.39616 

.15302 

6.53503 

.17093 

5.85024 

18 

43 

.10011 

9.98931 

.11777 

8.49128 

.13550 

7.37999 

.15332 

6.52234 

.17123 

5.84001 

17 

44 

.10040 

9.96007 

.11806 

8.47007 

.13580 

7.36389 

.15362 

6.50970 

.17153 

5.82982 

16 

45 

.10069 

9.93101 

.11836 

8.44896 

.13609 

7.34786 

.15391 

6.49710 

.17183 

5.81966 

15 

46 

.10099 

9.90211 

.11865 

8.42795 

.13639 

7.33190 

.15421 

6.48456 

.17213 

5.80953 

14 

47 

.10128 

9.87338 

.11895 

8.40705 

.13669 

7.31600 

.15451 

6.47206 

.17243 

5.79944 

13 

48 

.10158 

9.84482 

.11924 

8.38625 

.13698 

7.30018 

.15481 

6.45961 

.17273 

5.78938 

12 

49 

.10187 

9.81641 

.11954 

8.36555 

.13728 

7.28442 

.15511 

6.44720 

.17303 

5.77936 

11 

50 

.10216 

9.78817 

.11983 

8.34496 

.13758 

7.26873 

.15540 

6.43484 

.17333 

5.76937 

10 

51 

.10246 

9.76009 

.12013 

8.32446 

.13787 

7.25310 

.15570 

6.42253 

.17363 

5.75941 

9 

52 

.10275 

9.73217 

.12042 

8.30406 

.13817 

7.23754 

.15600 

6.41026 

.17393 

5.74949 

8 

53 

.10305 

9.70441 

.12072 

8.28376 

.13846 

7.22204 

.15630 

6.39804 

.17423 

5.73960 

7 

54 

.10334 

9.67680 

.12101 

8.26355 

.13876 

7.20661 

.15660 

6.38587 

.17453 

5.72974 

6 

55 

.10363 

9.64935 

.12131 

8.24345 

.13906 

7.19125 

.15689 

6.37374 

.17483 

5.71992 

5 

56 

.10393 

9.62205 

.12160 

8.22344 

.13935 

7.17594 

.15719 

6.36165 

.17513 

5.71013 

4 

57 

.10422 

9.59490 

.12190 

8.20352 

.13965 

7.16071 

.15749 

6.34961 

.17543 

5.70037 

3 

58 

.10452 

9.56791 

.12219 

8.18370 

.13995 

7.14553 

.15779 

6.33761 

.17.573 

5.69064 

2 

59 

.10481 

9.54106 

.12249 

8.16398 

.14024 

7.13042 

.15809 

6.32566 

.17603 

5.68094 

1 

60 

.10510 

9.51436 

.12278 

8.14435 

.14054 

7.11537 

.15838 

6.31375 

.17633 

5.67128 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

840 

83° 

82° 

81° 

80° 

466 


NATURAL  TANGENTS  AND  COTANGENTS. 


10° 

IP 

12° 

13° 

14° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.17633 

5.67128 

.19438 

5.14455 

.21256 

4.70463 

.23087 

4.33148 

.24933 

4.01078 

60 

1 

.17663 

5.66165 

.19468 

5.13658 

.21286 

4.69791 

.23117 

4.32573 

.24964 

4.00582 

59 

2 

.17693 

5.65205 

.19498 

5.12862 

.21316 

4.69121 

.23148 

4.32001 

.24995 

4.00086 

58 

3 

.17723 

5.64248 

.19529 

5.12069 

.21347 

4.68452 

.23179 

4.31430 

.25026 

3.99592 

57 

4 

.17753 

5.63295 

.19559 

5.11279 

.21377 

4.67786 

.23209 

4.30860 

.25056 

3.99099 

56 

5 

.17783 

5.62344 

.19589 

5.10490 

.21408 

4.67121 

.23240 

4.30291 

,25087 

3.98607 

55 

6 

.17813 

5.61397 

.19619 

5.09704 

.21438 

4.66458 

.23271 

4.29724 

.25118 

3.98117 

54 

7 

.17843 

5.60452 

.19649 

5.08921 

.21469 

4.65797 

.23301 

4.29159 

.25149 

3.97627 

53 

8 

.17873 

5.59511 

.19680 

5.08139 

.21499 

4.65138 

.23332 

4.28595 

.25180 

3.97139 

52 

9 

.17903 

5.58573 

.19710 

5.07360 

.21529 

4.64480 

.23363 

4.28032 

.25211 

3.96651 

51 

10 

.17933 

5.57638 

.19740 

5.06584 

.21560 

4.63825 

.23393 

4.27471 

.25242 

3.96165 

50 

11 

.17963 

5.56706 

.19770 

5.05809 

.21590 

4.63171 

.23424 

4.26911 

.25273 

3.95680 

49 

12 

.17993 

5.55777 

.19801 

5.05037 

.21621 

4.62518 

.23455 

4.26352 

.2.5304 

3.95196 

48 

13 

.18023 

5.54851 

.19831 

5.04267 

.21651 

4.61868 

.23485 

4.25795 

.25335 

3.94713 

47 

14 

.18053 

5.53927 

.19861 

5.03499 

.21682 

4.61219 

.23516 

4.25239 

.25366 

3.94232 

46 

15 

.18083 

5.53007 

.19891 

5.02734 

.21712 

4.60572 

.23547 

4.24685 

.25397 

3.93751 

45 

16 

.18113 

5.52090 

.19921 

5.01971 

.21743 

4.59927 

;23578 

4.24132 

.25428 

3.93271 

44 

17 

.18143 

5.51176 

.19952 

5.01210 

.21773 

4.59283 

.23608 

4.23580 

.25459 

3.92793 

43 

18 

.18173 

5.50264 

.19982 

5.00451 

.21804 

4.58641 

.23639 

4.23030 

.25490 

3.92316 

42 

19 

.18203 

5.49356 

.20012 

4.99695 

.21834 

4.58001 

.23670 

4.22481 

.25521 

3.91839 

41 

20 

.18233 

5.48451 

.20042 

4.98940 

.21864 

4.57363 

.23700 

4.21933 

.25552 

3.91364 

40 

21 

.18263 

5.47548 

.20073 

4.98188 

.21895 

4.56726 

.23731 

4.21387 

.25583 

3.90890 

39 

22 

.18293 

5.46648 

.20103 

4.97438 

.21925 

4.56091 

.23762 

4.20842 

.25614 

3.90417 

38 

23 

.18323 

5.45751 

.20133 

4.96690 

.21956 

4.55458 

.23793 

4.20298 

.25645 

3.89945 

37 

24 

.18353 

5.44857 

.20164 

4.95945 

.21986 

4.54826 

.23823 

4.19756 

.25676 

3.89474 

36 

25 

.18384 

5.43966 

.20194 

4.95201 

.22017 

4.54196 

.23854 

4.19215 

.25707 

3.89004 

35 

26 

.18414 

5.43077 

.20224 

4.94460 

.22047 

4.53568 

.23885 

4.18675 

.25738 

3.88536 

34 

27 

.18444 

5.42192 

.20254 

4.93721 

.22078 

4.52941 

.23916 

4.18137 

.25769 

3.88068 

33 

28 

.18474 

5.41309 

.20285 

4.92984 

.22108 

4.52316 

.23946 

4.17600 

.25800 

3.87601 

32 

29 

.18504 

5.40429 

.20315 

4.92249 

.22139 

4.51693 

.23977 

4.17064 

.25831 

3.87136 

31 

30 

.18534 

5.39552 

.20345 

4.91516 

.22169 

4.51071 

.24008 

4.16530 

.25862 

3.86671 

30 

31 

.18564 

5.38677 

.20376 

4.90785 

.22200 

4.50451 

.24039 

4.15997 

.25893 

3.86208 

29 

32 

.18594 

5.37805 

.20406 

4.90056 

.22231 

4.49832 

.24069 

4.15465 

.25924 

3.85745 

28 

33 

.18624 

5.36936 

.20436 

4.89330 

.22261 

4.49215 

.24100 

4.14934 

.25955 

3.85284 

27 

34 

.18654 

5.36070 

.20466 

4.88605 

.22292 

4.48600 

.24131 

4.14405 

.25986 

3.84824 

26 

35 

.18684 

5.35206 

.20497 

4.87882 

.22322 

4.47986 

.24162 

4.13877 

.26017 

3.84364 

25 

36 

.18714 

5.34345 

.20527 

4.87162 

.22353 

4.47374 

.24193 

4.13350 

.26048 

3.83906 

24 

37 

.18745 

5.33487 

.20557 

4.86444 

.22383 

4.46764 

.24223 

4.12825 

.26079 

3.83449 

23 

38 

.18775 

5.32631 

.20588 

4.85727 

.22414 

4.46155 

.24254 

4.12301 

.26110 

3.82992 

22 

39 

.18805 

5.31778 

.20618 

4.85013 

.22444 

4.45548 

.24285 

4.11778 

.26141 

3.82537 

21 

40 

.18835 

5.30928 

,20648 

4.84300 

.22475 

4.44942 

.24316 

4.11256 

.26172 

3.82083 

20 

41 

.18865 

5.30080 

.20679 

4.83590 

,22505 

4.44338 

.24347 

4.10736 

.26203 

3.81630 

19 

42 

.18895 

5.29235 

.20709 

4.82882 

.22536 

4.43735 

.24377 

4.10216 

.26235 

3.81177 

18 

43 

.18925 

5.28393 

.20739 

4.82175 

.22567 

4.43134 

.24408 

4.09699 

.26266 

3.80726 

17 

44 

.18955 

5.27553 

.20770 

4.81471 

.22597 

4.42534 

.24439 

4.09182 

.26297 

3.80276 

16 

45 

.18986 

5.26715 

.20800 

4.80769 

.22628 

4.41936 

.24470 

4.08666 

.26328 

3.79827 

15 

46 

.19016  . 

5.25880 

.20830 

4.80068 

.22658 

4.41340 

.24501 

4.08152 

.26359 

3.79378 

14 

47 

.19046 

5.25048 

.20861 

4.79370 

.22689 

4.40745 

.24532 

4.07639 

.26390 

3.78931 

13 

48 

.19076 

5.24218 

.20891 

4.78673 

.22719 

4.40152 

.24562 

4.07127 

.26421 

3.78485 

12 

49 

.19106 

5.23381 

.20921 

4.77978 

.22750 

4.39560 

.24593 

4 06616 

.26452 

3.78040 

11 

50 

.19136 

5.22566 

.20952 

4.77286 

.22781 

4.38969 

.24624 

4.06107 

.26483 

3.77595 

10 

51 

.19166 

5.21744 

.20982 

4.76595 

.22811 

4.38381 

.24655 

4.05599 

.26515 

3.77152 

9 

52 

.19197 

5.20925 

.21013 

4.75906 

.22842 

4.37793 

.24686 

4.05092 

.26546 

3.76709 

8 

53 

.19227 

5.20107 

.21043 

4.75219 

.22872 

4.37207 

.24717 

4.04586 

.26577 

3.76268 

7 

54 

.19257 

5.19293 

.21073 

4.74534 

.22903 

4.36623 

.24747 

4.04081 

.26608 

3.75828 

6 

55 

.19287 

5.18480 

.21104 

4.78851 

.22934 

4.36040 

.24778 

4.03578 

,26639 

3.75388 

5 

56 

.19317 

5.17671 

.21134 

4.73170 

.22964 

4.35459 

,24809 

4.03076 

.26670 

3.r4950 

4 

57 

.19347 

5.16863 

.21164 

4.72490 

,22995 

4.34879 

.24840 

4.02574 

.26701 

3.74512 

3 

58 

.19378 

5.16058 

.21195 

4.71813 

.23026 

4.34300 

.24871 

4.02074 

.26733 

3.74075 

2 

59 

.19408 

5.15256 

.21225 

4.71137 

.23056 

4.33723 

.24902 

4.01576 

.26764 

3.73640 

1 

60 

.19438- 

5.14455 

.21256 

4.70463 

.23087 

4.33148 

.24933 

4.01078 

.26795 

3.73205 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

79° 

78° 

77° 

76° 

75° 

NATURAL  TANGENTS  AND  COTANGENTS. 


467 


150 

16° 

170 

18° 

190 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.26795 

3.73205 

.28675 

3.48741 

.30573 

3.27085 

.32492 

3.07768 

.34433 

2 90421 

60 

1 

.26826 

3.72771 

.28706 

3.48359 

.30605 

3.26745 

.32524 

3.07464 

.34465 

2.90147 

59 

2 

26857 

3.72338 

.28738 

3.47977 

.30637 

3.26406 

.32556 

3.07160 

.34498 

2.89873 

58 

3 

.26888 

3.71907 

.28769 

3.47596 

.30669 

3.26067 

.32588 

3.06857 

.34530 

2.89600 

57 

4 

.26920 

3.71476 

.28800 

3.47216 

.30700 

3.25729 

.32621 

3.06554 

.34563 

2,89327 

56 

5 

.26951 

3.71046 

.28832 

3.46837 

.30732 

3.25392 

.32653 

3.06252 

.34596 

2.89055 

55 

6 

.26982 

3.70616 

.28864 

3.46458 

.30764 

3.25055 

.32685 

3.05950 

.34628 

2 88783 

54 

7 

.27013 

3.70188 

.28895 

3.46080 

.30796 

3.24719 

.32717 

3.05649 

.34661 

2.88511 

53 

8 

.27044 

3.69761 

.28927 

3.45703 

.30828 

3.24383 

.32749 

3.05349 

.34693 

2.88240 

52 

9 

.27076 

3.69335 

.28958 

3.45327 

.30860 

3.24049 

.32782 

3.05049 

.34726 

2.87970 

51 

10 

.27107 

3.68909 

.28990 

3.44951 

.30891 

3.23714 

.32814 

3.04749 

.34758 

2.87700 

50 

11 

.27138 

3.68485 

.29021 

3.44576 

.30923 

3.23381 

.32846 

3.04450 

.34791 

2.87430 

49 

12 

.27169 

3.68061 

.29053 

3.44202 

.30955 

3.23048 

.32878 

3.04152 

.34824 

2.87161 

48 

13 

.27201 

3.67638 

.29084 

3.43829 

.30987 

3.22715 

.32911 

3.03854 

.34856 

2.86892 

47 

14 

.27232 

3.67217 

.29116 

3.43456 

.31019 

3.22384 

.32943 

3.03556 

.34889 

2.86624 

46 

15 

.27263 

3.66796 

.29147 

3.43084 

.31051 

3.22053 

.32975 

3 03260 

.34922 

2.86356 

45 

16 

.27294 

3.66376 

.29179 

3.42713 

.31083 

3.21722 

.33007 

3.02963 

.34954 

2.86089 

44 

17 

.27326 

3.65957 

.29210 

3.42343 

.31115 

3.21392 

.33040 

3.02667 

.34987 

2.85822 

43 

18 

.27357 

3.65538 

.29242 

3.41973 

.31147 

3.21063 

.33072 

3.02372 

.35020 

2.85555 

42 

19 

.27388 

3.65121 

.29274 

3.41604 

.31178 

3.20734 

.33104 

3.02077 

.35052 

2.85289 

41 

20 

.27419 

3.64705 

.29305 

3.41236 

.31210 

' 3.20406 

.33136 

3.01783 

.35085 

2.85023 

40 

21 

.27451 

3.64289 

.29337 

3.40869 

.31242 

3.20079 

.33169 

3.01489 

.35118 

2.84758 

39 

22 

.27482 

3.63874 

.29368 

3.40502 

.31274 

3.19752 

.33201 

3.01196 

.35150 

2.84494 

38 

23 

.27513 

3.63461 

.29400 

3.40136 

.31306 

3.19426 

.33233 

3 00903 

.35183 

2.84229 

37 

24 

.27545 

3.63048 

.29432 

3.39771 

.31338 

3.19100 

.33266 

3.00611 

.35216 

2.83965 

36 

25 

.27576 

3.62636 

.29463 

3.39406 

.31370 

3.18775 

.33298 

3.00319 

.35248 

2.83702 

35 

26 

.27607 

3.62224 

.29495 

3.39042 

.31402 

3 18451 

.33330 

3.00028 

.35281 

2.83439 

34 

27 

.27638 

3.61814 

.29526 

3.38679 

.31434 

3.18127 

.33363 

2.99738 

.35314 

2.83176 

33 

28 

.27670 

3.61405 

.29558 

3 38317 

.31466 

3.17804 

.33395 

2.99447 

.35346 

2.82914 

32 

29 

.27701 

3.60996 

.29590 

3.37955 

.31498 

3.17481 

.33427 

2.99158 

.35379 

2.82653 

31 

30 

.27732 

3.60588 

.29621 

3.37594 

.31530 

3.17159 

.33460 

2.98868 

.35412 

2.82391 

30 

31 

.27764 

3.60181 

.29653 

3.37234 

.31562 

3.16838 

.33492 

2.98580 

.35445 

2.82130 

29 

32 

.27795 

3.59775 

.29685 

3.36875 

.31594 

3.16517 

.33524 

2.98292 

.35477 

2.81870 

28 

33 

.27826 

3.59370 

.29716 

3.36516 

.31626 

3.16197 

.33557 

2.98004 

.35510 

2 81610 

27 

34 

.27858 

3.58966 

.29748 

3.361.58 

.31658 

3.15877 

.33589 

2 97717 

.35543 

2.81350 

26 

35 

.27889 

3.58562 

.29780 

3.3.5800 

.31690 

3.15558 

.33621 

2.97430 

.35576 

2.81091 

25 

36 

.27921 

3.58160 

.29811 

3.35443 

.31722 

3.15240 

.33654 

2 97144 

.35608 

2 80833 

24 

37 

.27952 

3.57758 

.29843 

3.35087 

.31754 

3.14922 

.33686 

2.96858 

.35641 

2.80574 

23 

38 

.27983 

3.57357 

.29875 

3.34732 

.31786 

3 14605 

.33718 

2.96573 

.35674 

2.80316 

22 

39 

.28015 

3.56957 

.29906 

3.34377 

.31818 

3.14288 

.33751 

2.96288 

.35707 

2.80059 

21 

40 

.28046 

3.56557 

.29938 

3.34023 

.31850 

3.13972 

.33783 

2.96004 

.35740 

2.79802 

20 

41 

.28077 

3.56159 

.29970 

3.33670 

.31882 

3.13656 

.33816 

2.95721 

.35772 

2.79545 

19 

42 

.28109 

3.55761 

.30001 

3.3.3317 

.31914 

3.13341 

.33848 

2.95437 

.35805 

2.79289 

18 

43 

.28140 

3.55364 

.30033 

3.32965 

.31946 

3.13027 

.33881 

2.95155 

.35838 

2.79033 

17 

44 

.28172 

3.54968 

.30065 

3.32614 

.31978 

3.12713 

.33913 

2.94872 

.35871 

2.78778 

16 

45 

.28203 

3.54573 

.30097 

3.32264 

.32010 

3.12400 

.33945 

2.94591 

.35904 

2.78523 

15 

46 

.28234 

3.54179 

.30128 

3.31914 

.32042 

3.12087 

.33978 

2.94309 

.35937 

2.78269 

14 

47 

.28266 

3.53785 

.30160 

3.31565 

.32074 

3.11775 

.34010 

2.94028 

.35969 

2.78014 

13 

48 

.28297 

3.53393 

.30192 

3.31216 

.32106 

3.11464 

.34043 

2.93748 

.36002 

2.77761 

12 

49 

.28329 

3.53001 

.30224 

3.30868 

.32139 

3.11153 

.34075 

2.93468 

.36035 

2.77507 

11 

50 

.28360 

3.52609 

.30255 

3.30521 

.32171 

3.10842 

.34108 

2.93189 

.36068 

2.77254 

10 

51 

.28391 

3.52219 

.30287 

3.30174 

.32203 

3.10532 

.34140 

2.92910 

.36101  ' 

2.77002 

9 

52 

.28423 

3.51829 

.30319 

3.29829 

,32235 

3.10223 

.34173 

2.92632 

.36134 

2.76750 

8 

53 

.28454 

3.51441 

.30351 

3.29483 

.32267 

3.09914 

.34205 

2.92354 

.36167 

2.76498 

7 

54 

.28486 

3.510.53 

.30382 

3.29139 

.32299 

3.09606 

.34238 

2.92076 

.36199 

2.76247 

6 

55 

.28517 

3. .50666 

.30414 

3.28795 

.32331 

3.09298 

.34270 

2.91799 

.36232 

2.75996 

5 

56 

.28549 

3.50279 

.30446 

3.28452 

.32363 

3.08991 

.34303 

2.91523 

.36265 

2.75746 

4 

57 

.28580 

3.49894 

.30478 

3.28109 

.32396 

3.08685 

.34335 

2.91246 

.36298 

2.75496 

3 

58 

.28612 

3.49509 

.30509 

3.27767 

.32428 

3.08379 

.34368 

2.90971 

.36331 

2.75246 

2 

59 

.28643 

3.49125 

.30541 

3.27426 

.32460 

3.08073 

.34400 

2.90696 

.36364 

2.74997 

1 

60 

.28675 

3.48741 

.30573 

3.27085 

.32492 

3.07768 

.34433 

2.90421 

.36397 

2.74748 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

740 

730 

72° 

710 

70° 

/ 

468 


NATURAL  TANGENTS  AND  COTANGENTS. 


20° 

21° 

22° 

23° 

24° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.36397 

2.74748 

.38386 

2.60509 

.40403 

2.47509 

.42447 

2.35585 

.44523 

2.24604 

60 

1 

.36430 

2.74499 

.38420 

2.60283 

.40436 

2.47302 

.42482 

2.35395 

.44558 

2.24428 

59 

2 

.36463 

2.74251 

.38453 

2.60057 

.40470 

2.47095 

.42516 

2.35205 

.44593 

2.24252 

58 

3 

.36496 

2.74004 

.38487 

2.59831 

.40504 

2.46888 

.42551 

2.35015 

.44627 

2.24077 

57 

4 

.36529 

2.73756 

.38520 

2.59606 

.40538 

2.46682 

.42585 

2.34825 

.44662 

2.23902 

56 

5 

.36562 

2.73509 

.38553 

2.59381 

.40572 

2.46476 

.42619 

2.34636 

.44697 

2.23727 

55 

6 

.36595 

2.73263 

.38587 

2.59156 

.40606 

2.46270 

.42654 

2.34447 

.44732 

2.23553 

54 

7 

.36628 

2.73017 

.38620 

2.58932 

.40640 

2.46065 

.42688 

2.34258 

.44767 

2.23378 

53 

8 

.36661 

2.72771 

.38654 

2.58708 

.40674 

2.45860 

.42722 

2.34069 

.44802 

2.23204 

52 

9 

.36694 

2.72526 

.38687 

2.58484 

.40707 

2.45655 

.42757 

2.33881 

.44837 

2.23030 

51 

10 

.36727 

2.72281 

.38721 

2.58261 

.40741 

2.45451 

.42791 

2.33693 

.44872 

2.22857 

50 

11 

.36760 

2.72036 

.38754 

2.58038 

.40775 

2.45246 

.42826 

2.33505 

.44907 

2.22683 

49 

12 

.36793 

2.71792 

.38787 

2.57815 

.40809 

2.45043 

.42860 

2.33317 

.44942 

2.22510 

48 

13 

.36826 

2.71548 

.38821 

2.57593 

.40843 

2.44839 

.42894 

2.33130 

.44977 

2.22337 

47 

14 

.36859 

2.71305 

.38854 

2.57371 

.40877 

2.44636 

.42929 

2.32943 

.45012 

2.22164 

46 

15 

.36892 

2.71062 

.38888 

2.57150 

.40911 

2.44433 

.42963 

2.32756 

.45047 

2.21992 

45 

16 

.36925 

2.70819 

.38921 

2.56928 

.40945 

2.44230 

.42998 

2.32570 

.45082 

2.21819 

44 

17 

.36958 

2.70577 

.38955 

2.56707 

.40979 

2.44027 

.43032 

2.32383 

.45117 

2.21647 

43 

18 

.36991 

2.70335 

.38988 

2.56487 

.41013 

2.43825 

.43067 

2.32197 

.45152 

2.21475 

42 

19 

.37024 

2.70094 

.39022 

2.56266 

.41047 

2.43623 

.43101 

2.32012 

.45187 

2.21304 

41 

20 

.37057 

2.69853 

.39055 

2.56046 

.41081 

2.43422 

.43136 

2.31826 

.45222 

2.21132 

40 

21 

.37090 

2.69612 

.39089 

2.55827 

.41115 

2.43220 

.43170 

2.31641 

.45257 

2.20961 

39 

22 

.37123 

2.69371 

.39122 

2.55608 

.41149 

2.43019 

43205 

2.31456 

.45292 

2.20790 

38 

23 

.37157 

2.69131 

.39156 

2.. 55389 

.41183 

2.42819 

.43230 

2.31271 

.45327 

2.20619 

37 

24 

.37190 

2.68892 

.39190 

2.55170 

.41217 

2.42618 

.43274 

2.31086 

.45362 

2.20449 

36 

25 

.37223 

2.68653 

.39223 

2.54952 

.41251 

2.42418 

.43308 

2.30902 

.45397 

2.20278 

35 

26 

.37256 

2.68414 

.39257 

2.54734 

.41285 

2.42218 

.43343 

2.30718 

.45432 

2.20108 

34 

27 

.37289 

2.68175 

.39290 

2.54516 

.41319 

2.42019 

.43378 

2.30534 

.45467 

2.19938 

33 

28 

.37322 

2.67937 

.39324 

2.54299 

.41353 

2.41819 

.43412 

2.30351 

.45502 

2.19769 

32 

29 

.37355 

2,67700 

.39357 

2.54082 

.41387 

2.41620 

.43447 

2.30167 

.45538 

2.19599 

31 

30 

.37388 

2.67462 

.39391 

2.53865 

.41421 

2.41421 

.43481 

2.29984 

.45573 

2.19430 

30 

31 

.37422 

2.67225 

.39425 

2.53648 

.41455 

2.41223 

.43516 

2.29801 

.45608 

2.19261 

29 

32 

.37455 

2.66989 

.39458 

2.53432 

.41490 

2.41025 

.43550 

2.29619 

.45643 

2.19092 

28 

33 

.37488 

2.66752 

.39492 

2.53217 

.41524 

2.40827 

.43585 

2.29437 

.45678 

2.18923 

27 

34 

.37521 

2.66516 

.39526 

2.53001 

.41558 

2.40629 

.43620 

2.29254 

.45713 

2.18755 

26 

35 

.37554 

2.66281 

.39559 

2.52786 

.41592 

2.40432 

.43654 

2.29073 

.45748 

2.18587 

25 

36 

.37588 

2.66046 

.39593 

2.52571 

.41626 

2.40235 

.43689 

2.28891 

.45784 

2.18419 

24 

37 

.37621 

2.65811 

.39626 

2.52357 

.41660 

2.40038 

.43724 

2.28710 

.45819 

2.18251 

23 

38 

.37654 

2.65576 

.39660 

2.52142 

.41694 

2.39841 

.43758 

2.28528 

.45854 

2.18084 

22 

39 

.37687 

2.65342 

.39694 

2.51929 

.41728 

2.39645 

.43793 

2.28348 

.45889 

2.17916 

21 

40 

.37720 

2.65109 

.39727 

2.51715 

.41763 

2.39449 

.43828 

2.28167 

.45924 

2.17749 

20 

41 

.37754 

2.64875 

.39761 

2.51502 

.41797 

2.39253 

.43862 

2.27987 

.45960 

2.17582 

19 

42 

.37787 

2.64642 

.39795 

2.51289 

.41831 

2.39058 

.43897 

2.27806 

.45995 

2.17416 

18 

43 

.37820 

2.64410 

.39829 

2.51076 

.41865 

2.38863 

.43932 

2.27626 

.46030 

2.17249 

17 

44 

.37853 

2.64177 

.39862 

2.50864 

.41899 

2.38668 

.43966 

2.27447 

.46065 

2.17083 

16 

45 

.37887 

2.63945 

.39896 

2.50652 

.41933 

2.38473 

.44001 

2.27267 

.46101 

2.16917 

15 

46 

.37920 

2.63714 

.39930 

2.50440 

.41968 

2.38279 

.44036 

2.27088 

.46136 

2.16751 

14 

47 

.37953 

2.63483 

.39963 

2.50229 

.42002 

2.38084 

.44071 

2.26909 

.46171 

2.16585 

13 

48 

.37986 

2.63252 

.39997 

2.50018 

.42036 

2.37891 

.44105 

2.26730 

.46206 

2.16420 

12 

49 

.38020 

2.63021 

.40031 

2.49807 

.42070 

2.37697 

.44140 

2.26552 

.46242 

2.16255 

11 

50 

.38053 

2.62791 

.40065 

2.49597 

.42105 

2.37504 

.44175 

2.26374 

.46277 

2.16090 

10 

51 

.38086 

2.62561 

.40098 

2.49386 

.42139 

2.37311 

.44210 

2.26196 

.46312 

2.15925 

9 

52 

.38120 

2.62332 

.40132 

2.49177 

.42173 

2.37118 

.44244 

2.26018 

.46348 

2.15760 

8 

53 

.38153 

2.62103 

.40166 

2.48967 

.42207 

2.36925 

.44279 

2.25840 

.46383 

2.15596 

7 

54 

.38186 

2.61874 

.40200 

2.48758 

.42242 

2.36733 

.44314 

2.25663 

.46418 

2.15432 

6 

55 

.38220 

2.61646 

.40234 

2.48549 

.42276 

2.36541 

.44349 

2.25486 

.46454 

2.15268 

5 

56 

.38253 

2.61418 

.40267 

2.48340 

.42310 

2.36349 

.44384 

2.25309 

.46489 

2.15104 

4 

57 

.38286 

2.61190 

.40301 

2.48132 

.42345 

2.36158 

.44418 

2.25132 

.46525 

2.14940 

S 

58 

.38320 

2.60963 

.40335 

2.47924 

.42379 

2.35967 

.44453 

2.24956 

.46560 

2.14777 

2 

59 

.38353 

2.60736 

.40369 

2.47716 

.42413 

2.35776 

.44488 

2.24780 

.46595 

2.14614 

1 

60 

.38386 

2.60509 

.40403 

2.47509 

.42447 

2.35585 

.44523 

2.24604 

.46631 

2.14451 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

69° 

68° 

67° 

66° 

65° 

/ 

NATURAL  TANGENTS  AND  COTANGENTS. 


469 


25° 

26° 

27° 

28° 

29° 

/ 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.46631 

2.14451 

.48773 

2.05030 

.50953 

1.96261 

.53171 

1.88073 

.55431 

1.80405 

60 

1 

.46666 

2.14288 

.48809 

2.04879 

.50989 

1.96120 

.53208 

1.87941 

.55469 

1.80281 

59 

2 

.46702 

2.14125 

.48845 

2.04728 

.51026 

1.95979 

.53246 

1.87809 

.55507 

1.80158 

58 

3 

.46737 

2.13963 

.48881 

2.04577 

.51063 

1.95838 

.53283 

1.87677 

.55545 

1.80034 

57 

4 

.46772 

2.13801 

.48917 

2.04426 

.51099 

1.95698 

.53320 

1.87546 

.55583 

1.79911 

56 

5 

.46808 

2.13639 

.48953 

2.04276 

.51136 

1.95557 

.53358 

1.87415 

.55621 

1.79788 

55 

6 

.46843 

2.13477 

.48989 

2.04125 

.51173 

1.95417 

.53395 

1.87283 

.55659 

1.79665 

54 

7 

.46879 

2.13316 

.49026 

2.03975 

.51209 

1.95277 

.53432 

1.87152 

.55697 

1.79542 

53 

8 

.46914 

2.13154 

.49062 

2.03825 

.51246 

1.95137 

.53470 

1.87021 

.55736 

1.79419 

52 

9 

.46950 

2.12993 

.49098 

2.03675 

.51283 

1.94997 

.53507 

1.86891 

.55774 

1.79296 

51 

10 

.46985 

2.12832 

.49134 

2.03526 

.51319 

1.94858 

.53545 

1.86760 

.55812 

1.79174 

50 

11 

.47021 

2.12671 

.49170 

2.03376 

.51356 

1.94718 

.53582 

1.86630 

.55850 

1.79051 

49 

12 

.47056 

2.12511 

.49206 

2.03227 

.51393 

1.94579 

.53620 

1.86499 

.55888 

1.78929 

48 

13 

.47092 

2.12350 

.49242 

2.03078 

.51430 

1.94440 

.53657 

1.86369 

.55926 

1.78807 

47 

14 

.47128 

2.12190 

.49278 

2.02929 

.51467 

1.94301 

.53694 

1.86239 

.55964 

1.78685 

46 

15 

.47163 

2.12030 

.49315 

2.02780 

.51503 

1.94162 

.53732 

1.86109 

.56003 

1.78563 

45 

16 

.47199 

2.11871 

.49351 

2.02631 

.51540 

1.94023 

.53769 

1.85979 

.56041 

1.78441 

44 

17 

.47234 

2.11711 

.49387 

2.02483 

.51577 

1.93885 

.53807 

1.85850 

.56079 

1.78319 

43 

18 

.47270 

2.11552 

.49423 

2.02335 

.51614 

' 1.93746 

.53844 

1.85720 

.56117 

1.78198 

42 

19 

.47305 

2.11392 

.49459 

2.02187 

.51651 

1.93608 

.53882 

1.85591 

.56156 

1.78077 

41 

20 

.47341 

2.11233 

.49495 

2.02039 

.51688 

1.93470 

.53920 

1.85462 

.56194 

1.77955 

40 

21 

.47377 

2.11075 

.49532 

2.01891 

.51724 

1.93332 

.53957 

1.85333 

.56232 

1.77834 

39 

22 

.47412 

2.10916 

.49568 

2.01743 

.51761 

1.93195 

.53995 

1.85204 

.56270 

1.77713 

38 

23 

.47448 

2.10758 

.49604 

2.01596 

.51798 

1.93057 

.54032 

1.85075 

.56309 

1.77592 

37 

24 

.47483 

2.10600 

.49640 

2.01449 

.51835 

1.92920 

.54070 

1.84946 

.56347 

1.77471 

36 

25 

.47519 

2.10442 

.49677 

2.01302 

.51872 

1.92782 

.54107 

1.84818 

.56385 

1.77351 

35 

26 

.47555 

2.10284 

.49713 

2.01155 

.51909 

1.92645 

.54145 

1.84689 

.56424 

1.77230 

34 

27 

.47590 

2.10126 

.49749 

2.01008 

.51946 

1.92508 

.54183 

1.84561 

.56462 

1.77110 

33 

28 

.47626 

2.09969 

.49786 

2.00862 

.51983 

1.92371 

.54220 

1.84433 

.56501 

1.76990 

32 

29 

.47662 

2.09811 

.49822 

2.00715 

.52020 

1.92235 

.54258 

1.84305 

.56539 

1.76869 

31 

30 

.47698 

2.09654 

.49858 

2.00569 

.52057 

1.92098 

.54296 

1.84177 

.56577 

1.76749 

30 

31 

.47733 

2.09498 

.49894 

2.00423 

.52094 

1.91962 

.54333 

1.84049 

.56616 

1.76629 

29 

82 

.47769 

2.09341 

.49931 

2.00277 

.52131 

1.91826 

.54371 

1.83922 

.56654 

1.76510 

28 

33 

.47805 

2.09184 

.49967 

2.00131 

.52168 

1.91690 

.54409 

1.83794 

.56693 

1.76390 

27 

34 

.47840 

2.09028 

.50004 

1.99986 

.52205 

1.91554 

.54446 

1.83667 

.56731 

1.76271 

26 

35 

.47876 

2.08872 

.50040 

1.99841 

.52242 

1.91418 

.54484 

1.83540 

.56769 

1.76151 

25 

36 

.47912 

2.08716 

.50076 

1.99695 

.52279 

1.91282 

.54522 

1.83413 

.56808 

1.76032 

24 

37 

.47948 

2.08560 

.50113 

1.99550 

.52316 

1.91147 

.54560 

1.83286 

.56846 

1.75913 

23 

38 

.47984 

2.08405 

.50149 

1.99406 

.52353 

1.91012 

.54597 

1.83159 

.56885 

1.75794 

22 

39 

.48019 

2.08250 

.50185 

1.99261 

.52390 

1 .90876 

.54635 

1.83033 

.56923 

1.75675 

21 

40 

.48055 

2.08094 

.50222 

1.99116 

.52427 

1.90741 

.54673 

1.82906 

.56962 

1.75556 

20 

41 

.48091 

2.07939 

.50258 

1.98972 

.52464 

1.90607 

.54711 

1.82780 

.57000 

1.75437 

19 

42 

.48127 

2.07785 

.50295 

1.98828 

.52501 

1.90472 

.54748 

1.82654 

.57039 

1.75319 

-18 

43 

.48163 

2.07630 

.50331 

1.98684 

.52538 

1.90337 

.54786 

1.82528 

.57078 

1.75200 

17 

44 

.48198 

2.07476 

.50368 

1.98540 

.52575 

1.90203 

.54824 

1.82402 

.57116 

1.75082 

16 

45 

.48234 

2.07321 

.50404 

1.98396 

.52613 

1.90069 

.54862 

1.82276 

.57155 

1.74964 

15 

46 

.48270 

2.07167 

.50441 

1.98253 

.52650 

1.89935 

.54900 

1.82150 

.57193 

1.74846 

14 

47 

.48306 

2.07014 

.50477 

1.98110 

.52687 

1.89801 

.54938 

1.82025 

.57232 

1.74728 

13 

48 

.48342 

2.06860 

.50514 

1.97966 

.52724 

1.89667 

.54975 

1.81899 

.57271 

1.74610 

12 

49 

.48378 

2.06706 

.50550 

1.97823 

.52761 

1.89533 

.55013 

1.81774 

.57309 

1.74492 

11 

50 

.48414 

2.06553 

.50587 

1.97681 

.52798 

1.89400 

.55051 

1.81649 

.57348 

1.74375 

10 

51 

.48450 

2.06400 

.50623 

1.97538 

.52836 

1.89266 

.55089 

1.81524 

.57386 

1.74257 

9 

52 

.48486 

2.06247 

.50660 

1.97395 

.52873 

1.891.33 

.55127 

1.81399 

.57425 

1.74140 

8 

53 

.48521 

2.06094 

.50696 

1.97253 

.52910 

1.89000 

.55165 

1.81274 

.57464 

1.74022 

7 

54 

.48557 

2.05942 

.50733 

1.97111 

.52947 

1.88867 

.55203 

1.81150 

.57503 

1.73905 

6 

55 

.48593 

2.05790 

.50769 

1.96969 

.52985 

1.88734 

.55241 

1.81025 

.57541 

1.73788 

5 

56 

.48629 

2.05637 

.50806 

1.96827 

.53022 

1.88602 

.55279 

1.80901 

.57580 

1.73671 

4 

57 

.48665 

2.05485 

.50843 

1.96685 

.53059 

1.88469 

.55317 

1.80777 

.57619 

1.73555 

3 

58 

.48701 

2.05333 

.50879 

1.96544 

.53096 

1.88337 

.55355 

1.80653 

.57657 

1.73438 

2 

59 

.48737 

2.05182 

.50916 

1.96402 

.53134 

1.88205 

.55393 

1.80529 

.57696 

1.73321 

1 

60 

.48773 

2.05030 

.50953 

1.96261 

.53171 

1.88073 

.5.5431 

1.80405 

.57735 

1.73205 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

64° 

63° 

62° 

61° 

60° 

470 


NATVRAL  TANGENTS  AND  COTANGENTS. 


30° 

31° 

CO 

33° 

34° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.57735 

1.73205 

.60086 

1.66428 

.62487 

1.60033 

.64941 

1.53986 

.67451 

1.48256 

60 

1 

.57774 

1.73089 

.60126 

1.66318 

.62527 

1.59930 

.64982 

1.53888 

.67493 

1.48163 

59 

2 

.57813 

1.72973 

.60165 

1.66209 

.62568 

1.59826 

.65024 

1.53791 

.67536 

1.48070 

58 

3 

.57851 

1.72857 

.60205 

1.66099 

.62608 

1.59723 

.65065 

1.53693 

.67578 

1.47977 

57 

4 

.57890 

1.72741 

.60245 

1.65990 

.62649 

1.59620 

.65106 

1.53595 

.67620 

1.47885 

56 

5 

.57929 

1.72625 

.60284 

1.65881 

.62689 

1.59517 

.65148 

1.53497 

.67663 

1.47792 

55 

6 

.57968 

1.72509 

.60324 

1.65772 

.62730 

1.59414 

.65189 

1.53400 

.67705 

1.47699 

54 

7 

.58007 

1.72393 

.60364 

1.65663 

.62770 

1.59311 

.65231 

1.53302 

.67748 

1.47607 

53 

8 

.58046 

1.72278 

.60403 

1.65554 

.62811 

1.59208 

.65272 

1.53205 

.67790 

1.47.514 

52 

9 

.58085 

1.72163 

.60443 

1.65445 

.62852 

1.59105 

.65314 

1.53107 

.67832 

1.47422 

51 

10 

.58124 

1.72047 

.60483 

1.65337 

.62892 

1.59002 

.65355 

1.53010 

.67875 

1.47330 

50 

11 

.58162 

1.71932 

.60522 

1.65228 

.62933 

1.58900 

.65397 

1.52913 

.67917 

1.47238 

49 

12 

.58201 

1.71817 

.60562 

1.65120 

.62973 

1.58797 

.65438 

1.52816 

.67960 

1.47146 

48 

13 

.58240 

1.71702 

.60602 

1.65011 

.63014 

1.58695 

.65480 

1.52719 

.68002 

1.47053 

47 

14 

.58279 

1.71588 

.60642 

1.64903 

.63055 

1.58593 

.65521 

1.52622 

.68045 

1.46962 

46 

15 

.58318 

1.71473 

.60681 

1.64795 

.63095 

1.58490 

.65563 

1.52525 

.68088 

1.46870 

45 

16 

.58357 

1.71358 

.60721 

1.64687 

.63136 

1.58388 

.65604 

1.52429 

.68130 

1.46778 

44 

17 

.58396 

1.71244 

.60761 

1.64579 

.63177 

1.58286 

.65646 

1.52332 

.68173 

1.46686 

43 

18 

..58435 

1.71129 

.60801 

1.64471 

.63217 

1.58184 

.65688 

1.52235 

.68215 

1.46595 

42 

19 

.58474 

1.71015 

.60841 

1.64363 

.63258 

1.58083 

.65729 

1.52139 

.68258 

1.46503 

41 

20 

.58513 

1.70901 

.60881 

1.64256 

.63299 

1.57981 

.65771 

1.52043 

.68301 

1.46411 

40 

21 

.58552 

1.70787 

.60921 

1.64148 

.63340 

1.57879 

.65813 

1.51946 

.68343 

1.46320 

39 

22 

.58591 

1.70673 

.60960 

1.64041 

.63380 

1.57778 

.65854 

1.51850 

.68386 

1.46229 

38 

23 

.58631 

1.70560 

.61000 

1.63934 

.63421 

1.57676 

.65896 

1.51754 

.68429 

1.46137 

37 

24 

.58670 

1.70446 

.61040 

1.63826 

.63462 

1.57575 

.65938 

1.51658 

.68471 

1.46046 

36 

25 

.58709 

1.70332 

.61080 

1.63719 

.63503 

1.57474 

.65980 

1.51562 

.68514 

1.45955 

35 

26 

.58748 

1.70219 

.61120 

1.63612 

.63544 

1.57372 

.66021 

1.51466 

.68557 

1.45864 

34 

27 

.58787 

1.70106 

.61160 

1.63505 

.63584 

1.57271 

.66063 

1.51370 

.68600 

1.45773 

33 

28 

.58826 

1.69992 

.61200 

1.63398 

.63625 

1.57170 

.66105 

1.51275 

.68642 

1.4.5682 

32 

29 

.58865 

1.69879 

.61240 

1.63292 

.63666 

1.57069 

.66147 

1.51179 

.68685 

1.45592 

31 

30 

.58905 

1.69766 

.61280 

1.63185 

.63707 

1.56969 

.66189 

1.51084 

.68728 

1.45501 

30 

31 

.58944 

1.69653 

.61320 

1.63079 

.63748 

1.56868 

.66230 

1.50988 

.68771 

1.45410 

29 

32 

.58983 

1.69541 

.61360 

1.62972 

.63789 

1.567C7 

.66272 

1.50893 

.68814 

1.45320 

28 

33 

.59022 

1.69428 

.61400 

1.62866 

.63830 

1.56667 

.66314 

1.50797 

.68857 

1.45229 

27 

34 

.59061 

1.69316 

.61440 

1.62760 

.63871 

1.56566 

.66356 

1.50702 

.68900 

1.45139 

26 

35 

.59101 

1.69203 

.61480 

1.62654 

.63912 

1.56466 

.66398 

1.50607 

.68942 

1.45049 

25 

36 

.59149 

1.69091 

.61520 

1.62548 

.63953 

1.56366 

.66440 

1.50512 

.68985 

1.44958 

24 

37 

.59179 

1.68979 

.61561 

1.62442 

.63994 

1.56265 

.66482 

1.50417 

.69028 

1.44868 

'23 

38 

.59218 

1.68866 

.61601 

1.62336 

.64035 

1.56165 

.66524 

1.50322 

.69071 

1.44778 

22 

39 

.59258 

1.68754 

.61641 

1.62230 

.64076 

1.56065 

.66566 

1.50228 

.69114 

1.44688 

21 

40 

.59297 

1.68643 

.61681 

1.62125 

.64117 

1.55966 

.66608 

1.50133 

.69157 

1.44598 

20 

41 

.59336 

1.68531 

.61721 

1.62019 

.64158 

1.55866 

.66650 

1.50038 

.69200 

1.44508 

19 

42 

.59376 

1.68419 

.61761 

1.61914 

.64199 

1.55766 

.66692 

1.49944 

.69243 

1.44418 

18 

43 

.59415 

1.68308 

.61801 

1.61808 

.64240 

1.55666 

.66734 

1.49849 

.69286 

1.44329 

17 

44 

.59454 

1.68196 

.61842 

1.61703 

.64281 

1.55567 

.66776 

1.49755 

.69329 

1.44239 

16 

45 

.59494 

1.68085 

.61882 

1.61598 

.64322 

1.55467 

.66818 

1.49661 

.69372 

1.44149 

15 

46 

.59533 

1.67974 

.61922 

1.61493 

.64363 

1.55368 

.66860 

1.49566 

.69416 

1.44060 

14 

47 

.59573 

1.67863 

.61962 

1.61388 

.64404 

1.55269 

.66902 

1.49472 

.69459 

1.43970 

13 

48 

.59612 

1.67752 

.62003 

1.61283 

.64446 

1.55170 

.66944 

1.49378 

.69502 

1.43881 

12 

49 

.59651 

1 .67641 

.62043 

1.61179 

.64487 

1.55071 

.66986 

1.49284 

.69545 

1.43792 

11 

50 

.59691 

1.67530 

.62083 

1.61074 

.64528 

1.54972 

.67028 

1.49190 

.69588 

1.43703 

10 

51 

.59730 

1.67419 

.62124 

1.60970 

.64569 

1.. 54873 

.67071 

1.49097 

.69631 

1.43614 

9 

52 

.59770 

1.67309 

.62164 

1.60865 

.64610 

1.54774 

.67113 

1.49003 

.69675 

1.43525 

8 

53 

.59803 

1.67198 

.62204 

1.60761 

.64652 

1.54675 

.67155 

1.48909 

.69718 

1.43436 

7 

54 

.59849 

1.67088 

.62245 

1.60657 

.64693 

1.54576 

.67197 

1.48816 

.69761 

1.43347 

6 

55 

.59888 

1.66978 

.62285 

1.60553 

.64734 

1.54478 

.67239 

1.48722 

.69804 

1.43258 

5 

56 

.59928 

1.66867 

.62325 

1.60449 

.64775 

1.54379 

.67232 

1.48629 

.69847 

1.43169 

4 

57 

.59967 

1.66757 

.62366 

1.60345 

.64817 

1.54281 

.67324 

1.48536 

.69891 

1.43080 

3 

58 

.60007 

1.66647 

.62406 

1.60241 

.64858 

1.54183 

.67366 

1.48442 

.69934 

1.42992 

2 

59 

.60046 

1.66538 

.62446 

1.60137 

.64899 

1.54085 

.67409 

1.48349 

.69977 

1 .42903 

1 

60 

.60086 

1.66428 

.62487 

1.60033 

.64941 

1.53986 

.67451 

1.48256 

.70021 

1.42815 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

f 

59° 

58° 

57° 

5()° 

55° 

9 

natvhal  tangents  and  cotangents. 


471 


350 

36° 

37° 

38° 

39° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.70021 

1.42815 

.72654 

1.37638 

.75.355 

1.32704 

.78129 

1.27994 

.80978 

1 

1.23490 

60 

1 

.70064 

1.42726 

.72699 

1.37554 

.75401 

1.32624 

.78175 

1.27917 

.81027 

1.23416 

59 

2 

.70107 

1.42638 

.72743 

1.37470 

.75447 

1.32544 

.78222 

1.27841 

.81075 

1.23343  i 

58 

3 

.70151 

1.42550 

.72788 

1.37386 

.75492 

1.32464 

.78269 

1.27764 

.81123 

1.23270  ^ 

57 

4 

.70194 

1.42462 

.72832 

1.37302 

.75538 

1.32384 

.78316 

1.27688 

.81171 

1.23196 

56 

5 

.70238 

1.42374 

.72877 

1.37218 

.75584 

1.32304 

.78363 

1.27611 

.81220 

1.23123 

55 

6 

.70281 

1.42286 

.72921 

1.37134 

.75629 

i. 32224 

.78410 

1.27535 

.81268 

1.23050 

54 

7 

.70325 

1.42198 

.72966 

1.37050 

.75675 

1.32144 

.78457 

1.27458 

.81316 

1.22977 

53 

8 

.70368 

1.42110 

.73010 

1.36967 

.75721 

1.32064 

.78504 

1.27382 

.81364 

1.22904 

52 

9 

.70412 

1.42022 

.73055 

1.36883 

.75767 

1.31984 

.78551 

1.27306 

.81413 

1.22831 

51 

10 

.70455 

1.41934 

.73100 

1.36800 

.75812 

1.31904 

.78598 

1.27230 

.81461 

1.22758 

50 

11 

.70499 

1.41847 

.73144 

1.36716 

.75858 

1.31825 

.78645 

1.27153 

.81510 

1.22685 

49 

12 

.70542 

1.41759 

.73189 

1.36633 

.75904 

1.31745 

.78692 

1.27077 

.81558 

1.22612 

48 

13 

.70586 

1.41672 

.73234 

1.36549 

.75950 

1.31666 

.78739 

1.27001 

.81606 

1.22539 

47 

14 

.70929 

1.41584 

.73278 

1.36466 

.75996 

1.31586 

.78786 

1 .26925 

.81655 

1.22467 

46 

15 

.70673 

1.41497 

.73323 

1.36383 

.76042 

1.31507 

.78834 

1.26849 

.81703 

1.22394 

45 

16 

.70717 

1.41409 

.73368 

1.36300 

.76088 

1.31427 

.78881 

1.26774 

.81752 

1.22321 

44 

17 

.70760 

1.41322 

.73413 

1.36217 

.76134 

1.31348 

.78928 

1.26698 

.81800 

1.22249 

43 

18 

.70804 

1.41235 

.73457 

1.36134 

.76180 

1.31269 

.78975 

1 .26622 

.81849 

1.22176 

42 

19 

.70848 

1.41148 

.73502 

1.36051 

.76226 

1.31190 

.79022 

1.26546 

.81898 

1.22104 

41 

20 

.70891 

1.41061 

.73547 

1 35968 

.76272 

1.31110 

.79070 

1.26471 

.81946 

1.22031 

40 

21 

.70935 

1.40974 

.73592 

1.35885 

.76318 

1.31031 

.79117 

1.26395 

.81995 

1.21959 

39 

22 

.70979 

1.40887 

.73637 

1.35802 

.76364 

1.30952 

.79164 

1.26319 

.82044 

1.21886 

38 

23 

.71023 

1.40800 

.73681 

1.35719 

.76410 

1.30873 

.79212 

1.26244 

.82092 

1.21814 

37 

24 

.71066 

1.40714 

.73726 

1.35637 

.76456 

1.30795 

.79259 

1.26169 

.82141 

1.21742 

36 

25 

.71110 

1.40627 

.73771 

1.35554 

.76502 

1.30716 

.79306 

1 .26093 

.82190 

1.21670 

35 

26 

.71154 

1.40540 

.73816 

1.35472 

.76548 

1.30637 

.79354 

1 .26018 

.82238 

1.21598 

34 

27 

.71198 

1.40454 

.73861 

1.35389 

.76594 

1.30558 

.79401 

1 .25943 

.82287 

1.21526 

33 

28 

.71242 

1.40367 

.73906 

1.35307 

.76640 

1.30480 

.79449 

1.25867 

.82336 

1.21454 

32 

29 

.71285 

1.40281 

.73951 

1.35224 

.76686 

1.30401 

.79496 

1.25792 

.82385 

1.21382 

31 

30 

.71329 

1.40195 

.73996 

1.35142 

.76733 

1.30323 

.79544 

1.25717 

.82434 

1.21310 

30 

31 

.71373 

1.40109 

.74041 

1.35060 

.76779 

1.30244 

.79591 

1.25642 

.82483 

1.21238 

29 

32 

.71417 

1 .40022 

.74086 

1.34978 

.76825 

1.30166 

.79639 

1.25567 

.82531 

1.21166 

28 

33 

.71461 

1.39936 

.74131 

1.34896 

.76871 

1.30087 

.79686 

1.25492 

.82580 

1.21094 

27 

34 

.71505 

1.39850 

.74176 

1.34814 

.76918 

1.30009 

.79734 

1.25417 

.82629 

1.21023 

26 

35 

.71549 

1.39764 

.74221 

1.34732 

.76964 

1.29931 

.79781 

1.25343 

.82678 

1.20951 

25 

36 

.71593 

1.39679 

.74267 

1.34650 

.77010 

1.29853 

.79829 

1.25268 

.82727 

1.20879 

24 

37 

.71637 

1.39593 

.74312 

1.34568 

.77057 

1.29775 

.79877 

1.25193 

.82776 

1.20808 

23 

38 

.71681 

1.39507 

.74357 

1.34487 

.77103 

1.29696 

.79924 

1.25118' 

.82825 

1.20736 

22 

39 

.71725 

1.39421 

.74402 

1.34405 

.77149 

1.29618 

.79972 

1.25044 

.82874 

1.20665 

21 

40 

.71769 

1.39336 

.74447 

1.34323 

.77196 

1.29541 

.80020 

1.24969 

.82923 

1.20593 

20 

41 

.71813 

1.39250 

.74492 

1 34242 

.77242 

1.29463 

.80067 

1.24895 

.82972 

1.20522 

19 

42 

.71857 

1.39165 

.74538 

1.34160 

.77289 

1.29385 

.80115 

1.24820 

.83022 

1.20451 

18 

43 

.71901 

1.39079 

.74583 

1.34079 

.77335 

1.29307 

.80163 

1.24746 

.83071 

1.20379 

17 

44 

.71946 

1.38994 

.74628 

1.33998 

.77382 

1.29229 

.80211 

1.24672 

.83120 

1.20308 

16 

45 

.71990 

1.38909 

.74674 

1.33916 

.77428 

1.29152 

.80258 

1.24597 

.83169 

1.20237 

15 

46 

.72034 

1.38824 

.74719 

1.33835 

.77475 

1.29074 

.80306 

1.24523 

.83218 

1.20166 

14 

47 

.72078 

1.38738 

.74764 

1.33754 

.77521 

1.28997 

.80354 

1.24449 

.83268 

1.20095 

13 

48 

.72122 

1.38653 

.74810 

1.33673 

.77568 

1 .28919 

.80402 

1.24375 

.83317 

1.20024 

12 

49 

.72167 

1.38568 

.74855 

1.33592 

.77615 

1.28842 

.80450 

1.24301 

.83366 

1.19953 

11 

50 

.72211 

1.38484 

.74900 

1.33511 

.77661 

1.28764 

.80498 

1.24227 

.83415 

1.19882 

10 

51 

.72255 

1.38399 

.74946 

1.33430 

.77708 

1.28687 

.80546 

1.24153 

.83465 

1.19811 

9 

52 

.72299 

1.38314 

.74991 

1.33349 

.77754 

1.28610 

.80594 

1.24079 

.83514 

1.19740 

8 

53 

.72344 

1.38229 

.75037 

1.3.3268 

.77801 

1.28533 

.80642 

1.24005 

.83564 

1.19669 

7 

54 

.72388 

1.38145 

.75082 

1.33187 

.77848 

1.28456 

.80690 

1.23931 

.83613 

1.19599 

6 

55 

.72432 

1.38060 

.75128 

1.3.3107 

.77895 

1.28379 

.80738 

1.23858 

.83662 

1.19528 

5 

56 

.72477 

1.37976 

.75173 

1.33026 

.77941 

1.28302 

.80786 

1.23784 

.83712 

1.19457 

4 

57 

.72521 

1.37891 

.75219 

1.32946 

.77988 

1.28225 

.80834 

1.23710 

.83761 

1.19387 

3 

58 

.72565 

1.37807 

.75264 

1.32865 

.78035 

1.28148 

.80882 

1.23637 

.83811 

1.19316 

2 

59 

.72610 

1.37722 

.75310 

1.32785 

.78082 

1.28071 

.80930 

1.23563 

.83860 

1.19246 

1 

60 

.72654 

1.37638 

.75355 

1.32704 

.78129 

1.27994 

.80978 

1.23490 

.83910 

1.19175 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

f 

54° 

53° 

52° 

51° 

50° 

472 


NATURAL  TANGENTS  AND  COTANGENTS. 


40°  t 

410 

42° 

440 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.83910 

1.19175 

.86929 

1.15037 

.90040 

1.11061 

.93252 

1.07237 

.96569 

1.03553 

60 

1 

.83960 

1.19105 

.86980 

1.14969 

.90098 

1.10996 

.93306 

1.07174 

.96625 

1.03493 

59 

2 

.84009 

1.19035 

.87031 

1.14902 

.90146 

1.10931 

.93360 

1.07112 

.96681 

1.03433 

58 

3 

.84059 

1.18964 

.87082 

1.14834 

.90199 

1.10867 

.93415 

1.07049 

.96738 

1.03372 

57 

4 

.84108 

1.18894 

.87133 

1.14767 

.90251 

1.10802 

.93469 

1.06987 

.96794 

1.03312 

56 

5 

.84158 

1.18824 

.87184 

1.14699 

.90304 

1.10737 

.93524 

1.06925 

.96850 

1.03252 

55 

6 

.84208 

1.18754 

.87236 

1.14632 

.90357  ■ 

1.10672 

.93578 

1.06862 

.96907 

1.03192 

54 

7 

.84258 

1.18684 

.87287 

1.14565 

.90410 

1.10607 

.93633 

1.06800 

.96963 

1.03132 

53 

8 

.84307 

1.18614 

.87338 

1.14498 

.90463 

1.10543 

.93688 

1.06738 

.97020 

1.03072 

52 

9 

.84357 

1.18544 

.87389 

1.14430 

.90516 

1.10478 

.93742 

1.06676 

.97076 

1.03012 

51 

10 

.84407 

1.18474 

.87441 

1.14363 

.90569 

1.10414 

.93797 

1.06613 

.97133 

1.02952 

50 

11 

.84457 

1.18404 

.87492 

1.14296 

.90621 

1.10349 

.93852 

1.06551 

.97189 

1.02892 

49 

12 

.84507 

1.18334 

.87543 

1.14229 

.90674 

1.10285 

.93906 

1.06489 

.97246 

1.02832 

48 

13 

.84556 

1.18264 

.87595 

1.14162 

.90727 

1.10220 

.93961 

1.06427 

.97302 

1.02772 

47 

14 

.84606 

1.18194 

.87646 

1.14095 

.90781 

1.10156 

.94016 

1.06365 

.97359 

1.02713 

46 

15 

.84656 

1.18125 

.87698 

1.14028 

.90834 

1.10091 

.94071 

1.06303 

.97416 

1.02653 

45 

16 

.84706 

1.18055 

.87749 

1.13961 

.90887 

1.10027 

.94125 

1.06241 

.97472 

1.02593 

44 

17 

.84756 

1.17986 

.87801 

1.13894 

.90940 

1.09963 

.94180 

1.06179 

.07529 

1.02533 

43 

18 

.84806 

1.17916 

.87852 

1.13828 

.90993 

1.09899 

.94235 

1.06117 

.97586 

1.02474 

42 

19 

.84856 

1.17846 

.87904 

1.13761 

.91046 

1.09834 

.94290 

1.06056 

.97643 

1.02414 

41 

20 

.84906 

1.17777 

.87955 

1.13694 

.91099 

1.09770 

.94345 

1.05994 

.97700 

1.02355 

40 

21 

.84956 

1.17708 

.88007 

1.13627 

.91153 

1.09706 

.94400 

1.05932 

.97756 

1.02295 

39 

22 

.85006 

1.17638 

.88059 

1.13561 

.91206 

1.09642 

.94455 

1.05870 

.97813 

1.02236 

38 

23 

.85057 

1.17569 

.88110 

1.13494 

.91259 

1.09578 

.94510 

1.05809 

.97870 

1.02176 

37 

24 

.85107 

1.17500 

.88162 

1.13428 

.91313 

1.09514 

.94565 

1.05747 

.97927 

1.02117 

36 

25 

.85157 

1.17430 

.88214 

1.13361 

.91366 

1.09450 

.94620 

1.05685 

.97984 

1.02057 

35 

26 

.85207 

1.17361 

.88265 

1.13295 

.91419 

1.09386 

.94676 

1.05624 

.98041 

1.01998 

34 

27 

.85257 

1.17292 

.88317 

1.13228 

.91473 

1.09322 

.94731 

1.05562 

.98098 

1.01939 

33 

28 

.85308 

1.17223 

.88369 

1.13162 

.91526 

1.09258 

.94786 

1.05501 

.98155 

1.01879 

32 

29 

.85358 

1.17154 

.88421 

1.13096 

.91580 

1.09195 

.94841 

1.05439 

.98213 

1.01820 

31 

30 

.85408 

1.17085 

.88473 

1.13029 

.91633 

1.09131 

.94896 

1.05378 

.98270 

1.01761 

30 

31 

.85458 

1.17016 

.88524 

1.12963 

.91687 

1.09067 

.94952 

1.05317 

.98327 

1.01702 

29 

32 

.85509 

1.16947 

.88576 

1.12897 

.91740 

1.09003 

.95007 

1.05255 

.98384 

1.01642 

28 

33 

.85559 

1.16878 

.88628 

1.12831 

.91794 

1.08940 

.95062 

1.05194 

.98441 

1.01583 

27 

34 

.85609 

1.16809 

.88680 

1.12765 

.91847 

1.08876 

.95118 

1.05133 

.98499 

1.01524 

26 

35 

.85660 

1.16741 

.88732 

1.12699 

.91901 

1.08813 

.95173 

1.05072 

.98556 

1.01465 

25 

36 

.85710 

1.16672 

.88784 

1.12633 

.91955 

1.08749 

.95229 

1.05010 

.98613 

1.01406 

24 

37 

.85761 

1.16603 

.88836 

1.12567 

.92008 

1.08686 

.95284 

1.04949 

.98671 

1.01347 

23 

38 

.85811 

1.16535 

.88888 

1.12501 

.92062 

1.08622 

.95340 

1.04888 

.98728 

1.01288 

22 

39 

.85862 

1.16466 

.88940 

1.12435 

.92116 

1.08559 

.95395 

1.04827 

.98786 

1.01229 

21 

40 

.85912 

1.16398 

.88992 

1.12369 

.92170 

1.08496 

.95451 

1.04766 

.98843 

1.01170 

20 

41 

.85963 

1.16329 

.89045 

1.12303 

.92224 

1.08432 

.95506 

1.04705 

.98901 

1.01112 

19 

42 

.86014 

1.16261 

.89097 

1.12238 

.92277 

1.08369 

.95562 

1.04644 

.98958 

1.01053 

18 

43 

.86064 

1.16192 

.89149 

1.12172 

.92331 

1.08306 

.95618 

1.04583 

.99016 

1.00994 

17 

44 

.86115 

1.16124 

.89201 

1.12106 

.92385 

1.08243 

.95673 

1.04522 

.99073 

1.00935 

16 

45 

.86166 

1.16056 

.89253 

1.12041 

.92439 

1.08179 

.95729 

1.04461 

.99131 

1.00876 

15 

46 

.86216 

1.15987 

.89306 

1.11975 

.92493 

1.08116 

.95785 

1.04401 

.99189 

1.00818 

14 

47 

.86267 

1.15919 

.89358 

1.11909 

.92547 

1.08053 

.95841 

1.04340 

.99247 

1.00759 

13 

48 

.86318 

1.15851 

.89410 

1.11844 

.92601 

1.07990 

.95897 

1.04279 

.99304 

1.00701 

12 

49 

.86368 

1.15783 

.89463 

1.11778 

.92655 

1.07927 

.95952 

1.04218 

.99362 

1.00642 

11 

50 

.86419 

1.15715 

.89515 

1.11713 

.92709 

1.07864 

.96008 

1.04158 

.99420 

1.00583 

10 

51 

.86470 

1.15647 

.89567 

1.11648 

.92763 

1.07801 

.96064 

1.04097 

.99478 

1.00525 

9 

52 

.86521 

1.15579 

.89620 

1.11582 

.92817 

1.07738 

.96120 

1.04036 

.99536 

1.00467 

8 

53 

.86572 

1.15511 

.89672 

1.11517 

.92872 

1.07676 

.96176 

1.03976 

.99594 

1.00408 

7 

54 

.86623 

1.15443 

.89725 

1.11452 

.92926 

1.07613 

.96232 

1.03915 

.99652 

1.00350 

6 

55 

.86674 

1.15375 

.89777 

1.11387 

.92980 

1.07550 

.96288 

1.03855 

.99710 

1.00291 

5 

56 

.86725 

1.15308 

.89830 

1.11321 

.93034 

1.07487 

.96344 

1.03794 

.99768 

1.00233 

4 

57 

.86776 

1.15240 

.89883 

1.11256 

.93088 

1.07425 

.96400 

1.03734 

.99826 

1.00175 

3 

58 

.86827 

1.15172 

.89935 

1.11191 

.93143 

1.07362 

.96457 

1.03674 

.99884 

1.00116 

2 

59 

.86878 

1.15104 

.89988 

1.11126 

.93197 

1.07299 

.96513 

1.03613 

.99942 

1.00058 

1 

60 

.86929 

1.15037 

.90040 

1.11061 

.93252 

1.07237 

.96569 

1.03553 

1.00000 

1.00000 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

49° 

48° 

470 

46° 

450 

LOGARITHMIC  TABLES. 


473 


LOGARITHMIC  TABLES. 

For  detailed  directions  as  to  the  use  of  logarithms  see  page  22. 

To  Find  the  Logarithmic  Sine,  Cosine,  Tangent,  or  Cotangent  of  an  Angle  From 
0°  to  45°.— In  the  table  Logarithms  of  Trigonometric  Functions,  find  the 
number  of  degrees  at  the  top  of  the  page,  and  the  number  of  minutes  in 
the  left-hand  column  headed  (');  opposite  the  latter,  and  under  the  proper 
head,  find  the  desired  logarithmic  sine,  cosine,  tangent,  or  cotangent. 

To  Find  the  Logarithmic  Sine,  Cosine,  Tangent,  or  Cotangent  of  an  Angle  From 
45°  to  90°.— In  the  table  Logarithms  of  Trigonometric  Functions,  find 
the  number  of  degrees  at  the  bottom  of  the  page,  and  the  number  of  minutes 
in  the  right-hand  column  headed  (');  oi)posite  the  latter,  and  above  the 
proper  head,  find  the  desired  logarithmic  sine,  cosine,  tangent,  or  cotangent. 

To  Find  the  Logarithmic  Functions  for  an  Angle  Containing  Degrees,  Minutes,  and 
Seconds. — Find  the  logarithm  for  the  degrees  and  minutes  in  the  manner  given 
above,  then  from  the  column  headed  “ d.”  take  the  number  next  below  the 
logarithm  thus  found;  under  the  heading  “P.  P.,”  find  a column  headed  by 
thjs  number,  and  find  in  this  column  the  number  opposite  the  given  number 
of  seconds;  add  it  to  the  logarithm  already  found  for  the  degrees  and  min- 
utes. If  the  exact  number  of  seconds  is  not  given  under  “P.  P.,”  the 
proper  values  may  be  found  by  interpolating  between  the  values  given. 
Since  the  differences  in  the  column  headed  “d.”  represent  differences  cor- 
responding to  60  seconds,  the  amount  to  be  added  after  the  logarithm  of  the 
degrees  arid  minutes  has  been  found  may  be  obtained  by  multiplying  the 
difference  by  the  number  of  seconds,  and  dividing  the  result  by  60. 

The  columns  headed  “Cpl.  S.”  and  “ Cpl.  T.”  on  pages  492-494  can  be  used  to 
find  logarithms  of  angles  including  seconds  less  than  3°  and  greater  than  86°. 
Reduce  the  degrees,  minutes,  and  seconds  to  seconds,  and  use  the  following 
formulas,  substituting  for  Cpl.  S.  and  Cpl.  T.  the  values  given  in  the  table,  and 
for  S.  and  T.,  the  difference  between  10  and  Cpl.  S.  and  Cpl.  T.  as  given. 

For  angles  less  than  IP,  log  sin  a = log  a"  S.;  log  tang  a = log  a" 
4-  T.;  log  cotg  a = Cpl.  log  a"  + Cpl.  T.  = Cpl.  log  tang  a;  log  a"  = log 
sin  a + Cpl.  S.  = log  tang  a + Cpl.  T.  = Cpl.  log  cotg  a -f  Cpl.  T. 

For  angles  greater  than  86^,  log  cos  a = log  (90°— a)"  + S.;  log  cotg  a 
= log  (90°  — a)"  -f  T.;  log  tang  a = Cpl.  log  (90°  — a)"  -t-  Cpl.  T.  = Cpl.  log 
cotg  a;  log  (90°  — a)"  = log  COS  a + Cpl.  S.  ==  log  COtg  a + Cpl.  T.  = Cpl. 
log  tang  a -h  Cpl.  T.  


COMMON  LOGARITHMS  OF  NUMBERS. 


No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

0 

— 00 

20 

30  103 

40 

60  206 

80 

77  815 

80 

90  309 

1 

00  000 

21 

32  222 

41 

61  278 

61 

78  533 

81 

90  849 

2 

30  103 

22 

34  242 

42 

62  325 

62 

79  239 

82 

91  381 

3 

47  712 

23 

36  173 

43 

63  347 

63 

79  934 

83 

91  908 

4 

60  206 

24 

38  021 

44 

64  345 

64 

80  618 

84 

92  428 

5 

69  897 

25 

39  794 

45 

65  321 

65 

81  291 

85 

92  942 

6 

77  815 

26 

41  497 

46 

66  276 

66 

81  954 

86 

93  450 

7 

84  510 

27 

43  136 

47 

67  210 

67 

82  607 

87 

93  952 

8 

90  309 

28 

44  716 

48 

68  124 

68 

83  251 

88 

94  448 

9 

95  424 

29 

46  240 

49 

69  020 

69 

83  885 

89 

94  939 

10 

00  000 

30 

47  712 

50 

69  897 

70 

84  510 

90 

95  424 

11 

04  139 

31 

49  136 

51 

70  757 

71 

85  126 

91 

95  904 

12 

07  918 

32 

50  515 

52 

71  600 

72 

85  733 

92 

96  379 

13 

11  394 

33 

51  851 

53 

72  428 

73 

86  332 

93 

96  848 

14 

14  613 

34 

53  148 

54 

73  239 

74 

86  923 

94 

97  313 

15 

17  609 

35 

54  407 

55 

74  036 

75 

87  506 

95 

97  772 

16 

20  412 

36 

55  630 

56 

74  819 

76 

88  081 

96 

98  227 

17 

23  045 

37 

56  820 

57 

75  587 

77 

88  649 

97 

98  677 

18 

25  527 

38 

57  978 

58 

76  343 

78 

89  209 

98 

99  123 

19 

27  875 

39 

59  106 

59 

77  085 

79 

89  763 

99 

99  564 

20 

30  103 

40 

60  206 

60 

77  815 

80 

90  309 

100 

00  000 

474 


LOGARrJHMS. 


N. 

L.o' 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

100 

00  000 

043 

087 

130 

173 

217 

260 

303 

346 

389 

101 

432 

475 

518 

561 

604 

647 

689 

732 

775 

817 

44 

43 

42 

102 

860 

903 

945 

988 

*030 

*072 

*115 

*157 

*199 

*242 

1 

4.4 

4.3 

4.2 

103 

01  284 

326 

368 

410 

452 

494 

536 

578 

620 

662 

2 

8!8 

8!6 

8^4 

104 

703 

745 

787 

828 

870 

912 

953 

995 

*036 

*078 

3 

13.2, 

12.9 

12.6 

105 

02  119 

160 

202 

243 

284 

325 

366 

407 

449 

490 

4 

17.6 

17.2 

16.8 

106 

531 

572 

612 

653 

694 

735 

776 

816 

857 

898 

5 

22,0 

21.5 

21.0 

107 

938 

979 

*019 

*060 

*100 

*141 

*181 

*222 

*262 

*302 

6 

7 

30.8 

2o.8 

30.1 

29.4 

108 

03  342 

383 

423 

463 

503 

543 

583 

623 

663 

703 

8 

35^2 

34‘.4 

33!6 

109 

743 

782 

822 

862 

902 

941 

981 

*021 

*060 

*100 

9 

39.6 

38.7 

37.8 

no 

04  139 

179 

218 

258 

297 

336 

376 

415 

454 

493 

111 

532 

571 

610 

650 

689' 

727 

766 

805 

844 

883 

41 

40 

39 

112 

922 

961 

999 

*038 

*077 

*115 

*154 

*192 

*231 

*269 

4.1 

4.0 

3.9 

113 

05  308 

346 

385 

423 

461 

500 

538 

576 

614 

652 

2 

8^0 

7^8 

114 

690 

729 

767 

805 

843 

881 

918 

956 

994 

*032 

3 

12.3 

12.0 

11.7 

115 

06  070 

108 

145 

183 

221 

258 

296 

333 

371 

408 

4 

16.4 

16.0 

15.6 

116 

446 

483 

521 

558 

595 

633 

670 

707 

744 

781 

5 

20.5, 

20.0 

19.5 

117 

819 

856 

893 

930 

967 

*004 

*041 

*078 

*115 

*151 

6 

7 

24.6 

28.7 

24.0 

28.0 

23.4 

27.3 

118 

07  188 

225 

. 262 

298 

335 

372 

408 

445 

482 

518 

8 

.32.8 

32!o 

3i!2 

119 

555 

591 

628 

664 

700 

737 

773 

809 

846 

882 

9 

36.9 

36.0 

35.1 

120 

918 

954 

990 

*027 

*063 

*099 

*135 

*171 

*207 

*243 

121 

08  279 

314 

350 

386 

422 

458 

493 

529 

565 

600 

38 

37 

36 

122 

636 

672 

707 

743 

778 

814 

849 

884 

920 

955 

j 

3.8 

3.7 

3.6 

123 

991 

*026 

*061 

*096 

*132 

*167 

*202 

*237 

*272 

*307 

2 

7]5 

7^4 

7.2 

124 

09  342 

377 

412 

447 

482 

517 

552 

587 

621 

656 

3 

11.4 

11.1 

10.8 

125 

691 

726 

760 

795 

830 

864 

899 

934 

968 

*003 

4 

15.2 

14.8 

14.4 

126 

10  037 

072 

106 

140 

175 

209 

243 

278 

312 

346 

5 

19.0 

18.5 

18.0 

127 

380 

415 

449 

483 

517 

551 

585 

619 

653 

687 

6 

7 

22.8 

26.6 

22 .2 
25.9 

25.2 

128 

721 

755 

789 

823 

857 

890 

924 

958 

992 

*025 

8 

3o!4 

29  6 

28.8 

129 

11  059 

093 

126 

160 

193 

227 

261 

294 

327 

361 

9 

.34.2 

33.3 

32.4 

130 

394 

428 

461 

494 

528 

561 

594 

628 

661 

694 

131 

727 

760 

793 

826 

860 

893 

926 

959 

992 

*024 

35 

34 

33 

132 

12  057 

090 

123 

156 

189 

222 

254 

287 

320 

352 

3.5 

3.4 

3.3 

133 

385 

418 

450 

483 

516 

548 

581 

613 

646 

678 

2 

7.0 

6.8 

6.6 

134 

710 

743 

775 

808 

840 

872 

905 

937 

969 

*001 

3 

10.5 

10.2 

9.9 

135 

13  033 

066 

098 

130 

162 

194 

226 

258 

290 

322 

4 

14.0 

13.6 

13.2 

136 

354 

386 

418 

450 

481 

513 

545 

577 

609 

640 

5 

17.5 

17.0 

16.5 

137 

672 

704 

735 

767 

799 

830 

862 

893 

925 

956 

6 

7 

21.0 

24.5 

23.8 

23.1 

138 

988 

*019 

*051 

*082 

*114 

*145 

*176 

*208 

*239 

*270 

8 

28!o 

27.2 

26.4 

139 

14  301 

333 

364 

395 

426 

457 

489 

520 

551 

582 

9 

31.5. 

30.6 

29.7 

140 

613 

644 

675 

706 

737 

768 

799 

829 

860 

891 

141 

922 

953 

983 

*014 

*045 

*076 

*106 

*137 

*168 

*19S 

32 

31 

1 30 

142 

15  229 

259 

290 

320 

351 

381 

412 

442 

473 

503 

3.2 

3.1 

3.0 

143 

534 

564 

594 

625 

655 

685 

715 

746 

776 

806 

e!! 

6.2 

6.0 

144 

836 

866 

897 

927 

957 

987 

*017 

*047 

*077 

*107 

3 

9.6 

9.3 

9.0 

145 

16  137 

167 

197 

20'7 

256 

286 

316 

346 

376 

406 

4 

12.8 

12.4 

! 12.0 

146 

435 

465 

495 

524 

551 

584 

613 

643 

673 

702 

5 

j 16.0 

15.5 

: 15.0 

147 

732 

761 

791 

820 

850 

879 

909 

938 

967 

997 

6 

1 19.2 

1 22.4 

18.6 

21.7 

j 21.0 

148 

17  026 

056 

085 

114 

143 

173 

202 

231 

260 

289 

8 

25  ]6 

24.8 

24.0 

149 

319 

348 

377 

406 

435 

464 

493 

522 

551 

580 

9 

1 28.8 

27.9 

127.0 

150 

609 

638 

667 

696 

1 

725 

754 

782 

811 

840 

869 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

LOGARITHMS. 


475 


476 


LOGARITHMS. 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

200 

201 

202 

203 

204 

205 

206 

207 

208 

209 

210 

211 

212 

213 

214 

215 

216 

217 

218 
219 

220 

221 

222 

223 

224 

225 

226 

227 

228 
229 

230 

231 

232 

233 

234 

235 

236 

237 

238 

239 

240 

241 

242 

243 

244 

245 

246 

247 

248 

249 

250 

30  103 

125 

146 

168 

190 

211 

233 

255 

276 

298 

22  21 

1 2.2  2.1 

2 4.4  4.2 

3 6.6  6.3 

4 8.8  8.4 

5 11.0  10.5 

6 13.2  12.6 

7 15.4  14.7 

8 17.8  16.8 

9 19.8  18.9 

20 

1 2.0 

2 4.0 

3 6.0 

4 8.0 

5 10.0 

6 12.0 

7 14.0 

8 16.0 

9 18.0 

19 

1 1.9 

2 3.8 

3 5.7 

4 7.6 

5 9.5 

6 11.4 

7 13.3 

8 15.2 

9 17.1 

18 

1 1.8 

2 3.6 

3 5.4 

4 7.2 

5 9.0 

6 10.8 

7 12.6 

8 14.4 

9 16.2 

17 

1 1.7 

2 3 4 

8 5.1 

4 6.8 

5 8.5 

6 10.2 

7 11.9 

8 13.6 

9 15.3 

320 

535 

750 

963 

31  175 
387 
597 
806 

32  015 

341 

557 

771 

984 

197 

408 

618 

827 

035 

363 

578 

792 

*006 

218 

429 

639 

848 

056 

384 

600 

814 

*027 

239 

450 

660 

869 

077 

406 

621 

835 

*048 

260 

471 

681 

890 

098 

428 

643 

856 

*069 

281 

492 

702 

911 

118 

449 

664 

878 

*091 

302 

513 

723 

931 

139 

471 

685 

899 

*112 

323 

534 

744 

952 

160 

492 

707 

920 

*133 

345 

555 

765 

973 

181 

514 

728 

942 

*154 

366 

576 

785 

994 

201 

222 

243 

263 

284 

305 

325 

346 

366 

387 

408 

428 

634 

838 

33  041 
244 
445 
646 
846 

34  044 

449 

654 

858 

062 

264 

465 

666 

866 

064 

469 

675 

879 

082 

284 

486 

686 

885 

084 

490 

695 

899 

102 

304 

506 

706 

905 

104 

510 

715 

919 

122 

325 

526 

726 

925 

124 

531 

736 

940 

143 

345 

546 

746 

945 

143 

552 

756 

960 

163 

365 

566 

766 

965 

163 

572 

777 

980 

183 

385 

586 

786 

985 

183 

593 

797 

*001 

203 

405 

606 

806 

*005 

203 

613 

818 

*021 

224 

425 

626 

826 

*025 

223 

242 

262 

282 

301 

321 

341 

361 

380 

400 

420 

439 
635 
830 
35  025 
218 
411 
603 
793 
984 

459 

655 

850 

044 

238 

430 

622 

813 

*003 

479 

674 

869 

064 

257 

449 

641 

832 

*021 

498 

694 

889 

083 

276 

468 

660 

851 

*040 

518 

713 

908 

102 

295 

488 

679 

870 

*059 

537 

733 

928 

122 

315 

507 

698 

889 

*078 

557 

753 

947 

141 

334 

526 

717 

908 

*097 

577 

772 

967 

160 

353 

545 

736 

927 

*116 

596 

792 

986 

180 

372 

564 

755 

946 

*135 

616 

811 

*005 

199 

392 

583 

774 

965 

*154 

36  173 

192 

211 

229 

248 

267 

286 

305 

324 

342 

361 
549 
736 
922 
37  107 
291 
475 
658 
840 

380 

568 

754 

940 

125 

310 

493 

676 

858 

399 

586 

773 

959 

144 

328 

511 

694 

876 

418 

605 

791 

977 

162 

346 

530 

712 

894 

436 

624 

810 

996 

181 

365 

548 

731 

912 

455 

642 

829 

*014 

199 

383 

566 

749 

931 

474 

661 

847 

*033 

218 

401 

585 

767 

949 

493 

680 

866 

*051 

236 

420 

603 

785 

967 

511 

698 

884 

*070 

254 

438 

621 

803 

985 

530 

717 

903 

*088 

273 

457 

639 

822 

*003 

38  021 

039 

057 

075 

093 

112 

130 

148 

166 

184 

202 
382 
561 
739 
917 
39  094 
270 
445 
620 

220 

399 

578 

757 

934 

111 

287 

463 

637 

238 

417 

596 

775 

952 

129 

305 

480 

655 

256 

435 

614 

792 

970 

146 

322 

498 

672 

274 

453 

632 

810 

987 

164 

340 

515 

690 

292 

471 

650 

828 

*005 

182 

358 

533 

707 

310 

489 

668 

846 

*023 

199 

375 

550 

724 

328 

507 

686 

863 

*041 

217 

393 

568 

742 

346 

525 

703 

881 

*058 

235 

410 

585 

759 

364 

543 

721 

899 

*076 

252 

428 

602 

777 

794 

811 

829 

846 

863 

881 

898 

915 

933 

950 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

LOGARITHMS. 


477 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

250 

39  794 

811 

829 

846 

863 

881 

898 

915 

933 

950 

251 

967 

985 

*002 

*019 

*037 

*054 

*071 

*088 

*106 

*123 

18 

252 

40  140 

157 

175 

192 

209 

226 

243 

261 

278 

295 

1 

1.8 

253 

312 

329 

346 

364 

381 

398 

415 

432 

449 

466 

2 

3!6 

254 

483 

500 

518 

535 

552 

569 

586 

603 

620 

637 

3 

5.4 

255 

654 

671 

688 

705 

722 

739 

756 

773 

790 

807 

4 

7.2 

256 

824 

841 

858 

875 

892 

909 

926 

943 

960 

976 

5 

9.0 

257 

993 

*010 

*027 

*044 

*061 

*078 

*095 

*111 

*128 

*145 

6 

7 

12.6 

258 

41  162 

179 

196 

212 

229 

246 

263 

280 

296 

313 

8 

14.4 

259 

330 

347 

363 

380 

397 

414 

430 

447 

464 

481 

9 

16.2 

260 

497 

514 

531 

547 

564 

581 

597 

614 

631 

647 

261 

664 

681 

697 

714 

731 

747 

764 

780 

797 

814 

17 

262 

830 

847 

863 

880 

896 

913 

929 

946 

963 

979 

1 

1.7 

263 

996 

*012 

*029 

*045 

*062 

*078 

*095 

*111 

*127 

*144 

2 

3.4 

264 

42  160 

177 

193 

210 

226 

243 

259 

275 

292 

308 

3 

5.1 

265 

325 

341 

357 

374 

390 

406 

423 

439 

455 

472 

4 

6.8 

266 

488 

504 

521 

537 

553 

570 

586 

602 

619 

635 

5 

8.5 

267 

651 

667 

684 

700 

716 

732 

749 

765 

781 

797 

7 

11.9 

268 

813 

830 

846 

862 

878 

894 

911 

927 

943 

959 

8 

13.6 

269 

975 

991 

*008 

*024 

*040 

*056 

*072 

*088 

*104 

*120 

9 

15.3 

270 

43  136 

152 

169 

185 

201 

217 

233 

249 

265 

281 

271 

297 

313 

329 

345 

361 

377 

393 

409 

425 

441 

16 

272 

457 

473 

489 

505 

521 

537 

553 

569 

584 

600 

1 

1.6 

273 

616 

632 

648 

664 

680 

696 

712 

727 

743 

759 

2 

3.2 

274 

775 

791 

807 

823 

838 

854 

870 

886 

902 

917 

3 

4.8 

275 

933 

949 

965 

981 

996 

*012 

*028 

*044 

*059 

*075 

4 

6.4 

276 

44  091 

107 

122 

138 

154 

170 

185 

201 

217 

232 

5 

8.0 

277 

248 

264 

279 

295 

311 

326 

342 

358 

373 

389 

7 

11.2 

278 

404 

420 

436 

451 

467 

483 

498 

514 

529 

545 

8 

12.8 

279 

560 

576 

592 

607 

623 

638 

654 

669 

685 

700 

9 

14.4 

280 

716 

731 

747 

762 

778 

793 

809 

824 

840 

855 

281 

871 

886 

902 

917 

932 

948 

963 

979 

994 

*010 

15 

282 

45  025 

040 

056 

071 

086 

102 

117 

133 

148 

163 

1 

1.5 

283 

179 

194 

209 

225 

240 

255 

271 

286 

301 

317 

2 

3.0 

284 

332 

347 

362 

378 

393 

408 

423 

439 

454 

469 

3 

4.5 

285 

484 

500 

515 

530 

545 

561 

576 

591 

606 

621 

4 

6.0 

286 

637 

652 

667 

682 

697 

712 

728 

743 

758 

773 

5 

7.5 

287 

788 

803 

818 

834 

849 

864 

879 

894 

909 

924 

7 

10.5 

288 

939 

954 

969 

984 

*000 

*015 

*030 

^045 

*060 

*075 

8 

12!o 

289 

46  090 

105 

120 

135 

150 

165 

180 

195 

210 

225 

9 

13.5 

290 

240 

255 

270 

285 

300 

315 

330 

345 

359 

374 

291 

389 

404 

419 

434 

449 

464 

479 

494 

509 

523 

14 

292 

538 

553 

568 

583 

598 

613 

627 

642 

657 

672 

1 

1.4 

293 

687 

702 

716 

731 

746 

761 

776 

790 

805 

820 

2 

2 8 

294 

835 

850 

864 

879 

894 

909 

923 

938 

953 

967 

3 

4.2 

295 

982 

997 

*012 

*026 

*041 

*056 

*070 

*085 

*100 

*114 

4 

5.6 

296 

47  129 

144 

159 

173 

188 

202 

217 

232 

246 

261 

5 

7.0 

297 

276 

290 

305 

319 

334 

349 

363 

378 

392 

407 

6 

7 

8.4 

9.8 

298 

422 

436 

451 

465 

480 

494 

509 

524 

538 

553 

8 

ii!2 

299 

567 

582 

596 

611 

625 

640 

654 

669 

683 

698 

9 

12.6 

300 

712 

727 

741 

756 

770 

784 

799 

813 

828 

842 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

478 


LOGARITHMS. 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

300 

301 

302 

303 

304 

305 

306 

307 

308 

309 

310 

311 

312 

313 

314 

315 

316 

317 

318 

319 

320 

321 

322 

323 

324 

325 

326 

327 

328 

329 

330 

331 

332 

333 

334 

335 

336 

337 

338 

339 

340 

341 

342 

343 

344 

345 

346 

347 

348 

349 

350 

47  712 

727 

741 

756 

770 

784 

799 

813 

828 

842 

986 

130 

273 

416 

558 

700 

841 

982 

*122 

15 

1 1.5 

2 3.0 

3 4.5 

4 6.0 

5 7.5 

6 9.0 

7 10.5 

8 12.0 

9 13.5 

14 

1 1.4 

2 2.8 

3 4.2 

4 5.6 

5 7.0 

6 8.4 

7 9.8 

8 11.2 

9 12.6 

13 

1 1.3 

2 2.6 

3 3.9 

4 5 2 

5 6.5 

6 7.8 

7 9.1 

8 10.4 

9 11.7 

12 

1 1.2 

2 2.4 

3 3.6 

4 4.8 

5 6.0 

6 7.2 

7 8.4 

8 9.6 

9 10.8 

857 
48  001 
144 
287 
430 
572 
714 
855 
996 

871 

015 

159 

302 

444 

586 

728 

869 

*010 

885 

029 

173 

316 

458 

601 

742 

883 

*024 

900 

044 

187 

330 

473 

615 

756 

897 

*038 

914 

058 

202 

344 

487 

629 

770 

911 

*052 

929 

073 

216 

359 

501 

643 

785 

926 

*066 

943 

087 

230 

373 

515 

657 

799 

940 

*080 

958 

101 

244 

387 

530 

671 

813 

954 

*094 

972 

116 

259 

401 

544 

686 

827 

968 

*108 

49  136 

150 

164 

178 

192 

206 

220 

234 

248 

262 

276 
415 
554 
693 
831 
969 
50  106 
243 
379 

290 

429 

568 

707 

845 

982 

120 

256 

393 

304 

443 

582 

721 

859 

996 

133 

270 

406 

318 

457 

596 

734 

872 

*010 

147 

284 

420 

332 

471 

610 

748 

886 

*024 

161 

297 

433 

346 

485 

624 

762 

900 

*037 

174 

311 

447 

360 

499 

638 

776 

914 

*051 

188 

325 

461 

374 

513 

651 

790 

927 

*065 

202 

338 

474 

388 

527 

665 

803 

941 

*079 

215 

352 

488 

402 

541 

679 

817 

955 

*092 

229 

365 

501 

515 

529 

542 

556 

569 

583 

596 

610 

623 

637 

651 
786 
920 
51  055 
188 
322 
455 
587 
720 

664 

799 

934 

068 

202 

335 

468 

601 

733 

678 

813 

947 

081 

215 

348 

481 

614 

746 

691 

826 

961 

095 

228 

362 

495 

627 

759 

705 

840 

974 

108 

242 

375 

508 

640 

772 

718 

853 

987 

121 

255 

388 

521 

654 

786 

732 

866 

*001 

135 

268 

402 

534 

667 

799 

745 

880 

*014 

148 

282 

415 

548 

680 

812 

759 

893 

*028 

162 

295 

428 

561 

693 

825 

772 

907 

*041 

175 

308 

441 

574 

706 

838 

851 

865 

878 

891 

904 

917 

930 

943 

957 

970 

983 

52  114 
244 
375 
504 
634 
763 
892 

53  020 

996 

127 

257 

388 

517 

647 

776 

905 

033 

*009 

140 

270 

401 

530 

660 

789 

917 

046 

*022 

153 

284 

414 

543 

673 

802 

930 

058 

*035 

166 

297 

427 

556 

686 

815 

943 

071 

*048 

179 

310 

440 

569 

699 

827 

956 

084 

*061 

192 

323 

453 

582 

711 

840 

969 

097 

*075 

205 

336 

466 

595 

724 

853 

982 

110 

*088 

218 

349 

479 

608 

737 

866 

994 

122 

*101 

231 

362 

492 

621 

750 

879 

*007 

135 

148 

161 

173 

186 

199 

212 

224 

237 

250 

263 

275 
403 
529 
656 
782 
908 
54  033 
158 
283 

288 

415 

542 

668 

794 

920 

045 

170 

295 

301 

428 

555 

681 

807 

933 

058 

183 

307 

314 

441 

567 

694 

820 

945 

070 

195 

320 

326 

453 

580 

706 

832 

958 

083 

208 

332 

339 

466 

593 

719 

845 

970 

095 

220 

345 

352 

479 

605 

732 

857 

983 

108 

233 

357 

364 

491 

618 

744 

870 

995 

120 

245 

370 

377 

504 

631 

757 

882 

*008 

133 

258 

382 

390 

517 

643 

769 

895 

*020 

145 

270 

394 

407 

419 

432 

444 

456 

469 

481 

494 

506 

518 

N. 

L 0 

1 

2 

3 

4 

5 

6 

7 

<S 

9 

P.  P. 

LOGARITHMS, 


479 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

350 

, 351 

352 

353 

354 

355 

356 

357 

358 

359 

360 

361 

362 

363 

364 

365 

366 

367 

368 

369 

370 

371 

372 

373 

374 

375 

376 

377 

378 

379 

380 

381 

382 

383 
' 384 

385 

386 

387 

388 

389 

390 

391 

392 

393 

394 

395 

396 

397 

398 

399 

400 

54  407 

419 

432 

444 

456 

469 

481 

494 

506 

518 

13 

1 1.3 

2 2.6 

3 3.9 

4 5.2 

5 6.5 

6 7.8 

7 9.1 

8 10.4 

9 11.7 

12 

1 1.2 

2 2.4 

a 3.6 

4 4.8 

5 6.0 

6 7.2 

7 8.4 

8 9.6 

9 10.8 

il 

1 1.1 

2 2.2 

3 3.3 

4 4.4  . 

5 5.5 

6 6.6 

7 7.7 

8 8.8 

9 9.9 

10 

1 1.0 

2 2,0 

3 3.0 

4 4.0 

5 5.0 

6 6.0 

7 7.0 

8 8.0 

9 9.0 

531 
654 
777 
900 
55  023 
145 
267 
388 
509 

543 

667 

790 

913 

035 

157 

279 

400 

522 

555 

679 

802 

925 

047 

169 

291 

413 

534 

568 

691 

814 

937 

060 

182 

303 

425 

546 

580 

704 

827 

949 

072 

194 

315 

437 

558 

593 

716 

839 

962 

084 

206 

328 

449 

570 

605 

728 

851 

974 

096 

218 

340 

461 

582 

617 

741 

864 

986 

108 

230 

352 

473 

594 

630 

753 

876 

998 

121 

242 

364 

485 

606 

642 

765 

888 

*011 

133 

255 

376 

497 

618 

630 

642 

654 

666 

678 

691 

703 

715 

727 

739 

751 
871 
991 
56  110 
229 
348 
467 
585 
703 

763 

883 

*003 

122 

241 

360 

478 

597 

714 

775 

895 

*015 

134 

253 

372 

490 

608 

726 

.787 

907 

*027 

146 

265 

384 

502 

620 

738 

799 

919 

*038 

158 

277 

396 

514 

632 

750 

811 

931 

*050 

170 

289 

407 

526 

644 

761 

823 

943 

*062 

182 

301 

419 

538 

656 

773 

835 

955 

*074 

194 

312 

431 

549 

667 

785 

847 

967 

*086 

205 

324 

443 

561 

679 

797 

859 

979 

*098 

217 

336 

455 

573 

691 

808 

820 

832 

844 

855 

867 

879 

891 

902 

914 

926 

937 
57  054 
171 
287 
403 
519 
634 
749 
864 

949 

066 

183 

299 

415 

530 

646 

761 

875 

961 

078 

194 

310 

426 

542 

657 

772 

887 

972 

089 

206 

322 

438 

553 

669 

784 

898 

984 

101 

217 

334 

449 

565 

680 

795 

910 

996 

113 

229 

345 

461 

576 

692 

807 

921 

*008 

124 

241 

357 

473 

588 

703 

818 

933 

*019 

136 

252 

368 

484 

600 

715 

830 

944 

*031 

148 

264 

380 

496 

611 

726 

841 

955 

*043 

159 

276 

392 

507 

623 

738 

852 

967 

978 

990 

*001 

*013 

*024 

*035 

*047 

*058 

*070 

*081 

58  092 
206 
320 
433 
546 
659 
771 
883 
995 

104 

218 

331 

444 

557 

670 

782 

894 

*006 

115 

229 

343 

456 

569 

681 

794 

906 

*017 

127 

240 

354 

467 

580 

692 

805 

917 

*028 

138 

252 

365 

478 

591 

704 

816 

928 

*040 

149 

263 

377 

490 

602 

715 

827 

939 

*051 

161 

274 

388 

501 

614 

726 

838 

950 

*062 

172 

286 

399 

512 

625 

737 

850 

961 

*073 

184 

297 

410 

524 

636 

749 

861 

973 

*084 

195 

309 

422 

535 

647 

760 

872 

984 

*095 

59  106 

118 

129 

140 

151 

162 

173 

184 

195 

207 

218 
329 
439 
550 
660 
770 
879 
988 
60  097 

229 

340 

450 

561 

671 

780 

890 

999 

108 

240 

351 

461 

572 

682 

791 

901 

*010 

119 

251 

362 

472 

583 

693 

802 

912 

*021 

130 

262 

373 

483 

594 

704 

813 

923 

*032 

141 

273 

384 

494 

605 

715 

824 

934 

*043 

152 

284 

395 

506 

616 

726 

835 

945 

*054 

163 

295 

406 

517 

627 

737 

846 

956 

*065 

173 

306 

417 

528 

638 

748 

857 

966 

*076 

184 

318 

428 

539 

649 

759 

868 

977 

*086 

195 

206 

217 

228 

239 

249 

260 

271 

282 

293 

304 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

480 


LOGARITHMS. 


N. 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

400 

401 

402 

403 

404 

405 

406 

407 

408 

409 

410 

411 

412 

413 

414 

415 

416 

417 

418 

419 

420 

421 

422 

423 

424 

425 

426 

427 

428 

429 

430 

431 

432 

433 

434 

435 

436 

437 

438 

439 

440 

441 

442 

443 

444 

445 

446 

447 

448 

449 

450 

60  206 

217 

228 

239 

249 

260 

271 

282 

293 

304 

II 

1 1.1 

2 2.2 

3 3.3 

4 4.4 

5 5.5 

6 6.6 

7 7.7 

8 8.8 

9 9.9 

10 

1 1.0 

2 2.0 

3 3.0 

4 4.0 

5 5.0  • 

6 6.0 

7 7.0 

8 8.0 

9 9.0 

9 

1 0.9 

2 1.8 

3 2.7 

4 3.6 

5 4.5 

6 5.4 

7 6.3 

8 7.2 

9 8.1 

314 

423 

531 

638 

746 

853 

959 

61  066 
172 

325 

433 

541 

649 

756 

863 

970 

077 

183 

336 

444 

552 

660 

767 

874 

981 

087 

194 

347 

455 

563 

670 

778 

885 

991 

098 

204 

358 

466 

574 

681 

788 

895 

*002 

109 

215 

369 

477 

584 

692 

799 

906 

*013 

119 

225 

379 

487 

595 

703 

810 

917 

*023 

130 

236 

390 

498 

606 

713 

821 

927 

*034 

140 

247 

401 

509 

617 

724 

831 

938 

*045 

151 

257 

412 

520 

627 

735 

842 

949 

*055 

162 

268 

278 

289 

300 

310 

321 

331 

342 

352 

363 

374 

384 
490 
595 
700 
805 
909 
62  014 
118 
221 

395 

500 

606 

711 

815 

920 

024 

128 

232 

405 

511 

616 

721 

826 

930 

034 

138 

242 

416 

521 

627 

731 

836 

941 

045 

149 

252 

426 

532 

637 

742 

847 

951 

055 

159 

263 

437 

542 

648 

752 

857 

962 

066 

170 

273 

448 

553 

658 

763 

868 

972 

076 

180 

284 

458 

563 

669 

773 

878 

982 

086 

190 

294 

469 

574 

679 

784 

888 

993 

097 

201 

304 

479 

584 

690 

794 

899 

*003 

107 

211 

315 

325 

335 

346 

356 

366 

377 

387 

397 

408 

418 

428 
531 
634 
737 
839 
941 
63  043 
144 
246 

439 

542 

644 

747 

849 

951 

053 

155 

256 

449 

552 

655 

757 

859 

961 

063 

165 

266 

459 

562 

665 

767 

870 

972 

073 

175 

276 

469 

572 

675 

778 

880 

982 

083 

185 

286 

480 

583 

685 

788 

890 

992 

094 

195 

296 

490 

593 

696 

798 

900 

*002 

104 

205 

306 

500 

603 

706 

808 

910 

*012 

114 

215 

317 

511 

613 

716 

818 

921 

*022 

124 

225 

327 

521 

624 

726 

829 

931 

*033 

134 

236 

337 

347 

357 

367 

377 

387 

397 

407 

417 

428 

438 

448 
548 
649 
749 
849 
949 
64  048 
147 
246 

458 

558 

659 

759 

859 

959 

058 

157 

256 

468 

568 

669 

769 

869 

969 

068 

167 

266 

478 

579 

679 

779 

879 

979 

078 

177 

276 

488 

589 

689 

789 

889 

988 

088 

187 

286 

498 

599 

699 

799 

899 

998 

098 

197 

296 

508 

609 

709 

809 

909 

*008 

108 

207 

306 

518 

619 

719 

819 

919 

*018 

118 

217 

316 

528 

629 

729 

829 

929 

*028 

128 

227 

326 

538 

639 

739 

839 

939 

*038 

137 

237 

335 

345 

355 

365 

375 

385 

395 

404 

414 

424 

434 

444 
542 
640 
738 
836 
933 
65  031 
128 
225 

454 

552 

650 

748 

846 

943 

040 

137 

234 

464 

562 

660 

758 

856 

953 

050 

147 

244 

473 

572 

670 

768 

865 

963 

060 

157 

254 

483 

582 

680 

777 

875 

972 

070 

167 

263 

493 

591 

689 

787 

885 

982 

079 

176 

273 

503 

601 

699 

797 

895 

992 

089 

186 

283 

513 

611 

709 

807 

904 

*002 

099 

196 

292 

523 

621 

719 

816 

914 

*011 

108 

205 

302 

532 

631 

729 

826 

924 

*021 

118 

215 

312 

321 

331 

341 

350 

360 

369 

379 

389 

398 

408 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

LOGARITHMS. 


481 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

450 

451 

452 

453 

454 

455 

456 

457 

458 

459 

460 

461 

462 

463 

464 

465 

466 

467 

468 

469 

470 

471 

472 

473 

474 

475 

476 

477 

478 

479 

480 

481 

482 

483 

484 

485 

486 

487 

488 

489 

490 

491 

492 

493 

494 

495 

496 

497 

498 

499 

500 

65  321 

331 

341 

350 

360 

369 

379 

389 

398 

408 

fO 

1 1.0 

2 2.0 

3 3.0 

4 4.0 

5 5.0 

6 6.0 

7 7.0 

8 8.0 

9 9.0 

9 

1 0.9 

2 1.8 

3 2.7 

4 3.6 

5 4.5 

6 5.4 

7 6.3 

8 7.2 

9 8.1 

8 

1 0.8 

2 1.6 

3 2.4 

4 3.2 

5 4.0 

6 4.8 

7 5.6 

8 6.4 

9 7.2 

418 
514 
610 
706 
801 
896 
992 
66  087 
181 

427 

523 

619 

715 

811 

906 

*001 

096 

191 

437 

533 

629 

725 

820 

916 

*011 

106 

200 

447 

543 

639 

734 

830 

925 

*020 

115 

210 

456 

552 

648 

744 

839 

935 

*030 

124 

219 

466 

562 

658 

753 

849 

944 

*039 

134 

229 

475 

571 

667 

763 

858 

954 

*049 

143 

238 

485 

581 

677 

772 

868 

963 

*058 

153 

247 

495 

591 

686 

782 

877 

973 

*068 

162 

257 

504 

600 

696 

792 

887 

982 

*077 

172 

266 

276 

285 

295 

304 

314 

323 

332 

342 

351 

361 

370 
464 
558 
652 
745 
839 
932 
67  025 
117 

380 

474 

567 

661 

755 

848 

941 

034 

127 

389 

483 

577 

671 

764 

857 

950 

043 

136 

398 

492 

586 

680 

773 

867 

960 

052 

145 

408 

502 

596 

689 

783 

876 

969 

062 

154 

417 

511 

605 

699 

792 

885 

978 

071 

164 

427 

521 

614 

708 

801 

894 

987 

080 

173 

436 

530 

624 

717 

811 

904 

997 

089 

182 

445 

539 

633 

727 

820 

913 

*006 

099 

191 

455 

549 

642 

736 

829 

922 

*015 

108 

201 

210 

219 

228 

237 

247 

256 

265 

274 

284 

293 

302 
394 
486 
578 
669 
761 
852 
943 
68  034 

311 

403 

495 

587 

679 

770 

861 

952 

043 

321 

413 

504 

596 

688 

779 

870 

961 

052 

330 

422 

514 

605 

697 

788 

879 

970 

061 

339 

431 

523 

614 

706 

797 

888 

979 

070 

348 

440 

532 

624 

715 

806 

897 

988 

079 

357 

449 

541 

633 

724 

815 

906 

997 

088 

367 

459 

550 

642 

733 

825 

916 

*006 

097 

376 

468 

560 

651 

742 

834 

925 

*015 

106 

385 

477 

569 

660 

752 

843 

934 

*024 

115 

205 

124 

133 

142 

151 

160 

169 

178 

187 

196 

215 

305 

395 

485 

574 

664 

753 

842 

931 

224 

314 

404 

494 

583 

673 

762 

851 

940 

233 

323 

413 

502 

592 

681 

771 

860 

949 

242 

332 

422 

511 

601 

690 

780 

869 

958 

251 

341 

431 

520 

610 

699 

789 

878 

966 

260 

350 

440 

529 

619 

708 

797 

886 

975 

269 

359 

449 

538 

628 

717 

806 

895 

984 

278 

368 

458 

547 

637 

726 

815 

904 

993 

287 

377 

467 

556 

646 

735 

824 

913 

*002 

090 

296 

386 

476 

565 

655 

744 

833 

922 

*011 

69  020 

028 

037 

046 

055 

064 

073 

082 

099 

108 

197 

285 

373 

461 

548 

636 

723 

810 

117 

205 

294 

381 

469 

557 

644 

732 

819 

126 

214 

302 

390 

478 

566 

653 

740 

827 

135 

223 

311 

399 

,487 

574 

662 

749 

836 

144 

232 

320 

408 

496 

583 

671 

758 

845 

152 

241 

329 

417 

504 

592 

679 

767 

854 

161 

249 

338 

425 

513 

601 

688 

775 

862 

170 

258 

346 

434 

522 

609 

697 

784 

871 

179 

267 

355 

443 

531 

618 

705 

793 

880 

188 

276 

364 

452 

539 

627 

714 

801 

888 

897 

906 

914 

923 

932 

940 

949 

958 

966 

975 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

4S2 


LOGARITHMS. 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

p.  p. 

500 

501 

502 

503 

504 

505 

506 

507 

508 

509 

510 

511 

512 

513 

514 

515 

516 

517 

518 

519 

520 

521 

522 

523 

524 

525 

526 

527 

528 

529 

530 

531 

532 

533 

534 

535 

536 

537 

538 

539 

540 

541 

542 

543 

544 

545 

546 

547 

548 

549 

550 

69  897 

906 

914 

923 

932 

940 

949 

958 

966 

975 

9 

1 0.9 

2 1.8 

3 2.7 

4 3.6 

5 4.5 

6 5.4 

7 6.3 

8 7.2 

9 8.1 

8 

1 0.8 

2 1.6 

3 2.4 

4 3.2 

5 4.0 

6 4.8 

7 5.6 

8 6.4 

9 7.2 

7 

1 0.7 

2 1.4 

3 2.1 

4 2.8 

5 3.5 

6 4.2 

7 4.9 

8 5 6 

9 6.3 

984 
70  070 
157 
243 
329 
415 
501 
586 
672 

992 

079 

165 

252 

338 

424 

509 

595 

680 

*001 

088 

174 

260 

346 

432 

518 

603 

689 

*010 

096 

183 

269 

355 

441 

526 

612 

697 

*018 

105 

191 

278 

364 

449 

535 

621 

706 

*027 

114 

200 

286 

372 

458 

544 

629 

714 

*036 

122 

209 

295 

381 

467 

552 

638 

723 

*044 

131 

217 

303 

389 

475 

561 

646 

731 

*053 

140 

226 

312 

398 

484 

569 

655 

740 

*062 

148 

234 

321 

406 

492 

578 

663 

749 

757 

766 

774 

783 

791 

800 

808 

817 

825 

834 

842 
927 
71  012 
096 
181 
265 
349 
433 
517 

851 

935 

020 

105 

189 

273 

357 

441 

525 

859 

944 

029 

113 

198 

282 

366 

450 

533 

868 

952 

037 

122 

206 

290 

374 

458 

542 

876 

961 

046 

130 

214 

299 

383 

466 

550 

885 

969 

054 

139 

223 

307 

391 

475 

559 

893 

978 

063 

147 

231 

315 

399 

483 

567 

902 

986 

071 

155 

240 

324 

408 

492 

575 

910 

995 

079 

164 

248 

332 

416 

500 

584 

919 

*003 

088 

172 

257 

341 

425 

508 

592 

600 

609 

617 

625 

634 

642 

650 

659 

667 

675 

684 
767 
850 
933 
72  016 
099 
181 
263 
346 

692 

775 

858 

941 

024 

107 

189 

272 

354 

700 

784 

867 

950 

032 

115 

198 

280 

362 

709 

792 

875 

958 

041 

123 

206 

288 

370 

717 

800 

883 

966 

049 

132 

214 

296 

378 

725 

809 

892 

975 

0.57 

140 

222 

304 

387 

734 

817 

900 

983 

066 

148 

230 

313 

395 

742 

825 

908 

991 

074 

156 

239 

321 

403 

750 

834 

917 

999 

082 

165 

247 

329 

411 

759 

842 

925 

*008 

090 

173 

255 

337 

419 

428 

436 

444 

452 

460 

469 

477 

485 

493 

501 

509 
591 
673 
754 
835 
916 
997 
73  078 
159 

518 

599 

681 

762 

843 

925 

*006 

086 

167 

526 

607 

689 

770 

852 

933 

*014 

094 

175 

534 

616 

697 

779 

860 

941 

*022 

102 

183 

542 

624 

705 

787 

868 

949 

*030 

111 

191 

550 

632 

713 

795 

876 

957 

*038 

119 

199 

558 

640 

722 

803 

884 

965 

*046 

127 

207 

567 

648 

730 

811 

892 

973 

*054 

135 

215 

575 

656 

738 

819 

90C 

981 

*062 

143 

223 

583 

665 

746 

827 

908 

989 

*070 

151 

231 

239 

247 

255 

263 

272 

280 

288 

296 

304 

312 

320 

400 

480 

560 

640 

719 

799 

878 

957 

328 

408 

488 

568 

648 

727 

807 

886 

965 

336 

416 

496 

576 

656 

735 

815 

894 

973 

344 

424 

504 

584 

664 

743 

823 

902 

981 

352 

432 

512 

592 

672 

751 

830 

910 

989 

360 

440 

520 

600 

679 

759 

838 

918 

997 

368 

448 

528 

608 

687 

767 

846 

926 

*005 

376 

456 

536 

616 

695 

775 

854 

933 

*013 

384 

464 

544 

624 

703 

783 

862 

941 

*020 

392 

472 

552 

632 

711 

791 

870 

949 

*028 

74  036 

044 

052 

060 

068 

076 

084 

092 

099 

107 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

LOGARITHMS. 


483 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

.P. 

550 

74  036 

044 

052 

060 

068 

076 

084 

092 

099 

107 

551 

115 

123 

131 

139 

147 

155 

162 

170 

178 

186 

552 

194 

202 

210 

218 

225 

233 

241 

249 

257 

265 

553 

273 

280 

288 

296 

304 

312 

320 

327 

335 

343 

554 

351 

359 

367 

374 

382 

390 

398 

406 

414 

421 

555 

429 

437 

445 

453 

461 

468 

476 

484 

492 

500 

556 

507 

515 

523 

531 

539 

547 

554 

562 

570 

578 

557 

586 

593 

601 

609 

617 

624 

632 

640 

648 

656 

558 

663 

671 

679 

687 

695 

702 

710 

718 

726 

733 

559 

741 

749 

757 

764 

772 

780 

788 

796 

803 

811 

560 

819 

827 

834 

842 

850 

858 

865 

873 

881 

889 

3 

561 

896 

904 

912 

920 

927 

935 

943 

950 

958 

966 

1 

562 

974 

981 

989 

997 

*005 

*012 

*020 

*028 

*035 

*043 

0.8 

563 

75  051 

059 

066 

074 

082 

089 

097 

105 

113 

120 

3 

2.4 

564 

128 

136 

143 

151 

159 

166 

174 

182 

189 

197 

4 

3!2 

565 

205 

213 

220 

228 

236 

243 

251 

259 

266 

274 

5 

4.0 

566 

282 

289 

297 

305 

312 

320 

328 

335 

343 

351 

6 

4.8 

567 

358 

366 

374 

381 

389 

397 

404 

412 

■420 

427 

7 

5.6 

568 

435 

442 

450 

458 

465 

473 

481 

488 

496 

504 

8 

9 

7.2 

569 

511 

519 

526 

534 

542 

549 

557 

565 

572 

580 

570 

587 

595 

603 

610 

618 

626 

633 

641 

648 

656 

571 

664 

671 

679 

686 

694 

702 

709 

717 

724 

732 

572 

740 

747 

755 

762 

770 

778 

785 

793 

800 

808 

573 

815 

823 

831 

838 

846 

853 

861 

868 

876 

884 

574 

891 

899 

906 

914 

921 

929 

937 

944 

952 

959 

575 

967 

974 

982 

989 

997 

*005 

*012 

*020 

*027 

*035 

576 

76  042 

050 

057 

065 

072 

080 

087 

095 

103 

110 

577 

118 

125 

133 

140 

148 

155 

163 

170 

178 

185 

578 

193 

200 

208 

215 

223 

230 

238 

245 

253 

260 

579 

268 

275 

283 

290 

298 

305 

313 

320 

328 

335 

580 

343 

350 

358 

365 

373 

380 

388 

395 

403 

410 

7 

581 

418 

425 

433 

440 

448 

455 

462 

470 

477 

485 

1 

0.7 

582 

492 

500 

507 

515 

522 

530 

537 

545 

552 

559 

2 

lA 

583 

567 

574 

582 

589 

597 

604 

612 

619 

626 

634 

3 

2.1 

584 

641 

649 

656 

664 

671 

678 

686 

693 

701 

708 

4 

2.8 

585 

716 

723 

730 

738 

745 

753 

760 

768 

775 

782 

5 

3.5 

586 

790 

797 

805 

812 

819 

827 

834 

842 

849 

856 

6 

7 

4.9 

587 

864 

871 

879 

886 

893 

901 

908 

916 

923 

930 

8 

5!6 

588 

938 

945 

953 

960 

967 

975 

982 

989 

997 

*004 

9 

6.3 

589 

77  012 

019 

026 

034 

041 

048 

056 

063 

070 

078 

590 

085 

093 

100 

107 

115 

122 

129 

137 

144 

151 

591 

159 

166 

173 

181 

188 

195 

203 

210 

217 

225 

592 

232 

240 

247 

254 

262 

269 

276 

283 

291 

298 

593 

305 

313 

320 

327 

335 

342 

349 

357 

364 

371 

594 

379 

386 

393 

401 

408 

415 

422 

430 

437 

444 

595 

452 

459 

466 

474 

481 

488 

495 

503 

510 

517 

596 

525 

532 

539 

546 

554 

561 

568 

576 

583 

590 

597 

597 

605 

612 

619 

627 

634 

641 

648 

656 

663 

598 

670 

677 

685 

692 

699 

706 

714 

721 

728 

735 

599 

743 

750 

757 

764 

772 

779 

786 

793 

801 

808 

600 

815 

822 

830 

837 

844 

851 

859 

866 

873 

880 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

. P. 

484 


LOGARITHMS. 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

600 

601 

602 

603 

604 

605 

606 

607 

608 

609 

610 

611 

612 

613 

614 

615 

616 

617 

618 
619 

620 

621 

622 

623 

624 

625 

626 

627 

628 
629 

630 

631 

632 

633 

634 

635 

636 

637 

638 

639 

640 

641 

642 

643 

644 

645 

646 

647 

648 

649 

650 

77  815 

822 

830 

837 

844 

851 

859 

866 

873 

880 

8 

1 0.8 

2 1.6 

3 2.4 

4 3.2 

5 4.0 

6 4.8 

7 5.6 

8 6.4 

9 7.2 

7 

1 0.7 

2 1.4 

3 2.1 

4 2.8 

5 3.5 

6 4.2 

7 4.9 

8 5.6 

9 6.3 

6 

1 0.6 

2 1.2 

3 1.8 

4 2.4 

5 3.0 

6 3.6 

7 4.2 

8 4.8 

9 5.4 

887 
960 
78  032 
104 
176 
247 
319 
390 
462 

895 

967 

039 

111 

183 

254 

326 

398 

469 

902 

974 

046 

118 

190 

262 

333 

405 

476 

909 

981 

053 

125 

197 

269 

340 

412 

483 

916 

988 

061 

132 

204 

276 

347 

419 

490 

924 

996 

068 

140 

211 

283 

355 

426 

497 

931 

*003 

075 

147 

219 

290 

362 

433 

504 

938 

*010 

082 

154 

226 

297 

369 

440 

512 

945 

*017 

089 

161 

233 

305 

376 

447 

519 

952 

*025 

097 

168 

240 

312 

383 

455 

526 

533 

540 

547 

554 

561 

569 

576 

583 

590 

597 

604 
675 
746 
817 
888 
958 
79  029 
099 
169 

611 

682 

753 

824 

895 

965 

036 

106 

176 

618 

689 

760 

831 

902 

972 

043 

113 

183 

625 

696 

767 

838 

909 

979 

050 

120 

190 

633 

704 

774 

845 

916 

986 

057 

127 

197 

640 

711 

781 

852 

923 

993 

064 

134 

204 

647 

718 

789 

859 

930 

*000 

071 

141 

211 

654 

725 

796 

866 

937 

*007 

078 

148 

218 

661 

732 

803 

873 

944 

*014 

085 

155 

225 

668 

739 

810 

880 

951 

*021 

092 

162 

232 

239 

246 

253 

260 

267 

274 

281 

288 

295 

302 

309 

379 

449 

518 

588 

657 

727 

796 

865 

316 

386 

456 

525 

595 

664 

734 

803 

872 

323 

393 

463 

532 

602 

671 

741 

810 

879 

330 

400 

470 

539 

609 

678 

748 

817 

886 

337 

407 

477 

546 

616 

685 

754 

824 

893 

344 

414 

484 

553 

623 

692 

761 

831 

900 

351 

421 

491 

560 

630 

699 

768 

837 

906 

358 

428 

498 

567 

637 

706 

775 

844 

913 

365 

•435 

505 

574 

644 

713 

782 

851 

920 

372 

442 

511 

581 

650 

720 

789 

858 

927 

934 

941 

948 

955 

962 

969 

975 

982 

989 

996 

80  003 
072 
140 
209 
277 
346 
414 
482 
550 

010 

079 

147 

216 

284 

353 

421 

489 

557 

017 

085 

154 

223 

291 

359 

428 

496 

564 

024 

092 

161 

229 

298 

366 

434 

502 

570 

030 

099 

168 

236 

305 

373 

441 

509 

577 

037 

106 

175 

243 

312 

380 

448 

516 

584 

044 

113 

182 

250 

318 

387 

455 

523 

591 

051 

120 

188 

257 

325 

393 

462 

530 

598 

058 

127 

195 

264 

332 

400 

468 

536 

604 

065 

134 

202 

271 

339 

407 

475 

543 

611 

618 

625 

632 

638 

645 

652 

659 

665 

672 

679 

686 
754 
821 
889 
956 
81  023 
090 
158 
224 

693 

760 

828 

895 

963 

030 

097 

164 

231 

699 

767 

835 

902 

969 

037 

104 

171 

238 

706 

774 

841 

909 

976 

043 

111 

178 

245 

713 

781 

848 

916 

983 

050 

117 

184 

251 

720 

787 

855 

922 

990 

057 

124 

191 

258 

726 

794 

862 

929 

996 

064 

131 

198 

265 

331 

733 

801 

868 

936 

*003 

070 

137 

204 

271 

338 

740 

808 

875 

943 

*010 

077 

144 

211 

278 

747 

814 

882 

949 

*017 

084 

151 

218 

285 

291 

298 

305 

311 

318 

325 

345 

351 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

LOGARITHMS. 


485 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

650 

81  291 

298 

305 

311 

318 

325 

331 

338 

345 

351 

, 651 

358 

365 

371 

378 

385 

391 

398 

405 

411 

418 

652 

425 

431 

438 

445 

451 

458 

465 

471 

478 

485 

653 

491 

498 

505 

511 

518 

525 

531 

538 

544 

551 

654 

558 

564 

571 

578 

584 

591 

598 

604 

611 

617 

655 

624 

631 

637 

644 

651 

657 

664 

671 

677 

684 

656 

690 

697 

704 

710 

717 

723 

730 

737 

743 

750 

657 

757 

763 

770 

776 

783 

790 

796 

803 

809 

816 

658 

823 

829 

836 

842 

849 

856 

862 

869 

875 

882 

659 

889 

895 

902 

908 

915 

921 

928 

935 

941 

948 

660 

954 

961 

968 

974 

981 

987 

994 

*000 

*007 

*014 

7 

661 

82  020 

027 

033 

040 

046 

053 

060 

066 

073 

079 

662 

086 

092 

099 

105 

112 

119 

125 

132 

138 

145 

1 

0.7 

663 

151 

158 

164 

171 

178 

184 

191 

197 

204 

210 

2 

3 

4 

1 .4 

2.1 

2.8 

664 

217 

223 

230 

236 

243 

249 

256 

263 

269 

276 

665 

282 

289 

295 

302 

308 

315 

321 

328 

334 

341 

5 

3.5 

666 

347 

354 

360 

367 

373 

380 

387 

393 

400 

406 

6 

4.2 

667 

413 

419 

426 

432 

439 

445 

452 

458 

465 

471 

7 

4.9 

668 

478 

484 

491 

497 

504 

510 

517 

523 

530 

536 

8 

9 

5.6 

6.3 

669 

543 

549 

556 

562 

569 

575 

582 

588 

595 

601 

670 

607 

614 

620 

627 

633 

640 

646 

653 

659 

666 

671 

672 

679 

685 

692 

698 

705 

711 

718 

724 

730 

672 

737 

743 

750 

756 

763 

769 

776 

782 

789 

795 

. 673 

802 

808 

814 

821 

827 

834 

840 

847 

853 

860 

674 

866 

872 

879 

885 

892 

898 

905 

911 

918 

924 

675 

930 

937 

943 

950 

956 

963 

969 

975 

982 

988 

: 676 

995 

*001 

*008 

*014 

*020 

*027 

*033 

*040 

*046 

*052 

' 677 

83  059 

065 

072 

078 

085 

091 

097 

104 

no 

117 

: 678 

123 

129 

136 

142 

149 

155 

161 

168 

174 

181 

679 

m 

193 

200 

206 

213 

219 

225 

232 

238 

245 

680 

251 

257 

264 

270 

276 

283 

289 

296 

302 

308 

6 

681 

315 

321 

327 

334 

340 

347 

353 

359 

366 

372 

1 

2 

0.6 

682 

378 

385 

391 

398 

404 

410 

417 

423 

429 

436 

1.2 

683 

442 

448 

455 

461 

467 

474 

480 

487 

493 

499 

3 

1.8 

684 

506 

512 

518 

525 

531 

537 

544 

550 

556 

563 

4 

2.4 

685 

569 

575 

582 

588 

594 

601 

607 

613 

620 

626 

5 

3.0 

3.6 

4.2 

686 

632 

639 

645 

651 

658 

664 

670 

677 

683 

689 

6 

7 

687 

696 

702 

708 

715 

721 

727 

734 

740 

746 

753 

8 

4!8 

688 

759 

765 

771 

778 

784 

790 

797 

803 

809 

816 

9 

5.4 

689 

822 

828 

835 

841 

847 

853 

860 

866 

872 

879 

690 

885 

891 

897 

904 

910 

916 

923 

929 

935 

942 

691 

948 

954 

960 

967 

973 

979 

985 

992 

998 

*004 

692 

84  on 

017 

023 

029 

036 

042 

048 

055 

061 

067 

693 

073 

080 

086 

092 

098 

105 

111 

117 

123 

130 

694 

136 

142 

148 

155 

161 

167 

173 

180 

186 

192 

695 

198 

205 

211 

217 

223 

230 

236 

242 

248 

255 

696 

261 

267 

273 

280 

286 

292 

298 

305 

311 

317 

697 

323 

330 

336 

342 

348 

354 

361 

367 

373 

379 

698 

386 

392 

398 

404 

410 

417 

423 

429 

435 

442 

699 

448 

454 

460 

466 

473 

479 

485 

491 

497 

504 

700 

510 

516 

522 

528 

535 

541 

547 

553 

559 

566 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

486  LOGARITHMS. 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

700 

84  510 

516 

522 

528 

535 

541 

547 

553 

559 

566 

701 

572 

578 

584 

590 

597 

603 

609 

615 

621 

628 

702 

634 

640 

646 

652 

658 

665 

671 

677 

683 

689 

703 

696 

702 

708 

714 

720 

726 

733 

739 

745 

751 

704 

757 

763 

770 

776 

782 

788 

794 

800 

807 

813 

705 

819 

825 

831 

837 

844 

850 

856 

862 

868 

874 

706 

880 

887 

893 

899 

905 

911 

917 

924 

930 

936 

707 

942 

948 

954 

960 

967 

973 

979 

985 

991 

997 

7 

708 

85  003 

009 

016 

022 

028 

034 

040 

046 

052 

058 

1 

0.7 

709 

065 

071 

077 

083 

089 

095 

101 

107 

114 

120 

2 

1.4 

710 

126 

132 

138 

144 

150 

156 

163 

169 

175 

181 

3 

4 

2.1 

2.8 

5 

3.5 

711 

187 

193 

199 

205 

211 

217 

224 

230 

236 

242 

6 

4.2 

712 

248 

254 

260 

266 

272 

278 

285 

291 

297 

303 

7 

4.9 

713 

309 

315 

321 

327 

333 

339 

345 

352 

358 

364 

8 

5.6 

714 

370 

376 

382 

388 

394 

400 

406 

412 

418 

425 

9 

6.3 

715 

431 

437 

443 

449 

455 

461 

467 

473 

479 

485 

716 

491 

497 

503 

509 

516 

522 

528 

534 

540 

546 

717 

552 

558 

564 

570 

576 

582 

588 

594 

600 

606 

718 

612 

618 

625 

631 

637 

643 

649 

655 

661 

667 

719 

673 

679 

685 

691 

697 

703 

709 

715 

721 

727 

720 

733 

739 

745 

751 

757 

763 

769 

775 

781 

788 

6 

721 

794 

800 

806 

812 

818 

824 

830 

836 

842 

848 

722 

854 

860 

866 

872 

878 

884 

890 

896 

902 

908 

1 

0.6 

723 

914 

920 

926 

932 

938 

944 

950 

956 

962 

968 

2 

1.2 

724 

974 

980 

986 

992 

998 

*004 

*010 

*016 

*022 

*028 

3 

4 

1.8 

2.4 

725 

86  034 

040 

046 

052 

058 

064 

070 

076 

082 

088 

5 

3!o 

726 

094 

100 

106 

112 

118 

124 

130 

136 

141 

147 

6 

3.6 

727 

153 

159 

165 

171 

177 

183 

189 

195 

201 

207 

7 

4.2 

728 

213 

219 

225 

231 

237 

243 

219 

255 

261 

267 

8 

4.8 

729 

273 

279 

285 

291 

297 

303 

308 

314 

320 

326 

9 

5.4 

730 

332 

338 

344 

350 

356 

362 

368 

374 

380 

386 

731 

392 

398 

404 

410 

415 

421 

427 

433 

439 

445 

732 

451 

457 

463 

469 

475 

481 

487 

493 

499 

504 

733 

510 

516 

522 

528 

534 

540 

546 

552 

558 

564 

734 

570 

576 

581 

587 

593 

599 

605 

611 

617 

623 

735 

629 

635 

641 

646 

652 

658 

664 

670 

676 

682 

736 

688 

694 

700 

705 

711 

717 

723 

729 

735 

741 

5 

737 

747 

753 

759 

764 

770 

776 

782 

788 

794 

800 

\ 

0.5 

738 

806 

812 

817 

823 

829 

835 

841 

847 

853 

859 

2 

i!o 

739 

864 

870 

876 

882 

888 

894 

900 

906 

911 

917 

3 

1.5 

4 

2.0 

740 

923 

929 

935 

941 

947 

953 

958 

964 

970 

976 

5 

2.5 

6 

3.0 

741 

982 

988 

994 

999 

*005 

*011 

*017 

*023 

*029 

*035 

7 

3.5 

742 

87  040 

046 

052 

058 

064 

070 

075 

081 

087 

093 

8 

4.0 

743 

099 

105 

111 

116 

122 

128 

134 

140 

146 

151 

9 

4 5 

744 

157 

163 

169 

175 

181 

186 

192 

198 

204 

210 

745 

216 

221 

227 

233 

239 

245 

251 

256 

262 

2,68 

746 

274 

280 

286 

291 

297 

303 

309 

315 

320 

326 

747 

332 

338 

344 

349 

355 

361 

367 

373 

379 

384 

748 

390 

396 

402 

408 

413 

419 

425 

431 

437 

442 

749 

448 

454 

460 

466 

471 

477 

483 

489 

495 

500 

750 

506 

512 

518 

523 

529 

535 

541 

547 

552 

558 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

LOGARITHMS. 


487 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

p 

.P. 

750 

87  506 

512 

518 

523 

529 

535 

541 

547 

552 

558 

751 

564 

570 

576 

581 

587 

593 

599 

604 

610 

616 

752 

622 

628 

633 

639 

645 

651 

656 

662 

668 

674 

753 

679 

685 

691 

697 

703 

708 

714 

720 

726 

731 

754 

737 

743 

749 

754 

760 

766 

772 

777 

783 

789 

755 

795 

800 

806 

812 

818 

823 

829 

835 

841 

846 

756 

852 

858 

864 

869 

875 

881 

887 

892 

898 

904 

757 

910 

915 

921 

927 

933 

938 

944 

950 

955 

961 

758 

967 

973 

978 

984 

990 

996 

*001 

*007 

*013 

*018 

759 

88  024 

030 

036 

041 

047 

053 

058 

064 

070 

076 

760 

081 

087 

093 

098 

104 

110 

116  1 

121 

127 

133 

e 

761 

138 

144 

150 

156 

161 

167 

173 

178 

184 

190 

0 

762 

195 

201 

207 

213 

218 

224 

230 

235 

241 

247 

1 

0.6 

763 

252 

258 

264 

270 

275 

281 

287 

292 

298 

304 

2 

3 

1.2 

1 8 

764 

309 

315 

321 

326 

332 

338 

343 

349 

355 

360 

4 

2!4 

765 

366 

3f2 

377 

383 

389 

395 

400 

406 

412 

417 

5 

3.0 

766 

423 

429 

434 

440 

446 

451 

457 

463 

468 

474 

6 

3.6 

767 

480 

485 

491 

497 

502 

508 

513 

519 

525 

530 

7 

4.2 

768 

536 

542 

547 

553 

559 

564 

570 

576 

581 

587 

8 

9 

4.8 

5.4 

769 

593 

598 

604 

610 

615 

621 

627 

632 

638 

643 

770 

649 

655 

660 

666 

672 

677 

683 

689 

694 

700 

771 

705 

711 

717 

722 

728 

734 

739 

745 

750 

756 

772 

762 

767 

773 

779 

784 

790 

795 

801 

807 

812 

773 

818 

824 

829 

835 

840 

846 

852 

857 

863 

868 

774 

874 

880 

885 

891 

897 

902 

908 

913 

919 

925 

775 

930 

936 

941 

947 

953 

958 

964 

969 

975 

981 

776 

986 

992 

997 

*003 

*009 

*014 

*020 

*025 

*031 

*037 

777 

89  042 

048 

053 

059 

064 

070 

076 

081 

087 

092 

778 

098 

104 

109 

115 

120 

126 

131 

137 

143 

148 

779 

154 

159 

165 

170 

176 

182 

187 

193 

198 

204 

780 

209 

215 

221 

226 

232 

237 

243 

248 

254 

260 

5 

781 

265 

271 

276 

282 

287 

293 

298 

304 

310 

315 

0 5 

782 

321 

326 

332 

337 

343 

348 

354 

360 

365 

371 

2 

i!o 

783 

376 

382 

387 

393 

398 

404 

409 

415 

421 

426 

3 

1.5 

784 

432 

437 

443 

448 

454 

459 

465 

470 

476 

481 

4 

2.0 

785 

487 

492 

498 

504 

509 

515 

520 

526 

531 

537 

5 

2.5 

786 

542 

548 

553 

559 

564 

570 

575 

581 

586 

592 

6 

3.0 

787 

597 

603 

609 

614 

620 

625 

631 

636 

642 

647 

8 

4.0 

788 

653 

658 

664 

669 

675 

680 

686 

691 

697 

702 

9 

4.5 

789 

708 

713 

719 

724 

730 

735 

741 

746 

752 

757 

790 

763 

768 

774 

779 

785 

790 

796 

801 

807 

812 

791 

818 

823 

829 

834 

840 

845 

851 

856 

862 

867 

792 

873 

878 

883 

889 

894 

900 

905 

911 

916 

922 

793 

927 

933 

938 

944 

949 

955 

960 

966 

971 

977 

794 

982 

988 

993 

998 

*004 

*009 

*015 

*020 

*026 

*031 

795 

90  037 

042 

048 

053 

059 

064 

069 

075 

080 

086 

796 

091 

097 

102 

108 

113 

119 

124 

129 

135 

140 

797 

146 

151 

157 

162 

168 

173 

179 

184 

189 

195 

798 

200 

206 

211 

217 

222 

227 

233 

238 

244 

249 

799 

255 

260 

266 

271 

276 

282 

287 

293 

298 

304 

800 

309 

314 

320 

325 

331 

336 

342 

347 

352 

358 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

.P. 

488 


LOGARITHMS. 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

.P. 

800 

90  309 

314 

320 

325 

331 

336 

342 

347 

352 

358 

801 

363 

369 

374 

380 

385 

390 

396 

401' 

407 

412 

802 

417 

423 

428 

434 

439 

445 

450 

455 

461 

466 

803 

472 

477 

482 

488 

493 

499 

504 

509 

515 

520 

804 

526 

531 

536 

542 

547 

553 

558 

563 

569 

574 

805 

580 

585 

590 

596 

601 

607 

612 

617 

623 

628 

806 

634 

639 

644 

650 

655 

660 

666 

671 

677 

682 

807 

687 

693 

698 

703 

709 

714 

720 

725 

730 

736 

808 

741 

747 

752 

757 

763 

768 

773 

779 

784 

789 

809 

795 

800 

806 

811 

816 

822 

827 

832 

838 

843 

810 

849 

854 

859 

865 

870 

875 

881 

886 

891 

897 

811 

902 

907 

913 

918 

924 

929 

934 

940 

945 

950 

6 

812 

956 

961 

966 

972 

977 

982 

988 

993 

998 

*004 

1 

0.6 

813 

91  009 

014 

020 

025 

030 

036 

041 

046 

052 

057 

2 

1.2 

814 

062 

068 

073 

078 

084 

089 

094 

100 

105 

110 

4 

2.4 

815 

116 

121 

126 

132 

137 

142 

148 

153 

158 

164 

5 

3!o 

816 

169 

174 

180 

185 

190 

196 

201 

206 

212 

217 

6 

3.6 

817 

222 

228 

233 

238 

243 

249 

254 

259 

265 

270 

7 

4.2 

818 

275 

281 

286 

291 

297 

302 

307 

312 

318 

323 

8 

g 

4.8 

819 

328 

334 

339 

344 

350 

355 

360 

365 

371 

376 

820 

381 

387 

392 

397 

403 

408 

413 

418 

424 

429 

821 

434 

440 

445 

450 

455 

461 

466 

471 

477 

482 

822 

487 

492 

498 

503 

508 

514 

519 

524 

529 

535 

823 

540 

545 

551 

556 

561 

566 

572 

577 

582 

587 

824 

593 

598 

603 

609 

614 

619 

624 

630 

635 

640 

825 

645 

651 

656 

661 

666 

672 

677 

682 

687 

693 

826 

698 

703 

709 

714 

719 

724 

730 

735 

740 

745 

827 

751 

756 

761 

766 

772 

777 

782 

787 

793 

798 

828 

803 

808 

814 

819 

824 

829 

834 

840 

845 

850 

829 

855 

861 

866 

871 

876 

882 

887 

892 

897 

903 

830 

908 

913 

918 

924 

929 

934 

939 

944 

950 

955 

5 

831 

960 

965 

971 

976 

981 

986 

991 

997 

*002 

*007 

4 

0.5 

832 

92  012 

018 

023 

028 

033 

038 

044 

049 

054 

059 

2 

i!o 

833 

065 

070 

075 

080 

085 

091 

096 

101 

106 

111 

3 

1.5 

834 

117 

122 

127 

132 

137 

143 

148 

153 

158 

163 

4 

2.0 

835 

169 

174 

179 

184 

189 

195 

200 

205 

210 

215 

5 

2.5 

836 

221 

226 

231 

236 

241 

247 

252 

257 

262 

267 

6 

7 

3.0 

3,5 

837 

273 

278 

283 

288 

293 

298 

304 

309 

314 

319 

8 

4^0 

838 

324 

330 

335 

340 

345 

350 

355 

361 

366 

371 

9 

4.5 

839 

376 

381 

387 

392 

397 

402 

407 

412 

418 

423 

840 

428 

433 

438 

443 

449 

454 

459 

464 

469 

474 

841 

480 

485 

490 

495 

500 

505 

511 

516 

521 

526 

842 

531 

536 

542 

547 

552 

557 

562 

567 

572 

578 

843 

583 

588 

593 

598 

603 

609 

614 

619 

624 

629 

844 

634 

639 

645 

650 

655 

660 

665 

670 

675 

681 

845 

586 

691 

696 

701 

706 

711 

716 

722 

727 

732 

846 

737 

742 

747 

752 

758 

763 

768 

773 

778 

783 

847 

788 

793 

799 

804 

809 

814 

819 

824 

829 

834 

848 

840 

845 

850 

855 

860 

865 

870 

875 

881 

886 

849 

891 

896 

901 

906 

911 

916 

921 

927 

932 

937 

850 

942 

947 

952 

957 

962 

967 

973 

978 

983 

988 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

. P. 

LOGARITHMS. 


489 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

. P. 

850 

92  942 

947 

952 

957 

962 

967 

973 

978 

983 

988 

' 851 

993 

998 

*003 

*008 

*013 

*018 

*024 

*029 

*034 

*039 

852 

93  044 

049 

054 

059 

064 

069 

075 

080 

085 

090 

853 

095 

100 

105 

110 

115 

120 

125 

131 

136 

141 

854 

146 

151 

156 

161 

166 

171 

176 

181 

186 

192 

855 

197 

202 

207 

212 

217 

222 

227 

232 

237 

242 

856 

247 

252 

258 

263 

268 

273 

278 

283 

288 

293 

0 

857 

298 

303 

308 

313 

318 

323 

328 

334 

339 

344 

858 

349 

354 

359 

364 

369 

374 

379 

384 

389 

394 

1 

0.6 

859 

399 

404 

409 

414 

420 

425 

430 

435 

440 

445 

2 

1.2 

860 

450 

455 

460 

465 

470 

475 

480 

485 

490 

495 

4 

2.4 

861 

500 

505 

510 

515 

520 

526 

531 

536 

541 

546 

6 

sie 

862 

551 

556 

561 

566 

571 

576 

581 

586 

591 

596 

7 

4.2 

863 

601 

606 

611 

616 

621 

626 

631 

636 

641 

646 

8 

g 

4.8 

5.4 

864 

651 

656 

661 

666 

671 

676 

682 

687 

692 

697 

865 

702 

707 

712 

717 

722 

727 

732 

737 

742 

747 

866 

752 

757 

762 

767 

772 

•777 

782 

787 

792 

797 

867 

802 

807 

812 

817 

822 

827 

832 

837 

842 

847 

868 

852 

857 

862 

867 

872 

877 

882 

887 

892 

897 

869 

902 

907 

912 

917 

922 

927 

932 

937 

942 

947 

870 

952 

957 

962 

967 

972 

977 

982 

987 

992 

997 

c 

871 

94  002 

007 

012 

017 

022 

027 

032 

037 

042 

047 

0 

872 

052 

057 

062 

067 

072 

077 

082 

086 

091 

096 

i 

0.5 

873 

101 

106 

111 

116 

121 

126 

131 

136 

141 

146 

2 

1.0 

874 

151 

156 

161 

166 

171 

176 

181 

186 

191 

196 

4 

2.'» 

875 

201 

206 

211 

216 

221 

226 

231 

236 

240 

245 

5 

2.5 

876 

250 

255 

260 

265 

270 

275 

280 

285 

290 

295 

6 

3.0 

877 

300 

305 

310 

315 

320 

325 

330 

335 

340 

345 

7 

3.5 

878 

349 

354 

359 

364 

369 

374 

379 

384 

389 

394 

8 

g 

4.0 

879 

399 

404 

409 

414 

419 

424 

429 

433 

438 

443 

880 

448 

453 

458 

463 

468 

473 

478 

483 

488 

493 

881 

498 

503 

507 

512 

517 

522 

527 

532 

537 

542 

882 

547 

552 

557 

562 

567 

571 

576 

581 

586 

591 

883 

596 

601 

606 

611 

616 

621 

626 

630 

635 

640 

884 

645 

650 

655 

660 

665 

670 

675 

680 

685 

689 

885 

694 

699 

704 

709 

714 

719 

724 

729 

734 

738 

886 

743 

748 

753 

758 

763 

768 

773 

778 

783 

787 

4 

887 

792 

797 

802 

807 

812 

817 

822 

827 

832 

836 

■[ 

0 4 

888 

841 

846 

851 

856 

861 

866 

871 

876 

880 

885 

2 

0^8 

889 

890 

895 

900 

905 

910 

915 

919 

924 

929 

934 

3 

1.2 

890 

939 

944 

949 

954 

959 

963 

968 

973 

978 

983 

4 

5 

1.6 

2.0 

891 

988 

993 

998 

*002 

*007 

*012 

*017 

*022 

*027 

*032 

6 

7 

2.4 

2.8 

892 

95  036 

041 

046 

051 

056 

061 

066 

071 

075 

080 

8 

3.2 

893 

085 

090 

095 

100 

105 

109 

114 

119 

124 

129 

9 

3.6 

894 

134 

139 

143 

148 

153 

158 

163 

168 

173 

177 

895 

182 

187 

192 

197 

202 

207 

211 

216 

221 

226 

896 

231 

236 

240 

245 

250 

255 

260 

265 

270 

274 

897 

279 

284 

289 

294 

299 

303 

308 

313 

318 

323 

898 

328 

332 

337 

342 

347 

352 

357 

361 

366 

371 

899 

376 

381 

386 

390 

395 

400 

405 

410 

415 

419 

900 

424 

429 

434 

439 

444 

448 

453 

458 

463 

468 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

490 


LOGARITHMS. 


N 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

.P' 

900 

95  424 

429 

434 

439 

444 

448 

453 

458 

463 

468 

901 

472 

477 

482 

487 

492 

497 

501 

506 

511 

516 

902 

521 

525 

530 

535 

540 

545 

550 

554 

559 

564 

903 

569 

574 

578 

583 

588 

593 

598 

602 

607 

612 

904 

617 

622 

626 

631 

636 

641 

646 

650 

655 

660 

905 

665 

670 

674 

679 

684 

689 

694 

698 

703 

708 

906 

713 

718 

722 

727 

732 

737 

742 

746 

751 

756 

907 

761 

766 

770 

775 

780 

785 

789 

794 

799 

804 

908 

809 

813 

818 

823 

828 

832 

837 

842 

847 

852 

909 

856 

861 

866 

871 

875 

880 

885 

890 

895 

899 

910 

904 

909 

914 

918 

923 

928 

933 

938 

942 

947 

911 

952 

957 

961 

966 

971 

976 

980 

985 

990 

995 

5 

912 

999 

*004 

*009 

*014 

*019 

*023 

*028 

*033 

*038 

*042 

1 

0.5 

913 

96  047 

052 

057 

061 

066 

071 

076 

080 

085 

090 

2 

1.0 

914 

095 

099 

104 

109 

114 

118 

123 

128 

133 

137 

4 

1 .5 

2.0 

915 

142 

147 

152 

156 

161 

166 

171 

175 

180 

185 

5 

2!5 

916 

190 

194 

199 

204 

209 

213 

218 

223 

227 

232 

6 

3.0 

917 

237 

242 

246 

251 

256 

261 

265 

270 

275 

280 

7 

3.5 

918 

284 

289 

294 

298 

303 

308 

313 

317 

322 

327 

8 

4.0 

919 

332 

336 

341 

346 

350 

355 

360 

365 

369 

374 

4.5 

920 

379 

384 

388 

393 

398 

402 

407 

412 

417 

421 

921 

426 

431 

435 

440 

445 

450 

454 

459 

464 

468 

922 

473 

478 

483 

487 

492 

497 

501 

506 

511 

515 

923 

520 

525 

530 

534 

539 

544 

548 

553 

558 

562 

924 

567 

572 

577 

581 

586 

591 

595 

600 

605 

609 

925 

614 

619 

624 

628 

633 

638 

642 

647 

652 

656 

926 

661 

666 

670 

675 

680 

685 

689 

694 

699 

703 

927 

708 

713 

717 

722 

727 

731 

736 

741 

745 

750 

928 

755 

759 

764 

769 

774 

778 

783 

788 

792 

797 

929 

802 

806 

811 

816 

820 

825 

830 

834 

839 

844 

930 

848 

853 

858 

,862 

867 

872 

876 

881 

886 

890 

4 

931 

895 

900 

904 

909 

914 

918 

923 

928 

932 

937 

932 

942 

946 

951 

956 

960 

965 

970 

974 

979 

984 

2 

0.8 

933 

988 

993 

997 

*002 

*007 

*011 

*016 

*021 

*025 

*030 

3 

1.2 

934 

97  035 

039 

044 

049 

053 

058 

063 

067 

072 

077 

4 

1.6 

935 

081 

086 

090 

095 

100 

104 

109 

114 

118 

123 

5 

2.0 

936 

128 

132 

137 

142 

146 

151 

155 

160 

165 

169 

6 

2.4 

937 

174 

179 

183 

188 

192 

197 

202 

206 

211 

216 

8 

3.2 

938 

220 

225 

230 

234 

239 

243 

248 

253 

257 

262 

9 

3.6 

939 

267 

271 

276 

280 

285 

290 

294 

299 

304 

308 

940 

313 

317 

322 

327 

331 

336 

340 

345 

350 

354 

941 

359 

364 

368 

373 

377 

382 

387 

391 

396 

400 

942 

405 

410 

414 

419 

424 

428 

433 

437 

442 

447 

943 

451 

456 

460 

465 

470 

474 

479 

483 

488 

493 

944 

497 

502 

506 

511 

516 

520 

525 

529 

534 

539 

945 

543 

548 

552 

557 

562 

566 

571 

575 

580 

585 

946 

589 

594 

598 

603 

607 

612 

617 

621 

626 

630 

947 

635 

640 

644 

649 

653 

658 

663 

667 

672 

676 

948 

681 

685 

690 

695 

699 

704 

708 

713 

717 

722 

949 

727 

731 

736 

740 

745 

749 

754 

759 

763 

768 

950 

772 

777 

782 

786 

791 

795 

800 

804 

809 

813 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

.P. 

LOGARITHM'S. 


491 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

950 

97  772 

777 

782 

786 

791 

795 

800 

804 

809 

813 

951 

818 

823 

827 

832 

836 

841 

845 

850 

855 

859 

952 

864 

868 

873 

877 

882 

886 

89] 

896 

900 

905 

953 

909 

914 

918 

923 

928 

932 

937 

941 

946 

950 

954 

955 

959 

964 

968 

973 

978 

982 

987 

991 

996 

955 

98  000 

005 

009 

014 

019 

023 

028 

032 

037 

041 

956 

046 

050 

055 

059 

064 

068 

073 

078 

082 

087 

957 

091 

096 

100 

105 

109 

114 

118 

123 

127 

132 

958 

137 

141 

146 

150 

155 

159 

164 

168 

173 

177 

959 

182 

186 

191 

195 

200 

204 

209 

214 

218 

223 

960 

227 

232 

236 

241 

245 

250 

254 

259 

263 

268 

961 

272 

277 

281 

286 

290 

295 

, 299 

304 

308 

313 

3 

962 

318 

322 

327 

331 

336 

340 

345 

349 

354 

358 

1 

0.5 

963 

363 

367 

372 

376 

381 

385 

390 

394 

399 

403 

2 

3 

1.0 

1.5 

964 

408 

412 

417 

421 

426 

430 

435 

439 

444 

448 

4 

2]o 

965 

453 

457 

462 

466 

471 

475 

480 

484 

489 

493 

5 

2.5 

966 

498 

502 

507 

511 

516 

520 

525 

529 

534 

538 

6 

3.0 

967 

543 

547 

552 

556 

561 

565 

570 

574 

579 

583 

1 

8.5 

968 

588 

592 

597 

601 

605 

610 

614 

619 

623 

628 

8 

9 

4^5 

969 

632 

637 

641 

646 

650 

655 

659 

664 

668 

673 

970 

677 

682 

686 

691 

695 

700 

704 

709 

713 

717 

971 

722 

726 

731 

735 

740 

744 

749 

753 

758 

762 

972 

767 

771 

776 

780 

784 

789 

793 

798 

802 

807 

973 

811 

816 

820 

825 

829 

834 

838 

843 

847 

851 

974 

856 

860 

865 

869 

874 

878 

883 

887 

892 

896 

975 

900 

905 

909 

914 

918 

923 

927 

932 

, 936 

941 

976 

945 

949 

954 

958 

963 

967 

972 

976 

981 

985 

977 

989 

994 

998 

*003 

*007 

*012 

*016 

*021 

*025 

*029 

978 

99  034 

038 

043 

047 

052 

056 

061 

065 

069 

074 

979 

078 

083 

087 

092 

096 

100 

105 

109 

114 

118 

980 

123 

127 

131 

136 

140 

145 

149 

154 

158 

162 

4 

981 

167 

171 

176 

180 

185 

189 

193 

198 

202 

207 

1 

0.4 

982 

211 

216 

220 

224 

229 

233 

238 

242 

247 

251 

2 

0.8 

983 

255 

260 

264 

269 

273 

277 

282 

286 

291 

295 

3 

1.2 

984 

300 

304 

308 

313 

317 

322 

326 

330 

335 

339 

4 

1.6 

985 

344 

348 

352 

357 

361 

366 

370 

374 

379 

383 

5 

2.0 

986 

388 

392 

396 

401 

405 

410 

414 

419 

423 

427 

7 

2.8 

987 

432 

436 

441 

445 

449 

454 

458 

463 

467 

471 

8 

3.2 

988 

476 

480 

484 

489 

493 

498 

502 

506 

511 

515 

9 

3.6 

989 

520 

524 

528 

533 

537 

542 

546 

550 

555 

559 

990 

564 

568 

572 

577 

581 

585 

590 

594 

599 

603 

991 

607 

612 

616 

621 

625 

629 

634 

638 

642 

647 

992 

651 

656 

660 

664 

669 

673 

677 

682 

686 

691 

993 

695 

699 

704 

708 

712 

717 

721 

726 

730 

734 

994 

739 

743 

747 

752 

756 

760 

765 

769 

774 

778 

995 

782 

787 

791 

795 

800 

804 

808 

813 

817 

822 

996 

826 

830 

835 

839 

843 

848 

852 

856 

861 

865 

997 

870 

874 

878 

883 

887 

891 

896 

900 

904 

909 

998 

913 

917 

922 

926 

930 

935 

939 

944 

948 

952 

999 

957 

961 

965 

970 

974 

978 

983 

987 

991 

996 

1000 

00  000 

004 

009 

013 

017 

022 

026 

030 

035 

039 

N., 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.  P. 

492  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

0° 


// 

f 

L.  Sin. 

d. 

Cpl.  S. 

Cpl.  T. 

L.  Tang. 

d.  c. 

L.  Cotg. 

L.Cos. 

6 

60 

120 

130 

240 

0 

1 

2 

3 

4 

6.46373 

6.76476 

6.94085 

7.06579 

30103 

17609 

12494 

9691 

7918 

6694 

5800 

5115 

4576 

4139 

3779 

3476 

3218 

2997 

2802 

2633 

2483 

2348 

2227 

2119 

2021 

1930 

1848 

1773 

1704 

1639 

1579 

1524 

1472 

1424 

1379 

1336 

1297 

1259 

1223 

1190 

1158 

1128 

1100 

1072 

1046 

1022 

999 

976 

954 

934 

914 

896 

877 

860 

843 

827 

812 

797 

782 

769 

755 

743 

730 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31442 

6.46373 

6.76476 

6.94085 

7.06579 

30103 

17609 

12494 

9691 

7918 

6694 

5800 

5115 

4576 

4139 

3779 

3476 

3219 

2996 

2803 

2633 

2482 

2348 

2228 

2119 

2020 

1931 

1848 

1773 

1704 

1639 

1579 

1524 

1473 

1424 

1379 

1336 

1297 

1259 

1223 

1190 

1159 

1128 

1100 

1072 

1047 

1022 

998 

976 

955 

934 

915 

895 

878 

860 

843 

828 

812 

797 

782 

769 

756 

742 

730 

3.53627 
' 3.23524 
3.05915 
2.93421 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

60 

59 

58 

57 

56 

300 

360 

420 

480 

540 

5 

6 

7 

8 

9 

7.16270 

7.24188 

7.30882 

7.36682 

7.41797 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31442 

5.31442 

5.31442 

5.31442 

5.31442 

7.16270 

7.24188 

7.30882 

7.36682 

7.41797 

2.83730 

2.75812 

2.69118 

2.63318 

2.58203 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

55 

54 

53 

52 

51 

GOO 

660 

720 

780 

840 

10 

11 

12 

13 

14 

7.46373 

7.50512 

7.54291 

7.57767 

7.60985 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31442 

5.31442 

5.31442 

5.31442 

5.31442 

7.46373 

7.50512 

7.54291 

7.57767 

7.60986 

2.53627 

2.49488 

2.45709 

2.42233 

2.39014 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

50 

49 

48 

47 

46 

900 
060 
i 020 
1080 
1140 

15 

16 

17 

18 
19 

7.63982 

7.66784 

7.69417 

7.71900 

7.74248 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31442 

5.31442 

5.31442 

5.31442 

5.31442 

7.63982 

7.66785 

7.69418 

7.71900 

7.74248 

2.36018 

2.33215 

2.30582 

2.28100 

2.25752 

0.00000 

0.00000 

9.99999 

9.99999 

9.99999 

45 

44 

43 

42 

41 

1200 

1260 

1320 

1380 

L440 

20 

21 

22 

23 

24 

7.76475 

7.78594 

7.80615 

7.82545 

7.84393 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31442 

5.31442 

5.31442 

5.31442 

5.31442 

7.76476 

7.78595 

7.80615 

7.82546 

7.84394 

2.23524 

2.21405 

2.19385 

2.17454 

2.15606 

9.99999 

9.99999 

9.99999 

9.99999 

9.99999 

40 

39 

38 

37 

36 

:5oo 

1560 

'620 

1680 

[740 

2.5 

26 

27 

28 
29 

7.86166 

7.87870 

7.89509 

7.91088 

7.92612 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31442 

5.31442 

5.31442 

5.31442 

5.31441 

7.86167 

7.87871 

7.89510 

7.91089 

7.92613 

2.13833 

2.12129 

2.10490 

2.08911 

2.07387 

9.99999 

9.99999 

9.99999 

9.99999 

9.99998 

35 

34 

33 

32 

31 

i800 

I860 

1920 

1980 

2040 

30 

31 

32 
33' 
34 

7.94084 

7.95508 

7.96887 

7.98223 

7.99520 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31441 

5.31441 

5.31441 

5.31441 

5.31441 

7.94086 

7.95510 

7.96889 

7.98225 

7.99522 

2.05914 

2.04490 

2.03111 

2.01775 

2.00478 

9.99998 

9.99998 

9.99998 

9.99998 

9.99998 

30 

29 

28- 

27 

26 

2100 

2160 

2220 

2280 

2340 

35 

36 

37 

38 

39 

8.00779 

8.02002 

8.03192 

8.04350 

8.05478 

5.31443 

5.31443 

5.31443 

5.31443 

5.31443 

5.31441 

5.31441 

5.31441 

5.31441 

5.31441 

8.00781 

8.02004 

8.03194 

8.04353 

8.0.5481 

1.99219 

1.97996 

1.96806 

1.95647 

1.94519 

9.99998 

9.99998 

9.99997 

9.99997 

9.99997 

25 

24 

23 

22 

21 

2400 

2460 

2520 

2580 

2640 

40 

41 

42 

43 

44 

8.06578 

8.07650 

8.08696 

8.09718 

8.10717 

5.31443 

5.31444 
5.31444 
5.31444 
5.31444 

5.31441 

5.31440 

5.31440 

5.31440 

*^.31440 

8.06581 

8.07653 

8.08700 

8.09722 

8.10720 

1.93419 

1.92347 

1.91300 

1.90278 

1.89280 

9.99997 

9.99997 

9.99997 

9.99997 

9.99996 

20 

X.9 

18 

17 

16 

2700 

2760 

2820 

2880 

2940 

45 

46 

47 

48 

49 

8.11693 

8.12647 

8.13581 

8.14495 

8.15391 

5.31444 

5.31444 

5.31444 

5.31444 

5.31444 

5.31440 

5.31440 

5.31440 

5.31440 

5.31440 

8.11696 

8.12651 

8.13585 

8.14500 

8.15395 

1.88304 

1.87349 

1.86415 

1.85500 

1.84605 

9.99996 

9.99996 

9.99996 

9.99996 

9.99996 

15 

14 

13 

12 

11 

3000 

3060 

3120 

3180 

3240 

50 

51 

52 

53 

54 

8.16268 

8.17128 

8.17971 

8.18798 

8.19610 

5.31444 

5.31444 

5.31444 

5.31444 

5.31444 

5.31439 

5.31439 

5.31439 

5.31439 

5.31439 

8.16273 

8.17133 

8.17976 

8.18804 

8.19616 

1.83727 

1.82867 

1.82024 

1.81196 

1.80384 

9.99995 

9.99995 

9.99995 

9.99995 

9.99995 

10 

9 

8 

7 

6 

3300 

3360 

3420 

3480 

3540 

55 

56 

57 

58 

59 

8.20407 

8.21189 

8.21958 

8.22713 

8.23456 

5.31444 

5.31444 

5.31445 
5.31445 
5.31445 
5.31445 

5.31439 

5.31439 

5.31439 

5.31438 

5.314.38 

8.20413 

8.21195 

8.21964 

8.22720 

8.23462 

1.79587 

1.78805 

1.78036 

1.77280 

1.76538 

9.99994 

9.99994 

9.99994 

9.99994 

9.99994 

5 

4 

3 

2 

1 

3600 

60 

8.24186 

5.314:38 

8.24192 
L.  Cotg. 

1.75808 

9.99993 

0 

L.  Cos.  i d.  1 

d.”^ 

L.  Tang. 

L.  Sin. 

/ 

89' 


LOOARimMS  OF  TRIGONOMETRIC  FUNCTIONS, 

r 


495 


// 

L.  Sin. 

d. 

Cpl.  S. 

Cpl.  T. 

L.  Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

60 

59 

68 

57 

56 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

3600 

3660 

3720 

3780 

3840 

0 

1 

2 

3 

4 

8.24186 

8.24903 

8.25609 

8.26304 

8.26988 

717 

706 

695 

684 

673 

663 

653 

644 

634 

624 

616 

608 

599 

590 

583 

575 

568 

560 

553 

547 

539 

533 

526 

520 

514 

508 

502 

496 

491 

485 

480 

474 

470 

464 

459 

455 

450 

445 

441 

436 

433 

427 

424 

419 

416 

411 

408 

404 

400 

396 

393 

390 

386 

382 

379 

376 

373 

369 

367 

363 

5.31445 

5.31445 

5.31445 

5.31445 

5.31445 

5.31438 

5.31438 

5.31438 

5.31438 

5.31437 

8.24192 

8.24910 

8.25616 

8.26312 

8.26996 

718 

706 

696 

684 

673 

663 

654 

643 

634 

625 

617 

607 

599 

591 

584 

575 

568 

561 

553 

546 

540 

533 

527 

520 

514 

509 

502 

496 

491 

486 

480 

475 

470 

464 

460 

455 

450 

446 

441 

437 

432 

428 

424 

420 

416 

412 

408 

404 

401 

397 

393 

390 

386 

383 

380 

376 

373 

370 

367 

363 

1.75808 

1.75090 

1.74384 

1.73688 

1.73004 

9.99993 

9.99993 

9.99993 

9.99993 

9.99992 

3900 

3960 

4020 

4080 

4140 

5 

6 

7 

8 

9 

8.27661 

8.28324 

8.28977 

8.29621 

8.30255 

5.31445 

5.31445 

5.31445 

5.31445 

5.31445 

5.31437 

5.31437 

5.31437 

5.31437 

5.31437 

8.27669 

8.28332 

8.28986 

8.29629 

8.30263 

1.72331 

1.71668 

1.71014 

1.70371 

1.69737 

9.99992 

9.99992 

9.99992 

9.99992 

9.99991 

4200 

4260 

4320 

4380 

4440 

10 

11 

12 

13 

14 

8.30879 

8.31495 

8.32103 

8.32702 

8.33292 

5.31446 

5.31446 

5.31446 

5.31446 

5.31446 

5.31437 

5.31436 

5.31436 

5.31436 

5.31436 

8.30888 

8.31505 

8.32112 

8.32711 

8.33302 

1.69112 

1.68495 

1.67888 

1.67289 

1.66698 

9.99991 

9.99991 

9.99990 

9.99990 

9.99990 

4500 

4560 

4620 

4680 

4740 

15 

16 

17 

18 
19 

8.33875 

8.34450 

8.35018 

8.35578 

8.36131 

5.31446 

5.31446 

5 31446 
5.31446 
5.31446 

5.31436 

5.31435 

5.31435 

5.31435 

5.31435 

8.33886 

8.34461 

8.35029 

8.35590 

8.36143 

1.66114 

1.65539 

1.64971 

1.64410 

1.63857 

9.99990 

9.99989 

9.99989 

9.99989 

9.99989 

45 

44 

43 

42 

41 

4800 

4860 

4920 

4980 

5040 

20 

21 

22 

23 

24 

8.36678 

8.37217 

8.37750 

8.38276 

8.38796 

5.31446 

5.31447 
5.31447 
5.31447 
5.31447 

5.31435 

5.31434 

5.31434 

5.31434 

5.31434 

8.36689 

8.37229 

8.37762 

8.38289 

8.38809 

1.63311 

1.62771 

1.62238 

1.61711 

1.61191 

9.99988 

9.99988 

9.99988 

9.99987 

9.99987 

40 

39 

38 

37 

36 

5100 

5160 

5220 

5280 

5340 

25 

26 

27 

28 
29 

8.39310 

8.39818 

8.40320 

8.40816 

8.41307 

5.31447 

5.31447 

5.31447 

5.31447 

5.31447 

5.31434 

5.31433 

5.31433 

5.31433 

5.31433 

8.39323 

8.39832 

8.40334 

8.40830 

8.41321 

1.60677 

1.60168 

1.59666 

1.59170 

1.58679 

9.99987 

9.99986 

9.99986 

9.99986 

9.99985 

35 

34 

33 

32 

31 

5400 

5460 

5520 

5580 

5640 

30 

31 

32 

33 

34 

8.41792 

8.42272 

8.42746 

8.43216 

8.43680 

5.31447 

5.31448 
5.31448 
5.31448 
5.31448 

5.31433 

5.31432 

5.31432 

5.31432 

5.31432 

8.41807 

8.42287 

8.42762 

8.43232 

8.43696 

1.58193 

1.57713 

1.57238 

1.56768 

1.56304 

9.99985 

9.99985 

9.99984 

9.99984 

9.99984 

30 

29 

28 

27 

26 

5700 

'5760 

5820 

5880 

5940 

35 

36 

37 

38 

39 

8.44139 

8.44594 

8.45044 

8.45489 

8.45930 

5.31448 

5.31448 

5.31448 

5.31448 

5.31449 

5.31431 

5.31431 

5.31431 

5.31431 

5.31431 

8.44156 

8.44611 

8.45061 

8.45507 

8.45948 

1.55844 

1.55389 

1.54939 

1.54493 

1.54052 

9.99983 

9.99983 

9.99983 

9.99982 

9.99982 

25 

24 

23 

22 

21 

6000 

6060 

6120 

6180 

6240 

40 

41 

42 

43 

44 

8.46366 

8.46799 

8.47226 

8.47650 

8.48069 

5.31449 

5.31449 

5.31449 

5.31449 

5.31449 

5.31430 

5.31430 

5.31430 

5.31430 

5.31429 

8.46385 

8.46817 

8.47245 

8.47669 

8.48089 

1.53615 

1.53183 

1.52755 

1.52331 

1.51911 

9.99982 

9.99981 

9.99981 

9.99981 

9.99980 

20 

19 

18 

17 

16 

6300 

6360 

6420 

6480 

6540 

45 

46 

47 

48 

49 

8.48485 

8.48896 

8.49304 

8.49708 

8.50108 

5.31449 

5.31449 

5.31450 
5.31450 
5.31450 

5.31429 

5.31429 

5.31428 

5.31428 

5.31428 

8.48505 

8.48917 

8.49325 

8.49729 

8.50130 

1.51495 

1.51083 

1.50675 

1.50271 

1.49870 

9.99980 

9.99979 

9.99979 

9.99979 

9.99978 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

6600 

6660 

6720 

6780 

6840 

50 

51 

52 

53 

54 

8.50504 

8.50897 

8.51287 

8.51673 

8.52055 

5.31450 

5.31450 

5.31450 

5.31450 

5.31450 

5.31428 

5.31427 

5.31427 

5.31427 

5.31427 

8.50527 

8.50920 

8.51310 

8.51696 

8.52079 

1.49473 

1.49080 

1.48690 

1.48304 

1.47921 

9.99978 

9.99977 

9.99977 

9.99977 

9.99976 

6900 

6960 

7020 

7080 

7140 

55 

56 

57 

58 

59 

8.52434 

8.52810 

8.53183 

8.53552 

8.53919 

5.31451 

5.31451 

5.31451 

5.31451 

5.31451 

5.31426 

5.31426 

5.31426 

5.31425 

5.31425 

8.52459 

8.52835 

8.53208 

8.53578 

8.53945 

1.47541 

1.47165 

1.46792 

1.46422 

1.46055 

9.99976 

9.99975 

9.99975 

9.99974 

9.99974 

5 

4 

3 

2 

1 

7200 

60 

8.54282 

5.31451 

5.31425 

8.54308 

1.45692 

9.99974 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.  Tansr. 

L.  Sin. 

' 

88‘ 


4P4  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


20 


// 

L.  Sin. 

d. 

Cpl.  S. 

Cpl.  T. 

L.  Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

7200 

7260 

7320 

7380 

7440 

0 

1 

2 

3 

4 

8.54282 

8.54642 

8.54999 

8.55354 

8.55705 

360 

357 

355 

351 

349 

346 

343 

341 

337 

336 

332 

330 

328 

325 

323 

320 

318 

316 

313 

311 

309 

307 

305 

302 

301 

298 

296 

294 

293 

290 

288 

287 

284 

283 

281 

279 

277 

276 

274 

272 

270 

269 

267 

266 

263 

263 

260 

259 

258 

256 

254 

253 

252 

250 

249 

247 

246 

244 

243 

242 

5.31451 

5.31451 

5.31452 
5.31452 
5.31452 

5.31425 

5.31425 

5.31424 

5.31424 

5.31424 

8.54308 

8.54669 

8.55027 

8.55882 

8.55734 

361 

358 

355 

352 

349 

346 

344 

341 

338 

336 

333 

330 

328 

326 

323 

321 

319 

316 

314 

311 

310 

307 

305 

303 

301 

299 

297 

295 

292 

291 

289 

287 

285 

284 

281 

280 

278 

276 

274 

273 

271 

269 

268 

266 

264 

263 

261 

260 

258 

257 

255 

254 

252 

251 

249 

248 

246 

245 

244 

243 

1.45692 

1.45331 

1.44973 

1.44618 

1.44266 

9.99974 

9.99973 

9.99973 

9.99972 

9.99972 

60 

59 

58 

57 

56 

7500 

7560 

7620 

7680 

7740 

5 

6 

7 

8 

9 

8.56054 

8.56400 

8.56743 

8.57084 

8.57421 

5.31452 

5.31452 

5.31452 

5.31453 
5.31453 

5.31423 

5.31423 

5.31423 

5.31422 

5.31422 

8.56083 

8.56429 

8.56773 

8.57114 

8.57452 

1.43917 

1.43571 

1.43227 

1.42886 

1.42548 

9.99971 

9.99971 

9.99970 

9.99970 

9.99969 

55 

54 

53 

52 

51 

7800 

7860 

7920 

7980 

8040 

10 

11 

12 

13 

14 

8.57757 

8.58089 

8.58419 

8.58747 

8.59072 

5.31453 

5.31453 

5.31453 

5.31453 

5.31454 

5.31422 

5.31421 

5.31421 

5.31421 

5.31421 

8.57788 

8.58121 

8.58451 

8.58779 

8.59105 

1.42212 

1.41879 

1.41549 

1.41221 

1.40895 

9.99969 

9.99968 

9.99968 

9.99967 

9.99967 

50 

49 

48 

47 

46 

8100 

8160 

8220 

8280 

8340 

15 

16 

17 

18 
19 

8.59395 

8.59715 

8.60033 

8.60349 

8.60662 

5.31454 

5.-31454 

5.31454 

5.31454 

5.31454 

5.31420 

5.31420 

5.31420 

5.31419 

5.31419 

8.59428 

8.59749 

8.60068 

8.60384 

8.60698 

1.40572 

1.40251 

1.39932 

1.39616 

1.39302 

9.99967 

9.99966 

9.99966 

9.99965 

9.99964 

45 

44 

43 

42 

41 

8400 

8460 

8520 

8580 

8640 

20 

21 

22 

23 

24 

8.60973 

8.61282 

8.61589 

8.61894 

8.62196 

5.31455 

5.31455 

5.31455 

5.31455 

5.31455 

5.31418 

5.31418 

5.31418 

5.31417 

5.31417 

8.61009 

8.61319 

8.61626 

8.61931 

8.62234 

1.38991 

1.38681 

1.38374 

1.38069 

1.37766 

9.99964 

9.99963 

9.99963 

9.99962 

9.99962 

40 

39 

38 

37 

36 

8700 

8760 

8820 

8880 

8940 

25 

26 

27 

28 
29 

8.62497 

8.62795 

8.63091 

8.63385 

8.63678 

5.31455 

5.31456 
5.31456 
5.31456 
5.31456 

5.31417 

5.31416 

5.31416 

5.31416 

5.31415 

8.62535 

8.62834 

8.63131 

8.63426 

8.63718 

1.37465 

1.37166 

1.36869 

1.36574 

1.36282 

9.99961 

9.99961 

9.99960 

9.99960 

9.99959 

35 

34 

33 

32 

31 

9000 

9060 

9120 

9180 

9240 

30 

31 

32 

33 

34 

8.63968 

8.64256 

8.64543 

8.64827 

8.65110 

5.31456 

5.31456 

5.31457 
5.31457 
5.31457 

5.31415 

5.31415 

5.31414 

5.31414 

5.31413 

8.64009 

8.64298 

8.64585 

8.64870 

8.65154 

1.35991 

1.35702 

1.35415 

1.35130 

1.34846 

9.99959 

9.99958 

9.99958 

9.99957 

9.99956 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

9300 

9360 

9420 

9480 

9540 

35 

36 

37 

38 

39 

8.65391 

8.65670 

8.65947 

8.66223 

8.66497 

5.31457 

5.31457 

5.31458 
5.31458 
5.31458 

5.31413 

5.31413 

5.31412 

5.31412 

5.31412 

8.65435 

8.65715 

8.65993 

8.66269 

8.66543 

1.34565 

1.34285 

1.34007 

1.33731 

1.33457 

9.99956 

9.99955 

9.99955 

9.99954 

9.99954 

9600 

9660 

9720 

9780 

9840 

40 

41 

42 

43 

44 

8.66769 

8.67039 

8.67308 

8.67575 

8.67841 

5.31458 

5.31458 

5.31459 
5.31459 
5.31459 

5.31411 

5.31411 

5.31410 

5.31410 

5.31410 

8.66816 

8.67087 

8.67356 

8.67624 

8.67890 

1.33184 

1.32913 

1.32644 

1.32376 

1.32110 

1.31846 

1.31583 

1.31322 

1.31062 

1.30804 

9.99953 

9.99952 

9.99952 

9.99951 

9.99951 

20 

19 

18 

17 

16 

9900 

9960 

10020 

10080 

10140 

45 

46 

47 

48 

49 

8.68104 

8.68367 

8.68627 

8.68886 

8.69144 

5.31459 

5.31459 

5.31460 
5.31460 
5.31460 

5.31409 

5.31409 

5.31408 

5.31408 

5.31408 

8.68154 

8.68417 

8.68678 

8.68938 

8.69196 

9.99950 

9.99949 

9.99949 

9.99948 

9.99948 

15 

14 

13 

12 

11 

10200 

10260 

10320 

10380 

10440 

50 

51 

52 

53 

54 

8.69400 

8.69654 

8.69907 

8.70159 

8.70409 

5.31460 

5.31460 

5.31461 
5.31461 
5.31461 

5.31407 

5.31407 

5.31406 

5.31406 

5.31405 

8.69453 

8.69708 

8.69962 

8.70214 

8.70465 

1.30547 

1.30292 

1.30038 

1.29786 

1.29535 

9.99947 

9.99946 

9.99946 

9.99945 

9.99944 

10 

9 

8 

7 

6 

10500 

10560 

10620 

10680 

10740 

55 

56 

57 

58 

59 

8.70658 

8.70905 

8.71151 

8.71395 

8.71638 

5.31461 

5.31461 

5.31462 
5.31462 
5.31462 

5.31405 

5.31405 

5.31404 

5.31404 

5.31403 

8.70714 

8.70962 

8.71208 

8.71453 

8.71697 

1.29286 

1.29038 

1.28792 

1.28547 

1.28303 

9.99944 

9.99943 

9.99942 

9.99942 

9.99941 

5 

4 

3 

2 

1 

10800 

60 

8.71880 

5.31462 

5.31403 

8.71940 

1.28060 

9.99940 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.  Tang. 

L.  Sin. 

87‘ 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


495 


/ 

L.  Sin. 

0 

8.71880 

1 

8.72120 

2 

8.72359 

3 

8.72597 

4 

8.72834 

5 

8.73069 

6 

8.73303 

7 

8.73535 

8 

8.73767 

9 

8.73997 

10 

8.74226 

11 

8.74454 

12 

8.74680 

13 

8.74906 

14 

8.75130 

15 

8.75353 

16 

8.75575 

17 

8.75795 

18 

8.76015 

19 

8.76234 

20 

8.76451 

21 

8.76667 

22 

8.76883 

23 

8.77097 

24 

8.77310 

25 

8.77522 

26 

8.77733 

27 

8.77943 

28 

8.78152 

29 

8.78360 

30 

8.78568 

31 

8.78774 

32 

8.78979 

33 

8.79183 

34 

8.79386 

35 

8.79588 

36 

8.79789 

37 

8.79990 

38 

8.80189 

39 

8.80388 

40 

8.80585 

41 

8.80782 

42 

8.80978 

43 

8.81173 

44 

8.81367 

45 

8.81560 

46 

8.81752 

47 

8.81944 

48 

8.82134 

49 

8.82324 

50 

8.82513 

51 

8.82701 

52 

8.82888 

53 

8.83075 

54 

8.83261 

55 

8.83446 

56 

8.83630 

57 

8.83813 

58 

8.83996 

59 

8.84177 

60 

'8.84358 

L.  Cos. 

L.Tang. 


d.  c, 


L.  Cotg. 

L.  Cos. 

1.28060 

9.99940 

60 

1.27819 

9.99940 

59 

6 

1.27580 

9.99939 

58 

7 

1.27341 

9.99938 

57 

s 

1.27104 

9.99938 

56 

9 

1.26868 

9.99937 

55 

10 

1.26634 

9.99936 

54 

20 

1.26400 

9.99936 

53 

30 

1.26168 

9.99935 

52 

40 

1.25937 

9.99934 

51 

50 

1.25708 

9.99934 

50 

1.25479 

9.99933 

49 

1.25252 

9.99932 

48 

o 

1.25026 

9.99932 

47 

/ 

Q 

1.24801 

9.99931 

46 

O 

9 

1.24577 

9.99930 

45 

10 

1.24355 

9.99929 

44 

20 

1.24133 

9.99929 

43 

30 

1.23913 

9.99928 

42 

40 

1.23694 

9.99927 

41 

50 

1.23475 

9.99926 

40 

1.23258 

9.99926 

39 

1.23042 

9.99925 

38 

6 

1.22827 

9.99924 

37 

7 

1.22613 

9.99923 

36 

8 

Q 

1.22400 

9.99923 

35 

y 

10 

1.22189 

9.99922 

34 

20 

1.21978 

9.99921 

33 

30 

1.21768 

0.99920 

32 

40 

1.21559 

9.99920 

31 

50 

1.21351 

9.99919 

30 

1.21145 

9.99918 

29 

1.20939 

9.99917 

28 

6 

1.20734 

9.99917 

27 

7 

1.20530 

9.99916 

26 

8 

1.20327 

9.99915 

25 

9 

1.20125 

9.99914 

24 

10 

1.19924 

9.99913 

23 

20 

1.19723 

9.99913 

22 

30 

1.19524 

9.99912 

21 

40 

50 

1.19326 

9.99911 

20 

1.19128 

9.99910 

19 

1.18932 

9.99909 

18 

6 

1.18736 

9.99909 

17 

7 

1.18541 

9.99908 

16 

8 

1.18347 

9.99907 

15 

9 

1.18154 

9.99906 

14 

10 

1.17962 

9.99905 

13 

20 

1.17770 

9.99904 

12 

30 

1.17580 

9.99904 

11 

40 

1.17390 

9.99903 

10 

ou 

1.17201 

9.99902 

9 

1.17013 

9.99901 

8 

6 

1.16825 

9.99900 

7 

7 

1.16639 

9.99899 

6 

8 

1.16453 

9.99898 

5 

9 

1.16268 

9.99898 

4 

10 

1.16084 

9.99897 

3 

20 

1.15900 

9.99896 

2 

30 

1.15718 

9.99895 

1 

40 

1.15536 

9.99894 

0 

50 

L.Tang. 

L.  Sin. 

/ 

P.  P. 


8.71940 

8.72181 

8.72420 

8.72659 

8.72896 


8.73132 

8.73366 

8.73600 

8.73832 

8.74063 


8.74292 

8.74521 

8.74748 

8.74974 

8.75199 


8.75423 

8.75645 

8.75867 

8.76087 

8.76306 


8.76525 

8.76742 

8.76958 

8.77173 

8.77387 


8.77600 

8.77811 

8.78022 

8.78232 

8.78441 


8.78649 

8.78855 

8.79061 

8.79266 

8.79470 


8.81653 

8.81846 

8.82038 

8.82230 

8.82420 


8.82610 

8.82799 

8.82987 

8.83175 

8.83361 


8.83547 

8.83732 

8.83916 

8.84100 

8.84282 


8.84464 


238 

23.8 

27.8 

31.7 

35.7 

39.7 

79.3 

119.0 

158.7 

198.3 

225 

22.5 

26.3 

30.0 

33.8 

37.5 

75.0 

112.5 

150.0 

187.5 

212 

21.2 

24.7 

28.3 

31.8 

35.3 

70.7 

106.0 

141.3 

176.7 

201 

20.1 

23.5 

26.8 

30.2 

33.5 

67.0 

100.5 

134.0 

167.5 

189 

18.9 

22.1 

25.2 

28.4 

31.5 
63.0 

94.5 

126.0 

157.5 


234 

23.4 
27.3 

31.2 

35.1 

39.0 

78.0 

117.0 

156.0 

195.0 

220 

22.0 

25.7 

29.3 

33.0 

36.7 

73.3 

110.0 

146.7 

183.3 

208 

20.8 

24.3 

27.7 

31.2 

34.7 

69.3 
104.0 

138.7 

173.3 

197 

19.7 

23.0 

26.3 

29.6 

32.8 

65.7 

98.5 

131.3 

164.2 

185 

18.5 

21.6 

24.7 

27.8 

30.8 
61.7 
92.5 

123.3 
154.2 


229 

22.9 

26.7 

30.5 
34.4 

38.2 

76.3 
114.5 

152.7 

190.8 

216 

21.6 

25.2 

28.8 

32.4 

36.0 

72.0 
108.0 

144.0 

180.0 

204 

20.4 
23.8 

27.2 

30.6 

34.0 

68.0 
102.0 

136.0 

170.0 

193 

19.3 

22.5 

25.7 

29.0 

32.2 

64.3 

96.5 

128.7 

160.8 

181 

18.1 
21.1 

24.1 

27.2 

30.2 

60.3 

90.5 

120.7 

150.8 


4 

3 

2 

1 

0.4 

0.3 

0.2 

0.1 

0.5 

0.4 

0.2 

0.1 

0.5 

0.4 

0.3 

0.1 

0.6 

0.5 

0.3 

0.2 

0.7 

0.5 

0.3 

0.2 

1.3 

1.0 

0.7 

0.3 

2.0 

1.5 

1.0 

0.5 

2.7 

2.0 

1.3 

0.7 

3.3 

2.5 

1.7 

0.8 

L.  Cotg. 


d.  c. 


P.  P. 


86‘ 


496  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


4° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

P.  P. 

0 

1 

2 

3 

4 

8.84358 

8.84539 

8.84718 

8.84897 

8.85075 

181 

179 

179 

178 

177 

177 

176 

175 

175 

173 

173 

173 

171 

171 

171 

169 

169 

169 

167 

168 
166 
166 
165 
164 
164 

163 

163 

162 

162 

160 

161 

159 

159 

159 

158 

157 

157 

156 

155 

155 

155 

154 

153 

153 

152 

152 

151 

151 

150 

150 

149 

149 

148 

147 

147 

147 

146 

146 

145 

145 

8.84464 

8.84646 

8.84826 

8.85006 

8.85185 

182 

180 

180 

179 

178 

177 

177 

176 

176 

174 

174 

174 

172 

172 

171 

171 

170 

169 

169 

168 

167 

167 

166 

165 

165 

165 

163 

163 

163 

161 

162 

160 

160 

160 

159 

158 

158 

157 

157 

156 

155 

155 

155 

153 

154 

153 

152 

152 

151 

151 

150 

150 

149 

148 

149 

147 

147 

147 

146 

146 

1.15536 

1.15354 

1.15174 

1.14994 

1.14815 

9.99894 

9.99893 

9.99892 

9.99891 

9.99891 

60 

59 

58 

57 

56 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 
10 
20 
30 
40 
50 

6 

7 

8 
9 

10 
20 
30 
40 
50 

181 

18.1 

21.1 

24.1 

27.2 

30.2 

60.3 

90.5 

120.7 

150.8 

175 

17.5 

20.4 

23.3 

26.3 

29.2 

58.3 

87.5 

116.7 

145.8 

168 

16.8 

19.6 

22.4 

25.2 
28.0 

56.0 

84.0 
112.0 

140.0 

162 

16.2 
18.9 

21.6 

24.3 

27.0 

54.0 

81.0 

108.0 
135.0 

155 

15.5 
18.1 

20.7 

23.3 

25.8 
51.7 

77.5 
103.3 
129.2 

149 

14.9 

17.4 

19.9 

22.4 
24.8 
49.7 

74.5 
99.3 

124.2 

179 

17.9 

20.9 

23.9 

26.9 
29.8 

59.7 

89.5 
119.3 

149.2 

173 

17.3 
20.2 

23.1 
26.0 

28.8 

57.7 

86.5 

115.3 

144.2 

166 

16.6 

19.4 

22.1 

24.9 

27.7 

55.3 

83.0 
110.7 

138.3 

159 

15.9 
18.6 
21.2 

23.9 

26.5 

53.0 

79.5 
106.0 

132.5 

153 

15.3 

17.9 

20.4 

23.0 

25.5 

51.0 

76.5 
102.0 

127.5 

147 

14.7 

17.2 

19.6 

22.1 

24.5 

49.0 

73.5 

98.0 

122.5 

177 

17.7 

20.7 

23.6 

26.6 

29.5 

59.0 

88.5 
118.0 

147.5 

171 

17.1 
20.0 

22.8 
25.7 

28.5 

57.0 

85.5 
114.0 

142.5 

164 

16.4 

19.1 

21.9 

24.6 

27.3 

54.7 
82.0 

109.3 

136.7 

157 

15.7 

18.3 

20.9 
23.6 

26.2 

52.3 

78.5 

104.7 

130.8 

151 

15.1 

17.6 

20.1 

22.7 

25.2 

50.3 
75.5 

100.7 

125.8 

o!l 

0.1 

0.1 

0.2 

0.2 

0.3 

0.5 

0.7 

0.8 

5 

6 

7 

8 

9 

8.85252 

8.85429 

8.85605 

8.85780 

8.85955 

8.85363 

8.85540 

8.85717 

8.85893 

8.86069 

1.14637 

1.14460 

1.14283 

1.14107 

1.13931 

9.99890 

9.99889 

9.99888 

9.99887 

9.99886 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

8.86128 

8.86301 

8.86474 

8.86645 

8.86816 

8.86243 

8.86417 

8.86591 

8.86763 

8.86935 

1.13757 

1.13583 

1.13409 

1.13237 

1.13065 

9.99885 

9.99884 

9.99883 

9.99882 

9.99881 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

8.86987 

8.87156 

8.87325 

8.87494 

8.87661 

8.87106 

8.87277 

8.87447 

8.87616 

8.87785 

1.12894 

1.12723 

1.12553 

1.12384 

1.12215 

9.99880 

9.99879 

9 99879 
9.99878 
9.99877 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

8.87829 

8.87995 

8.88161 

8o88326 

8.88490 

8.87953 

8.88120 

8.88287 

8.88453 

8.88618 

1.12047 

1.11880 

1.11713 

1.11547 

1.11382 

9.99876 

9.99875 

9.99874 

9.99873 

9.99872 

40 

39 

38 

37 

36 

25 

26 

27 

28  , 
29 

8.88654 

8.88817 

8.88980 

8.89142 

8.89304 

8.88783 

8.88948 

8.89111 

8.89274 

8.89437 

1.11217 

1.11052 

1.10889 

1.10726 

1.10563 

9.99871 

9.99870 

9.99869 

9.99868 

9.99867 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

8.89464 

8.89625 

8.89784 

8.89943 

8.90102 

8.89598 

8.89760 

8.89920 

8.90080 

8.90240 

1.10402 

1.10240 

1.10080 

1.09920 

1.09760 

9.99866 

9.99865 

9.99864 

9.99863 

9.99862 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

8.90260 

8.90417 

8.90574 

8.90730 

8.90885 

8.90399 

8.90557 

8.90715 

8.90872 

8.91029 

1.09601 

1.09443 

1.09285 

1.09128 

1.08971 

9.99861 

9.99860 

9.99859 

9.99858 

9.99857 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

8.91040 

8.91195 

8.91349 

8.91502 

8.91655 

8.91185 

8.91340 

8.91495 

8.91650 

8.91803 

1.08815 

1.08660 

1.08505 

1.08350 

1.08197 

9.99856 

9.99855 

9.99854 

9.99853 

9.99852 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

8.91807 

8.91959 

8.92110 

8.92261 

8.92411 

8.91957 

8.92110 

8.92262 

8.92414 

8.92565 

1.08043 

1.07890 

1.07738 

1.07586 

1.07435 

9.99851 

9.99850 

9.99848 

9.99847 

9.99816 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

8.92561 

8.92710 

8.92859 

8.93007 

8.93154 

8.92716 

8.92866 

8.93016 

8.93165 

8.93313 

1.07284 

1.07134 

1.06984 

1.06835 

1.06687 

9.99845 

9.99844 

9.99843 

9.99842 

9.99841 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

8.93301 

8.93448 

8.93594 

8.93740 

8.93885 

8.93462 

3.93609 

8.93756 

8.93903 

8.94049 

1.06538 

1.06391 

1.06244 

1.06097 

1.05951 

9.99840 

9.99839 

9.99838 

9.99837 

9.99836 

5 

4 

3 

2 

1 

60 

8.94030 

8.94195 

1.05805 

9.99834 

0 

L.  Cos.  1 d. 

L.  Cotg. 

d.  c.  L.Tang. 

L.  Sin. 

' 

P.  P. 

85' 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS,  497 


5° 


! 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

P.  P. 

0 

1 

2 

3 
, 4 

8.94030 

8.94174 

8.94317 

8.94461 

8.94603 

144 

143 

144 

142 

143 

141 

142 
141 
140 
140 
139 
139 
139 
138 
138 
137 
137 
136 
136 
136 
135 
135 
134 
134 
133 

133 

133 

132 

132 

131 

131 

131 

130 

130 

129 

129 

129 

128 

128 

128 

127 

127 

126 

126 

126 

125 

125 

124 

125 

123 

124 
123 
123 
122 
122 

122 

121 

121 

121 

120 

8.94195 

8.94340 

8.94485 

8.94630 

8.94773 

145 

145 

145 

143 

144 
143 
142 
142 
142 
141 

140 

141 

139 

140 

138 

139 
138 

137 

138 

136 

137 

135 

136 
135 
135 

134 

134 

133 

133 

133 

132 

132 

131 

131 

131 

130 

130 

130 

129 

128 

129 

128 

127 

128 
127 
126 
126 
126 
126 
125 

125 

124 

124 

124 

123 

123 

123 

122 

122 

122 

1.05805 

1.05660 

1.05515 

1.05370 

1.05227 

9.99834 

9.99833 

9.99832 

9.99831 

9.99830 

60 

59 

58 

57 

56 

6 

7 

8 
9 

10 

20 

30 

40 

50 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 
10 
20 
30 
40 
50 

6 

7 

8 
9 

10 
20 
30 
40 
50 

145 

14.5 

16.9 
19.3 
21.8 

24.2 

48.3 

72.5 

96.7 
120.8 

139 

13.9 
16.2 

18.5 

20.9 

23.2 

46.3 

69.5 

92.7 

115.8 

135 

13.5 

15.8 
18.0 

20.3 

22.5 

45.0 

67.5 

90.0 

112.5 

129 

12.9 

15.1 

17.2 

19.4 

21.5 

43.0 

64.5 

86.0 

107.5 

125 

12.5 

14.6 

16.7 

18.8 
20.8 
41.7 
62.5 

83.3 
104.2 

121 

12.1 

14.1 

16.1 
18.2 
20.2 
40.3 
60.5 
80.7 

100.8 

143 

14.3 

16.7 

19.1 

21.5 

23.8 

47.7 

71.5 

95.3 
119.2 

138 

13.8 

16.1 

18.4 

20.7 

23.0 

46.0 

69.0 

92.0 
115.0 

133 

13.3 

15.5 

17.7 

20.0 
22.2 

44.3 

66.5 

88.7 
110.8 

128 

12.8 
14.9 

17.1 

19.2 

21.3 
42.7 

64.0 

85.3 
106.7 

123 

12.3 

14.4 

16.4 

18.5 

20.5 

41.0 

61.5 

82.0 
102.5 

120 

12.0 

14.0 

16.0 
18.0 
20.0 

40.0 

60.0 
80.0 

100.0 

141 

14.1 

16.5 
18.8 

21.2 

23.5 

47.0 

70.5 

94.0 
117.5 

136 

13.6 

15.9 

18.1 

20.4 

22.7 

45.3 
68.0 

90.7 
113.3 

131 

13.1 

15.3 

17.5 

19.7 

21.8 

43.7 

65.5 

87.3 
109.2 

126 

12.6 

14.7 

16.8 

18.9 
21.0 

42.0 

63.0 

84.0 
105.0 

122 

12.2 

14.2 

16.3 

18.3 

20.3 
40,7 

61.0 

81.3 
101.7 

1 

0.1 

0.1 

0.1 

0.2 

0.2 

0.3 

0.5 

0.7 

0.8 

5 

6 

7 

8 

9 

8.94746 

8.94887 

8.95029 

8.95170 

8.95310 

8.94917 

8.95060 

8.95202 

8.95344 

8.95486 

1.05083 

1.04940 

1.04798 

1.04656 

1.04514 

9.99829 

9.99828 

9.99827 

9.99825 

9.99824 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

8.95450 

8.95589 

8.95728 

8.95867 

8.96005 

8.95627 

8.95767 

8.95908 

8.96047 

8.96187 

1.04373 

1.04233 

1.04092 

1.03953 

1.03813 

9.99823 

9.99822 

9.99821 

9.99820 

9.99819 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

15 

16 

17 

18 
19 

8.96143 

8.96280 

8.96417 

8.96553 

8.96689 

8.96325 

8.96464 

8.96602 

8.96739 

8.96877 

1.03675 

1.03536 

1.03398 

1.03261 

1.03123 

9.99817 

9.99816 

9.99815 

9.99814 

9.99813 

20 

21 

22 

23 

24 

8.96825 

8.96960 

8.97095 

8.97229 

8.97363 

8.97013 

8.97150 

8.97285 

8.97421 

8.97556 

1.02987 

1.02850 

1.027i5 

1.02579 

1.02444 

9.99812 

9.99810 

9.99809 

9.99808 

9.99807 

25 

26 

27 

28 
29 

8.97496 

8.97629 

8.97762 

8.97894 

8.98026 

8.97691 

8.97825 

8.97959 

8.98092 

8.98225 

1.02309 

1.02175 

1.02041 

1.01908 

1.01775 

9.99806 

9.99804 

9.99803 

9.99802 

9.99801 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

8.98157 

8.98288 

8.98419 

8.98549 

8.98679 

8.98358 

8.98490 

8.98622 

8.98753 

8.98884 

1.01642 

1.01510 

1.01378 

1.01247 

1.01116 

9.99800 

9.99798 

9.99797 

9.99796 

9.99795 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

8.98808 

8.98937 

8.99066 

8.99194 

8.99322 

8.99015 

8.99145 

8.99275 

8.99405 

8.99534 

1.00985 

1.00855 

1.00725 

1.00595 

1.00466 

9.99793 

9.99792 

9.99791 

9.99790 

9.99788 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

40 

41 

42 

43 

44 

8.99450 

8.99577 

8.99704 

8.99830 

8.99956 

8.99662 

8.99791 

8.99919 

9.00046 

9.00174 

1.00338 

1.00209 

1.00081 

0.99954 

0.99826 

9.99787 

9.99786 

9.99785 

9.99783 

9.99782 

45 

46 

47 

48 

49 

9.00082 

9.00207 

9.00332 

9.00456 

9.00581 

9.00301 

9.00427 

9.00553 

9.00679 

9.00805 

0.99699 

0.99573 

0.99447 

0.99321 

0.99195 

9.99781 

9.99780 

9.99778 

9.99777 

9.99776 

50 

51 

52 

53 

54 

9.00704 

9.00828 

9.00951 

9.01074 

9.01196 

9.00930 

9.01055 

9.01179 

9.01303 

9.01427 

0.99070 

0.98945 

0.98821 

0.98697 

0.98573 

9.99775 

9.99773 

9.99772 

9.99771 

9.99769 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.01318 

9.01440 

9.01561 

9.01682 

9.01803 

9.01550 

9.01673 

9.01796 

9.01918 

9.02040 

0.98450 

0.98327 

0.98204 

0.98082 

0.97960 

9.99768 

9.99767 

9.99765 

9.99764 

9.99763 

5 

4 

3 

2 

1 

0 

60 

9.01923 

9.02162 

0.97838 

9.99761 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

t 

P.  P. 

84^ 


498 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS, 


6° 


/ 

L.  Sin. 

d. 

L.Tang.l  d.  c. 

L.  Cotg. 

L.  Cos. 

P.  P. 

0 

1 

2 

3 

4 

9.01923 

9.02043 

9.02163 

9.02283 

9.02402 

120 

120 

120 

119 

118 

119 

118 

117 

118 
117 
117 
116 
116 
116 
116 
115 
115 

114 

115 

113 

114 
114 
113 
112 
113 

112 

112 

112 

111 

111 

111 

110 

110 

110 

110 

109 

109 

109 

108 

109 

108 

107 

108 
107 
107 
106 
107 
106 

105 

106 
105 
105 
105 
105 
104 

104 

104 

103 

103 

103 

9.02162 

9.02283 

9.02404 

9.02525 

9.02645 

121 

121 

121 

120 

121 

119 

120 
119 
118 
119 

118 

118 

117 

118 
116 
117 
116 
116 
116 
115 
115 
115 
115 
114 
114 

113 

114 
113 
112 
113 

112 

112 

112 

111 

111 

111 

110 

111 

110 

109 

110 
109 
109 
108 
109 

108 

108 

107 

108 
107 

106 

107 

106 

106 

106 

106 

105 

105 

105 

104 

0.97838 

0.97717 

0.97596 

0.97475 

0.97355 

9.99761 

9.99760 

9.99759 

9.99757 

9.99756 

60 

59 

58 

57 

56 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 
9 

10 

20 

30 

40 

50 

6 

7 

8 
9 

10 
20 
30 
40 
50 

6 

7 

8 
9 

10 

20 

30 

40 

50 

6 

7 

8 
9 

10 

20 

30 

40 

50 

6 

7 

8 
9 

10 

20 

30 

40 

50 

121 

12.1 

14.1 

16.1 
18.2 
20.2 

40.3 

60.5 

80.7 
100.8 

118 

11.8 
13.8 

15.7 

17.7 

19.7 

39.3 

59.0 

78.7 

98.3 

115 

11.5 

13.4 

15.3 

17.3 

19.2 

38.3 

57.5 

76.7 

95.8 

112 

11.2 

13.1 

14.9 
16.8 

18.7 

37.3 

56.0 

74.7 

93.3 

109 

10.9 

12.7 

14.5 

16.4 

18.2 

36.3 

54.5 

72.7 

90.8 

106 

10.6 

12.4 

14.1 

15.9 

17.7 

35.3 
53.0 

70.7 

88.3 

120 

12.0 

14.0 

16.0 
18.0 
20.0 

40.0 

60.0 
80.0 

100.0 

117 

11.7 

13.7 

15.6 

17.6 

19.5 

39.0 

58.5 

78.0 

97.5 

114 

11.4 

13.3 

15.2 

17.1 

19.0 

38.0 

57.0 

76.0 

95.0 

III 

11.1 

13.0 

14.8 

16.7 

18.5 

37.0 

55.5 

74.0 

92.5 

108 

10.8 

12.6 

14.4 

16.2 

18.0 

36.0 

54.0 

72.0 

90.0 

105 

10.5 
12.3 

14.0 
15.8 

17.5 

35.0 

52.5 

70.0 

87.5 

119 

11.9 

13.9 

15.9 

17.9 
19.8 
39.7 
59.5 
79.3 
99.2 

116 

11.6 

13.5 

15.5 

17.4 

19.3 

38.7 

58.0 

77.3 

96.7 

113 

11.3 

13.2 

15.1 

17.0 

18.8 

37.7 

56.5 

75.3 

94.2 

no 

11.0 

12.8 

14.7 

16.5 

18.3 

36.7 

55.0 

73.3 

91.7 

107 

10.7 

12.5 

14.3 

16.1 

17.8 
35.7 

53.5 

71.3 

89.2 

104 

10.4 
12.1 

13.9 

15.6 

17.3 

34.7 
52.0 

69.3 

86.7 

5 

6 

7 

8 

9 

9.02520 

9.02639 

9.02757 

9.02874 

9.02992 

9.02766 

9.02885 

9.03005 

9.03124 

9.03242 

0.97234 

0.97115 

0.96995 

0.96876 

0.96758 

9.99755 

9.99753 

9.99752 

9.99751 

9.99749 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.03109 

9.03226 

9.03342 

9.03458 

9.03574 

9.03361 

9.03479 

9.03597 

9.03714 

9.03832 

0.96639 

0.96521 

0.96403 

0.96286 

0.96168 

9.99748 

9.99747 

9.99745 

9.99744 

9.99742 

60 

49 

48 

47 

46 

15' 

16 

17 

18 
19 

9.03690 

9.03805 

9.03920 

9.04034 

9.04149 

9.03948 

9.04065 

9.04181 

9.04297 

9.04413 

0.96052 

0.95935 

0.95819 

0.95703 

0.95587 

9.99741 

9.99740 

9.99738 

9.99737 

9.99736 

45 

44 

43 

42 

41 

20 

21 

22 

23 

21 

9.04262 

9.04376 

9.04490 

9.04603 

9.04715 

9.04528 

9.04643 

9.04758 

9.04873 

9.04987 

0.95472 

0.95357 

0.95242 

0.95127 

0.95013 

9.99734 

9.99733 

9.99731 

9.99730 

9.99728 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.01828 

9.04940 

9.05052 

9.05164 

9.05275 

9.05101 

9.05214 

9.05328 

9.05441 

9.05553 

0.94899 

0.94786 

0.94672 

0.94559 

0.94447 

9.99727 

9.99726 

9.99724 

9.99723 

9.99721 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.05386 

9.05497 

9.05607 

9.05717 

9.05827 

9.05666 

9.05778 

9.05890 

9.06002 

9.06113 

0.94334 

0.94222 

0.94110 

0.93998 

0.93887 

9.99720 

9.99718 

9.99717 

9.99716 

9.99714 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.05937 

9.06046 

9.06155 

9.06264 

9.06372 

9.06224 

9.06335 

9.06445 

9.06556 

9.06666 

0.93776 
. 0.93665 
0.93555 
0.93444 
0.93334 

9.99713 

9.99711 

9.99710 

9.99708 

9.99707 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.06481 

9.06589 

9.06696 

9.06804 

9.06911 

9.06775 

9.06885 

9.06994 

9.07103 

9.07211 

0.93225 

0.93115 

0.93006 

0.92897 

0.92789 

9.99705 

9.99704 

9.99702 

9.99701 

9.99699 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.07018 

9.07124 

9.07231 

9.07337 

9.07442 

9.07320 

9.07428 

9.07536 

9.07643 

9.07751 

0.92680 

0.92572 

0.92464 

0.92357 

0.92249 

9.99698 

9.99696 

9.99695 

9.99693 

9.99692 

15 

14 

13 

12 

11 

50 

51 

52 

53 
51 

9.07548 

9.07653 

9.07758 

9.07863 

9.07968 

9.07858 

9.07964 

9.08071 

9.08177 

9.08283 

0.92142 

0.92036 

0.91929 

0.91823 

0.91717 

9.99690 

9.99689 

9.99687 

9.99686 

9.99684 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.08072 

9.08176 

9.08280 

9.08383 

9.08486 

9.08389 

9.08495 

9.08600 

9.08705 

9.08810 

0.91611 

0.91505 

0.91400 

0.91295 

0.91190 

9.99683 

9.99681 

9.99680 

9.99678 

9.99677 

5 

4 

3 

2 

1 

60 

9.08589 

9.08914 

0.91086 

9.99675 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

/ 

P.  P. 

Q3^ 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


499 


L.  Sin. 

0 

9.08589 

1 

9.08692 

2 

9.08795 

3 

9.08897 

4 

9.08999 

5 

9.09101 

6 

9.09202 

7 

9.09304 

8 

9.09405 

9 

9.09506 

10 

9.09606 

11 

9.09707 

12 

9.09807 

13 

9.09907 

14 

9.10006 

15 

9.10106 

16 

9.10205 

17 

9.10304 

18 

9.10402 

19 

9.10501 

20 

9.10599 

21 

9.10697 

22 

9.10795 

23 

9.10893 

24 

9.10990 

25 

9.11087 

26 

9.11184 

27 

9.11281 

28 

9.11377 

29 

9.11474 

30 

9.11570 

31 

9.11666 

32 

9.11761 

33 

9.11857 

34 

9.11952 

35 

9.12047 

36 

9.12142 

37 

9.12236 

38 

9.12331 

39 

9.12425 

40 

9.12519 

41 

9.12612 

42 

9.12706 

43 

9.12799 

44 

9.12892 

45 

9.12985 

46 

9.13078 

47 

9.13171 

48 

9.13263 

49 

9.13355 

50 

9.13447 

51 

9.13539 

52 

9.13630 

53 

9.13722 

54 

9.13813 

55 

9.13904 

56 

9.13994 

57 

9.14085 

58 

9.14175 

50 

9.14266 

60 

9.14356 

L.  Cos. 

d.  L.Tang.t  d.  c.  L.  Cotg. 


L.  Cos. 


P.  P. 


103 

103 

102 

102 

102 

101 

102 

101 

101 

100 

101 

100 

100 

99 

100 

99 

99 

98 

99 
98 
98 
98 
98 
97 
97 
97 
97 

96 

97 
96 
96 

95 

96 
95 
95 
95 

94 

95 
94 
94 

93 

94 
93 
93 
93 
93 
93 
92 
92 
92 
92 

91 

92 
91 
91 

90 

91 

90 

91 
90 


9.08914 

9.09019 

9.09123 

9.09227 

9.09330 

9.09434 

9.09537 

9.09640 

9.09742 

9.09845 

9.09947 

9.10049 

9.10150 

9.10252 

9.10353 

9.10454 

9.10555 

9.10656 

9.10756 

9.10856 

9.10956 

9.11056 

9.11155 

9.11254 

9.11353 

9.11452 

9.11551 

9.11649 

9.11747 

9.11845 

9.11943 

9.12040 

9.12138 

9.12235 

9.12332 

9.12428 

9.12525 

9.12621 

9.12717 

9.12813 

9.12909 

9.13004 

9.13099 

9.13194 

9.13289 

9.13384 

9.13478 

9.13573 

9.13667 

9.13761 

9.13854 

9.13948 

9.14041 

9.14134 

9.14227 

9.14320 

9.14412 

9.14504 

9.14597 

9.14688 

9.14780 

L.  Cotg. 

105 

104 

104 

103 

104 
103 
103 
102 
103 
102 
102 
101 
102 
101 
101 
101 
101 
100 
100 
100 
100 

99 

99 

99 

99 

99 

98 

98 

98 

98 

97 

98 
97 
97 

96 

97 
96 
96 
96 
96 
95 
95 
95 
95 
95 

94 

95 
94 
94 

93 

94 
93 
93 
93 
93 
92 

92 

93 

91 

92 


d.  c 


0.91086 

0.90981 

0.90877 

0.90773 

0.90670 


9.99675 

9.99674 

9.99672 

9.99670 

9.99669 


0.90566 

0.90463 

0.90360 

0.90258 

0.90155 


9.99667 

9.99666 

9.99664 

9.99663 

9.99661 


0.90053 

0.89951 

0.89850 

0.89748 

0.89647 


9.99659 

9.99658 

9.99656 

9.99655 

9.99653 


0.89546 

0.89445 

0.89344 

0.89244 

0.89144 


9.99651 

9.99650 

9.99648 

9.99647 

9.99645 


0.89044 

0.88944 

0.88845 

0.88746 

0.88647 


9.99643 

9.99642 

9.99640 

9.99638 

9.99637 


0.88548 

0.88449 

0.88351 

0.88253 

0.88155 


9.99635 

9.99633 

9.99632 

9.99630 

9.99629 


0.88057 

0.87960 

0.87862 

0.87765 

0.87668 


9.99627 

9.99625 

9.99624 

9.99622 

9.99620 


0.87572 

0.87475 

0.87379 

0.87283 

0.87187 


9.99618 

9.99617 

9.99615 

9.99613 

9.99612 


0.87091 

0.86996 

0.86901 

0.86806 

0.86711 


9.99610 

9.99608 

9.99607 

9.99605 

9.99603 


0.86616 

0.86522 

0.86427 

0.86333 

0.86239 


9.99601 

9.99600 

9.99598 

9.99596 

9.99595 


0.86146 

0.86052 

0.85959 

0.85866 

0.85773 


9.99593 

9.99591 

9.99589 

9.09588 

9.99586 


0.85680 

0.85588 

0.85496 

0.85403 

0.85312 


9.99584 

9.99582 

9.99581 

9.99579 

9.99577 


105 

104 

103 

6 

10.5 

10.4 

10.3 

7 

12.3 

12.1 

12.0 

8 

14.0 

13.9 

13.7 

9 

15.8 

15.6 

15.5 

10 

17.5 

17.3 

17.2 

20 

35.0 

34.7 

34.3 

30 

52.5 

52.0 

51.5 

40 

70.0 

69.3 

68.7 

50 

87.5 

86.7 

85.8 

102 

101 

ICO 

6 

10.2 

10.1 

10.0 

7 

11.9 

11.8 

11.7 

8 

13.6 

13.5 

13.3 

9 

15.3 

15.2 

15.0 

10 

17.0 

16.8 

16.7 

20 

34.0 

33.7 

33.3 

30 

51.0 

50.5 

50.0 

40 

68.0 

67.3 

66.7 

50 

85.0 

84.2 

83.3 

99 

9.9 

11.6 

13.2 

14.9 

16.5 

33.0 

49.5 

66.0 

82.5 


98 

9.8 

11.4 

13.1 

14.7 

16.3 

32.7 
49.0 

65.3 

81.7 


0.8522C 


9.99575 


97 

9.7 

11.3 
12.9 

14.6 
16.2 

32.3 
48.5 

64.7 


94 

9.4 

11.0 

12.5 

14.1 

15.7 

31.3 
47.0 

62.7 

78.3 


9.1 

10.6 

12.1 

13.7 

15.2 

30.3 
45.5 

60.7 

75.8 


96 

9.6 

11.2 

'12.8 

14.4 
16.0 

32.0 

48.0 

64.0 

80.0 

93 

9.3 

10.9 

12.4 

14.0 

15.5 

31.0 

46.5 

62.0 

77.5 

90 

9.0 

10.5 

12.0 

13.5 
15.0 


95 

9.5 

11.1 

12.7 

14.3 

15.8 

31.7 
47.5 

63.3 

79.2 

92 

9.2 

10.7 

12.3 

13.8 

15.3 

30.7 
46.0 

61.3 

76.7 

2 

0.2 

0.2 

0.3 

0.3 

0.3 


30.0  0.7 

45.0  1.0 

60.0  1.3 

75.0  1.7 


L.Tang. 


L.  Sin. 


P.  P. 


QZ 


500  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS, 

8° 


/ 

L.  Sin. 

0 

9.14356 

1 

9.14445 

2 

9.14535 

3 

9.14624 

4 

9.14714 

5 

9.14803 

6 

9.14891 

7 

9.14980 

8 

9.15069 

9 

9.15157 

10 

9.15245 

11 

9.15333 

12 

6.15421 

13 

9.15508 

14 

9.15596 

15 

9.15683 

16 

9.15770 

17 

9.15857 

18 

9.15944 

19 

9.16030 

20 

9.16116 

21 

9.16203 

22 

9.16289 

23 

9.16374 

24 

9.16460 

25 

9.16545 

26 

9.16631 

27 

9.16716 

28 

9.16801 

29 

9.16886 

30 

9.16970 

31 

9.17055 

32 

9.17139 

33 

9.17223 

34 

9.17307 

35 

9.17391 

36 

9.17474 

37 

9.17558 

38 

9.17641 

39 

9.17724 

40 

9.17807 

41 

9.17890 

42 

9.17973 

43 

9.18055 

44 

9.18137 

45 

9.18220 

46 

9.18302 

47 

9.18383 

48 

9.18465 

49 

9.18547 

50 

9.18628 

51 

9.18709 

52 

9.18790 

53 

9.18871 

54 

9.18952 

55 

9.19033 

56 

9.19113 

57 

9.19193 

58 

9.19273 

59 

9.19353 

60 

9.19433 

L.  Cos. 

L.Tang, 


9.14780 

9.14872 

9.14963 

9.15054 

9.15145 


9.15236 

9.15327 

9.15417 

9.15508 

9.15598 


9.15688 

9.15777 

9.15867 

9.15956 

9.16046 


9.16135 

9.16224 

9.16312 

9.16401 

9.16489 


9.16577 

9.16665 

9.16753 

9.16841 

9.16928 


9.17016 

9.17103 

9.17190 

9.17277 

9.17363 


9.17450 

9.17536 

9.17622 

9.17708 

9.17794 


9.17880 

9.17965 

9.18051 

9.18136 

9.18221. 


9.18306 

9.18391 

9.18475 

9.18560 

9.18644 


9.18728 

9.18812 

9.18896 

9.18979 

9.19063 


9.19146 

9.19229 

9.19312 

9.19395 

9.19478 


9.19561 

9.19643 

9.19725 

9.19807 

9.19889 


9.19971 


L.  Cotg. 


d.  c. 

92 

91 

91 

91 

91 

91 

90 

91 
90 
90 

89 

90 

89 

90 
89 
89 
88 
89 


88 


87 

88 
87 
87 
87 
86 
87 
86 
86 
86 
86 
86 

85 

86 
85 
85 
85 
85 

84 

85 
84 
84 
84 
84 

83 

84 
83 
83 
83 
83 
83 
83 
82 
82 
82 
82 
82 


d.  c. 


L.  Cotg. 

L.  Cos. 

0.85220 

9.99575 

60 

0.85128 

9.99574 

59 

0.85037 

9.99572 

58 

0.84946 

9.99570 

57 

0.84855 

9.99568 

56 

0.84764 

9.99566 

55 

0.84673 

9.99565 

54 

0.84583 

9.99563 

53 

0.84492 

9.99561 

52 

0.84402 

9.99559 

51 

0.84312 

9.99557 

50 

0.84223 

9.99556 

49 

0.84133 

9.99554 

48 

0.84044 

9.99552 

47 

0.83954 

9.99550 

46 

0.83865 

9.99548 

45 

0.83776 

9.99546 

44 

0.83688 

9.99545 

43 

0.83599 

9.99543 

42 

0.83511 

9.99541 

41 

0.83423 

9.99539 

40 

0.83335 

9.99537 

39 

0.83247 

9.99535 

38 

0.83159 

9.99533 

37 

0.83072 

9.99532 

36 

0.82984 

9.99530 

35 

0.82897 

9.99528 

34 

0.82810 

9.99526 

33 

0.82723 

9.99524 

32 

0.82637 

9.99522 

31 

0.82550 

9.99520 

30 

0.82464 

9.99518 

29 

0.82378 

9.99517 

28 

0.82292 

9.99515 

27 

0.82206 

9.99513 

26 

0.82120 

9.99511 

25 

0.82035 

9.99509 

24 

0.81949 

9.99507 

23 

0.81864 

9.99505 

22 

0.81779 

9.99503 

21 

0.81694 

9.93501 

2U 

0.81609 

9.99409 

19 

0.81525 

9.99497 

18 

0.81440 

9.99495 

17 

0.81356 

9.99494 

16 

0.81272 

9.99492  1 

15 

i 0.81188 

9.99490  1 

1 14 

! 0.81104 

9.99488 

13 

i 0.81021 

9.99486 

12 

! 0.80937 

9.99484 

11 

0.80854 

9.99482 

10 

0.80771 

9.99480 

9 

0.80688 

9.99478 

8 

0.80605 

9.09476 

7 

0.80522 

9.99474 

6 

0.80439 

9.99472 

5 

0.80357 

9.99470 

4 

1 0.80275 

9.99468 

3 

1 0.80193 

9.99466 

2 

0.80111 

9.99464 

1 

0.80029 

9.99462 

0 

L.Tang. 

L.  Sin. 

f 

P.  P. 


92 

9! 

6 

9.2 

9.1 

7 

10.7 

10.6 

8 

12.3 

12.1 

9 

13.8 

13.7 

10 

15.3 

15.2 

20 

30.7 

30.3 

30 

46.0 

45.5 

40 

61,3 

60.7 

50 

76.7 

75.8 

90 

9.0 

10.5 
12.0 

13.5 

15.0 

30.0 

45.0 

60.0 
75.0 


89 

8.9 

10.4 
11.9 

13.4 

]t.8 

20.7 

44.5 
59.3 

74.2 

87 

8.7 

10.2 

11.6 

13.1 

14.5 

29.0 

43.5 

58.0 

72.5 

85 

8.5 

9.9 
11.3 

12.8 

14.2 

28.3 

42.5 

56.7 

70.8 

83 

8.3 

9.7 

11.1 

12.5 

13.8 
27.7 

41.5 

55.3 
69.2 


88 

8.8 

10.3 

11.7 

13.2 

14.7 

29.3 

44.0 

58.7 

73.3 

86 

8.6 

10.0 

11.5 

12.9 

14.3 

28.7 

43.0 

57.3 

71.7 

84 

8.4 

9.8 

11.2 

12.6 

14.0 

28.0 

42.0 

56.0 

70.0 

82 

8.2 

9.6 

10.9 

12.3 

13.7 

27.3 

41.0 

54.7 

68.3 


81 

80 

2 

8.1 

8.0 

0.2 

9.5 

9.3 

0.2 

10.8 

10.7 

0.3 

12.2 

12.0 

0.3 

13.5 

13.3 

0.3 

27.0 

26.7 

0.7 

40.5 

40.0 

1.0 

54.0 

53.3 

1.3 

67.5 

66.7 

1.7 

P.  P. 


8r 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS,  501 


9° 


/ 

L.  Sin. 

0 

9.19433 

1 

9.19513 

2 

9.19592 

3 

9.19672 

4 

9.19751 

5 

9.19830 

6 

9.19909 

7 

9.19988 

8 

9.20067 

9 

9.20145 

10 

9.20223 

11 

9.20302 

12 

9.20380 

13 

9.20458 

14 

9.20535 

15 

9.20613 

16 

9.20691 

17 

9.20768 

18 

9.20845 

19 

9.20922 

20 

9.20999 

21 

9.21076 

22 

9.21153 

23 

9.21229 

24 

9.21306 

25 

9.21382 

26 

9.21458 

27 

9.21534 

28 

9.21610 

29 

9.21685 

30 

9.21761 

31 

9.21836 

32 

9.21912 

33 

9.21987 

34 

9.22062 

35 

9.22137 

36 

9.22211 

37 

9.22286 

38 

9.22361 

39 

9.22435 

40 

9.22509 

41 

9.22583 

42 

9.22657 

43 

9.22731 

44 

9.22805 

45 

9.22878 

46 

9.22952 

47 

9.23025 

48 

9.23098 

49 

9.23171 

50 

9.23244 

51 

9.23317 

52 

9.23390 

53 

9.23462 

54 

9.23535 

55 

9.23607 

56 

9.23679 

57 

9.23752 

58 

9.23823 

59 

9.23895 

60 

9.23967 

L.  Cos. 

d. 


L.Tang. 


80 

79 

80 
79 
79 
79 
79 
79 
78 

78 

79 
78 
78 

77 

78 
78 
77 
77 
77 
77 
77 
77 

76 

77 
76 
76 
76 
76 

75 

76 

75 

76 
75 
75 
75 

74 

75 
75 
74 
74 
74 
74 
74 
74 

73 

74 
73 
73 
73 
73 
73 
73 

72 

73 
72 

72 

73 

71 

72 
72 


9.19971 

9.20053 

9.20134 

9.20216 

9.20297 


9.20378 

9.20459 

9.20540 

9.20621 

9.20701 


9.20782 

9.20862 

9.20942 

9.21022 

9.21102 


d.  C. 


9.21971 

9.22049 

9.22127 

9.22205 

9.22283 


9.22361 

9.22438 

9.22516 

9.22593 

9.22670 


9.23510 

9.23586 

9.23661 

9.23737 

9.23812 


9.23887 

9.23962 

9.24037 

9.24112 

9.24186 


9.24261 

9.24335 

9.24410 

9.24484 

9.24558 


9.24632 


L.  Cotg. 


d.  c. 


L.  Cotg. 

L.  Cos. 

0.80029 

9.99462 

60 

0.79947 

9.99460 

59 

0.79866 

9.99458 

58 

0.79784 

9.99456 

57 

0.79703 

9.99454 

56 

0.79622 

9.99452 

55 

0.79541 

9.99450 

54 

0.79460 

9.99448 

53 

0.79379 

9.99446 

52 

0.79299 

9.99444 

51 

0.79218 

9.99442 

50 

0.79138 

9.99440 

49 

0.79058 

9.99438 

48 

0.78978 

9.99436 

47 

0.78898 

9.99434 

46 

0.78818 

9.99432 

45 

0.78739 

9.99429 

44 

0.78659 

9.99427 

43 

0.78580 

9.99425 

42 

0.78501 

9.99423 

41 

0.78422 

9.99421 

40 

0.78343 

9.99419 

39 

0.78264 

9.99417 

38 

0.78186 

9.99415 

37 

0.78107 

9.99413 

36 

0.78029 

9.99411 

35 

0.77951 

9.99409 

34 

0.77873 

9.99407 

33 

0.77795 

9.99404 

32 

0.77717 

9.99402 

31 

0.77639 

9.99400 

30 

0.77562 

9.99398 

29 

0.77484 

9.99396 

28 

0.77407 

9.99394 

27 

0.77330 

9.99392 

26 

0.77253 

9.99390 

25 

0.77176 

9.99388 

2^1 

0.77099 

9.99385 

23 

0.77023 

9.99383 

22 

0.76946 

9.99381 

21 

0.76870 

9.99379 

20 

0.76794 

9.99377 

19 

0.76717 

9.99375 

18 

0.76641 

9.99372 

17 

0.76565 

9.99370, 

16 

0.76490 

9.99368 

15 

0.76414 

9.99366 

14 

0.76339 

9.99364 

13 

0.76263 

9.99362 

12 

0.76188 

9.99359 

11 

0.76113 

9.99357 

10 

0.76038 

9.99355 

9 

0.75963 

9.99353 

8 

0.75888 

9.99351 

7 

0.75814 

9.99348 

6 

0.75739 

9.99346 

5 

0.75665 

9.99344 

4 

0.75590 

9.99342 

3 

0.75516 

9.99340 

2 

0.75442 

9.99337 

1 

0.75368” 

9.99335 

0 

. L.Tang, 

’ L.  Sin. 

f 

P.  P. 


82 

81 

6 

8.2 

8.1 

7 

9.6 

9.5 

8 

10.9 

10.8 

9 

12.3 

12.2 

10 

13.7 

13.5 

20 

27.3 

27.0 

30 

41.0 

40.5 

40 

54.7 

54.0 

50 

68.3 

67.5 

79 

7.9 

9.2 

10.5 
11.9 

13.2 

26.3 

39.5 

52.7 

65.8 

77 

7.7 

9.0 

10.3 

11.6 

12.8 

25.7 

38.5 

51.3 

64.2 

75 

7.5 

8.8 

10.0 

11.3 

12.5 

25.0 

37.5 

50.0 

62.5 

73 

7.3 

8.5 
9.7 

11.0 
12.2 

24.3 

36.5 

48.7 

60.8 


80 

8.0 

9.3 

10.7 
12.0 

13.3 

26.7 
40.0 

53.3 

66.7 

78 

7.8 
9.1 

10.4 

11.7 

13.0 

26.0 

39.0 

52.0 

65.0 

76 

7.6 

8.9 

10.1 

11.4 

12.7 

25.3 

38.0 

50.7 

63.3 

74 

7.4 

8.6 

9.9 

11.1 

12.3 

24.7 

37.0 

49.3 
i 61.7 

72 

7.2 

8.4 
9.6 

10.8 

12.0 

24.0 

36.0 

48.0 

60.0 


71 

3 

2 

7.1 

0.3 

0.2 

8.3 

0.4 

0.2 

9.5 

0.4 

0.3 

10.7 

0.5 

0.3 

11.8 

0.5 

0.3 

23.7 

1.0 

0.7 

35.5 

1.5 

1.0 

47.3 

2.0 

1.3 

59.2 

2.5 

1.7 

P.  P. 


90° 


502  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


10° 


f 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

P.  P. 

0 

1 

2 

3 

4 

9.23967 

9.24039 

9.24110 

9.24181 

9.24253 

72 

71 

71 

72 

71 

71 

71 

70 

71 

70 

71 

70 

70 

70 

70 

70 

70 

69 

70 

69 

69 

69 

69 

69 

69 

69 

68 

69 

68 
, 68 

68 

68 

68 

68 

68 

67 

68 

67 

67 

67 

67 

67 

67 

67 

66 

67 

66 

67 

66 

66 

66 

66 

65 

66 

66 

65 

65 

66 

65 

65 

9.24632 

9.24706 

9.24779 

9.24853 

9.24926 

74 

73 

74 

73 

74 

73 

73 

73 

73 

73 

72 

73 

72 

73 

72 

72 

72 

72 

72 

71 

72 

71 

72 

71 

71 

71 

71 

70 

71 

71 

70 

70 

71 

70 

70 

70 

70 

69 

70 

69 

70 

69 

69 

69 

69 

69 

69 

69 

68 

69 

68 

69 

68 

68 

68 

68 

67 

68 

68 

67 

0.75368 

0.75294 

0.75221 

0.75147 

0.75074 

9.99335 

9.99333 

9.99331 

9.99328 

9.99326 

60 

59 

58 

57 

56 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 

10 

. 20 
30 
40 
50 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 
10 
20 
30 
40 
50 

6 

7 

8 
9 

10 
10 
30 
40 
50 

74 

7.4 
8.6 

9.9 
11.1 

12.3 

24.7 

37.0 

49.3 

61.7 

72 

7.2 

8.4 

9.6 

10.8 

12.0 

24.0 

36.0 

48.0 

60.0 

70 

7.0 

8.2 
9.3 

10.5 

11.7 

23.3 

35.0 

46.7 

58.3 

68 

6.8 

7.9 

9.1 
10.2 

11.3 

22.7 

34.0 

45.3 

56.7 

66 

6.6 

7.7 

8.8 

9.9 

11.0 
22.0 

33.0 

44.0 

55.0 

3 

0.3 

0.4 

0.4 

0.5 

0.5 

1.0 

1.5 
2.0 

2.5 

73 

7.3 

8.5 

9.7 

11.0 

12.2 

24.3 

36.5 

48.7 

60.8 

71 

7.1 

8.3 

9.5 

10.7 

11.8 

23.7 

35.5 

47.3 

59.2 

69 

6.9 

8.1 

9.2 

10.4 

11.5 

23.0 

34.5 

46.0 

57.5 

67 

6.7 

7.8 

8.9 

10.1 

11.2 

22.3 

33.5 

44.7 

55.8 

65 

6.5 

7.6 

8.7 

9.8 

10.8 

21.7 

32.5 

43.3 

54.2 

2 

0.2 

0.2 

0.3 

0.3 

0.3 

0.7 

1.0 

1.3 

1.7 

5 

6 

7 

8 

9 

9.24324 

9.24395 

9.24466 

9.24536 

9.24607 

9.25000 

9.25073 

9.25146 

9.25219 

9.25292 

0.75000 

0.74927 

0.74854 

0.74781 

0.74708 

9.99324 

9.99322 

9.99319 

9.99317 

9.99315 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.24677 

9.24748 

9.24818 

9.24888 

9.24958 

9.25365 

9.25437 

9.25510 

9.25582 

9.25655 

0.74635 

0.74563- 

0.74490 

0.74418 

0.7434f 

9.99313 

9.99310 

9.99308 

9.99306 

9.99304 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.25028 

9.25098 

9.25168 

9.25237 

9.25307 

9.25727 

9.25799 

9.25871 

9.25943 

9.26015 

0.74273 

0.74201 

0.74129 

0.74057 

0.73985 

9.99301 

9.99299 

9.99297 

9.99294 

9.99292 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.25376 

9.25445 

9.25514 

9.25583 

9.25652 

9.26086 

9.26158 

9.26229 

9.26301 

9.26372 

0.73914 

0.73842 

0.73771 

0.73699 

0.73628 

9.99290 

9.99288 

9.99285 

9.99283 

9.99281 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.25721 

9.25790 

9.25858 

9.25927 

9.25995 

9.26443 

9.26514 

9.26585 

9.26655 

9.26726 

0.73557 

0.73486 

0.73415 

0.73345 

0.73274 

9.99278 

9.99276 

9.99274 

9.99271 

9.99269 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.26063 

9.26131 

9.26199 

9.26267 

9.26335 

9.26797 

9.26867 

9.26937 

9.27008 

9.27078 

0.73203 

0.73133 

0.73063 

0.72992 

0.72922 

9.99267 

9.99264 

9.99262 

9.99260 

9.99257 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.26403 

9.26470 

9.26538 

9.26605 

9.26672 

9.27148 

9.27218 

9.27288 

9.27357 

9.27427 

0.72852 

0.72782 

0.72712 

0.72643 

0.72573 

9.99255 

9.99252 

9.99250 

9.99248 

9.99245 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.26739 

9.26806 

9.26873 

9.26940 

9.27007 

9.27496 

9.27566 

9.27635 

9.27704 

9.27773 

0.72504 

0.72434 

0.72365 

0.72296 

0.72227 

9.99243 

9.99241 

9.99238 

9.99236 

9.99233 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.27073 

9.27140 

9.27206 

9.27273 

9.27339 

9.27842 

9.27911 

9.27980 

9.28049 

9.28117 

0.72158 

0.72089 

0.72020 

0.71951 

0.71883 

9.99231 

9.99229 

9.99226 

9.99224 

9.99221 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.27405 

9.27471 

9.27537 

9.27602 

9.27668 

9.28186 

9.28254 

9.28323 

9.28391 

9.28459 

0.71814 

0.71746 

0.71677 

0.71609 

0.71541 

9.99219 

9.99217 

9.99214 

9.99212 

9.99209 

10 

9 

8 

7 

6 

DO 

56 

57 

58 

59 

9.27734 

9.27799 

9.27864 

9.27930 

9.27995 

9.28527 

9.28595 

9.28662 

9.28730 

9.28798 

0.71473 

0.71405 

0.71338 

0.71270 

0.71202 

9.99207 

9.99204 

9.99202 

9.99200 

9.99197 

5 

4 

3 

2 

1 

60 

9.28060 

9.28865 

0.71135 

9.99195 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.T.ang. 

L.  Sin. 

/ 

P.  P. 

79° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS.  503 


11° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

P.  P. 

0 

1 

2 

3 

4 

9.28060 

9.28125 

9.28190 

9.28254 

9.28319 

65 

65 

64 

65 

65 

64 

64 

65 

64 

64 

64 

64 

63 

64 

64 

63 

63 

64 

63 

63 

63 

63 

63 

62 

63 

62 

63 

62 

62 

63 

62 

62 

61 

62 

62 

61 

62 

61 

62 

61 

61 

61 

61 

61 

61 

60 

61 

60 

61 

60 

61 

60 

60 

60 

60 

59 

60 

60 

59 

60 

9.28865 

9.28933 

9.29000 

9.29067 

9.29134 

68 

67 

G7 

67 

67 

67 

67 

67 

66 

67 

66 

67 

66 

66 

66 

66 

66 

66 

66 

65 

66 

65 

65 

66 

65 

65 

65 

65 

65 

64 

65 

64 

65 

64 

64 

65 

64 

64 

64 

64 

63 

64 

63 

64 

63 

64 

63 

63 

63 

63 

63 

63 

63 

62 

63 

62 

63 

62 

62 

62 

0.71135 

0.710C7 

0.71000 

0.70933 

0.70866 

9.99195 

9.99192 

9.99190 

9.99187 

9.99185 

60 

59 

58 

57 

56 

68 

6 6.8 

7 7.9 

8 9.1 

9 10.2 
10  11.3 
20  22.7 
30  34.0 
40  45.3 
50  56.7 

66 

6 6.6 

7 7.7 

8 8.8 

9 9.9 

10  11.0 
20  22.0 
30  33.0 
40  44.0 
50  55.0 

64 

6 6.4 

7 7.5 

8 8.5 

67 

6.7 

7.8 

8.9 

10.1 

11.2 

22.3 

33.5 

44.7 

55.8 

65 

6.5 

7.6 

8.7 

9.8 

10.8 

21.7 

32.5 

43.3 

54.2 

63 

1 6.3 
! 7.4 
! 8.4 

5 

6 

7 

8 

9 

9.28384 

9.28448 

9.28512 

9.28577 

9.28641 

9.29201 

9.29268 

9.29335 

9.29402 

9.29468 

0.70799 

0.70732 

0.70665 

0.70598 

0.70532 

9.99182 

9.99180 

9.99177 

9.99175 

9.99172 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.28705 

9.28769 

9.28833 

9.28896 

9.28960 

9.29535 

9.29601 

9.29668 

9.29734 

9.29800 

0.70465 

0.70399 

0.70332 

0.70266 

0.70200 

9.99170 

9.99167 

9.99165 

9.99162 

9.99160 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.29024 

9.29087 

9.29150 

9.29214 

9.29277 

9.29866 

9.29932 

9.29998 

9.30064 

9.30130 

0.70134 

0.70068 

0.70002 

0.69936 

0.69870 

9.99157 

9.99155 

9.99152 

9.99150 

9.99147 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.29340 

9.29403 

9.29466 

9.29529 

9.29591 

9.30195 

9.30261 

9.30326 

9.30391 

9.30457 

0.69805 

0.69739 

0.69674 

0.69609 

0.69543 

9.99145 

9.99142 

9.99140 

9.99137 

9.99135 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.29654 

9.29716 

9.29779 

9.29841 

9.29903 

9.30522 

9.30587 

9.30652 

9.30717 

9.30782 

0.69478 

0.69413 

0.69348 

0.69283 

0.69218 

0.69154 

0.69089 

0.69025 

0.68960 

0.68896 

9.99132 

9.99130 

9.99127 

9.99124 

9.99122 

35 

34 

33 

32 

31 

y y.t)  y.o 

10  10.7  10.5 

20  21.3  21.0 

30  32.0  31.5 

40  42.7  42,0 
.fsn  .P.9 

30 

31 

32 

33 

34 

9.29966 

9.30028 

9.30090 

9.30151 

9.30213 

9.30846 

9.30911 

9.30975 

9.31040 

9.31104 

9.99119 

9.99117 

9.99114 

9.99112 

9.99109 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

62 

6 6.2 

7 7.2 

8 8.3 

9 9.3 
10  10.3 
20  20.7 
30  31.0 
40  41.3 
50  51.7 

60 

6 6.0 

7 7.0 

8 8.0 

9 9.0 
10  10.0 
20  20.0 
30  30.0 
40  40.0 
50  50.0 

3 

6 0.3 

7 0.4 

8 0.4 

9 0.5 

10  0.5 

20  1.0 

30  1.5 

40  2.0 

50  2.5 

61 

6.1 

7.1 

8.1 

9.2 

10.2 

20.3 

30.5 

40.7 

50.8 

59 

5.9 

6.9 

7.9 

8.9 

9.8 

19.7 

29.5 

39.3 

49.2 

2 

0.2 

0.2 

0.3 

0.3 

0.3 

0.7 

1.0 

1.3 

1.7 

35 

36 

37 

38 

39 

9.30275 

9.30336 

9.30398 

9.30459 

9.30521 

9.31168 

9.31233 

9.31297 

9.31361 

9.31425 

0.68832 

0.68767 

0.68703 

0.68639 

0.68575 

9.99106 

9.99104 

9.99101 

9.99099 

9.99096 

40 

41 

42 

43 

44 

9.30582 

9.30643 

9.30704 

9.30765 

9.30826 

9.31489 

9.31552 

9.31616 

9.31679 

9.31743 

0.68511 

0.68448 

0.68384 

0.68321 

0.68257 

9.99093 

9.99091 

9.99088 

9.99086 

9.99083 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.30887 

9.30947 

9.31008 

9.31068 

9.31129 

9.31806 

9.31870 

9.31933 

9.31996 

9.32059 

0.68194 

0.68130 

0.68067 

0.68004 

0.67941 

9.99080 

9.99078 

9.99075 

9.99072 

9.99070 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

50 

51 

52 

53 

54 

9.31189 

9.31250 

9.31310 

9.31370 

9.31430 

9.32122 

9.32185 

9.32248 

9.32311 

9.32373 

0.67878 

0.67815 

0.67752 

0.67689 

0.67627 

9.99067 

9.99064 

9.99062 

9.99059 

9.99056 

55 

56 

57 

58 

59 

9.31490 

9.31549 

9.31609 

9.31669 

9.31728 

9.32436 

9.32498 

9.32561 

9.32623 

9.32685 

0.67564 

0.67502 

0.67439 

0.67377 

0.67315 

9.99054 

9.99051 

9.99048 

9.99046 

9.99043 

5 

4 

3 

2 

1 

60 

9.31788 

9.32747 

0.67253 

9.99040 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin: 

' 

P.  P. 

78‘ 


504  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


12° 


t 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

P.  P. 

0 

9.31788 

9.32747 

0.67253 

9.99040 

60 

1 

9.31847 

59 

9.32810 

63 

0.67190 

9.99038 

59 

06 

62 

2 

9.31907 

60 

9.32872 

62 

0.67128 

9.99035 

58 

6 

6.3 

6.2 

3 

9.31966 

59 

9.32933 

61 

0.67067 

9.99032 

57 

7 

7.4 

7.2 

4 

9.32025 

59 

59 

9.32995 

62 

62 

0.67005 

9.99030 

56 

8 

9 

8.4 

9.5 

8.3 

9.3 

5 

9.32084 

9.33057 

0.66943 

9.99027 

55 

10 

io!5 

io!3 

6 

9.32143 

59 

9.33119 

62 

0.66881 

9.99024 

54 

20 

21.0 

20.7 

7 

9.32202 

59 

9.33180 

61 

0.66820 

9.99022 

53 

30 

31.5 

31.0 

8 

9.32261 

59 

9.33242 

62 

0.66758 

9.99019 

52 

40 

42.0 

41.3 

9 

9.32319 

58 

59 

9.33303 

61 

62 

0.66697 

9.99016 

51 

50 

52.5 

51.7 

10 

9.32378 

9.33365 

0.66635 

9.99013 

50 

11 

9.32437 

59 

9.33426 

61 

0.66574 

9.99011 

49 

61 

60 

12 

9.32495 

58 

9.33487 

61 

0.66513 

9.99008 

48 

6 

6.1 

6.0 

13 

9.32553 

58 

9.33548 

61 

0.66452 

9.99005 

47 

7 

7.1 

7.0 

14 

9.32612 

59 

9.33609 

61 

0.66391 

9.99002 

46 

8 

8.1 

8.0 

61 

o 

o o 

Q A 

15 

9.32670 

9.33670 

0.66330 

9.99000 

45 

y 

10 

v.Z 

10.2 

y.u- 

10.0 

16 

9.32728 

58 

9.33731 

61 

0.66269 

9.98997 

44 

20 

20.3 

20.0 

17 

9.32786 

58 

9.33792 

61 

0.66208 

9.98994 

43 

30 

30.5 

30  0 

18 

9.32844 

58 

9.33853 

61 

0.66147 

9.98991 

42 

40 

40.7 

40.0 

19 

9.32902 

58 

9.33913 

60 

61 

0.66087 

9.98989 

41 

50 

5o!8 

50.0 

20 

9.32960 

9.33974 

0.66026 

9.98986 

40 

21 

9.33018 

58 

9.34034 

60 

0.65966 

9.98983 

39 

59 

22 

9.33075 

57 

9.34095 

61 

0.65905 

9.98980 

38 

6 

5.9 

23 

9.33133 

58 

9.34155 

60 

0.65845 

9.98978 

37 

7 

6.9 

24 

9.33190 

57 

9.34215 

60 

61 

0.65785 

9.98975 

36 

8 

7.9 

25 

9.33248 

9.34276 

0.65724 

9.98972 

35 

9 

8.9 

26 

9.33305 

57 

9.34336 

60 

0.65664 

9.98969 

34 

10 

9.8 

27 

9.33362 

57 

9.34396 

60 

0.65604 

9.98967 

33 

20 

19.7 

28 

9.33420 

58 

9.34456 

60 

0.65544 

9.98964 

32 

30 

29.5 

29 

9.33477 

57 

9.34516 

60 

60 

0.65484 

9.98961 

31 

40 

50 

39.3 

dQ  9 

30 

9.33534 

Ol 

9.34576 

0.65424 

9.98958 

30 

31 

9.33591 

57 

9.34635 

59 

0.65365 

9.98955 

29 

58 

57 

32 

9.33647 

56 

9.34695 

60 

0.65305 

9.98953 

28 

6 

5.8 

5.7 

33 

9.33704 

57 

9.34755 

60 

0.65245 

9.98950 

27 

7 

6.8 

6.7 

34 

9.33761 

57 

9.34814 

59 

60 

0.65186 

9.98947 

26 

8 

7.7 

7.6 

35 

9.33818 

O/ 

9.34874 

0.65126 

9.98944 

25 

9 

1 8.7 

8.6 

36 

9.33874 

56 

9.34933 

59 

0.65067 

9.98941 

24 

10 

9.7 

9.5 

37 

9.33931 

57 

9.34992 

59 

0.65008 

9.98938 

23 

20 

19.3 

19.0 

38 

9.33987 

56 

9.35051 

59 

0.64949 

9.98936 

22 

30 

29.0 

28.5 

39 

9.34043 

56 

57  i 

9.35111 

60 

59 

0.64889 

9.98933 

21 

40 

50 

38.7 

AO  O 

38.0 

47.5 

40 

9.34100 

9.35170 

0.64830 

9.98930 

20 

41 

9.34156 

56 

9.35229 

59 

0.64771 

9.98927 

19 

56 

55 

42 

9.34212 

56 

9.35288 

59 

0.64712 

9.98924 

18 

6 

5.6 

5.5 

43 

9.34268 

56 

9.35347 

59 

0.64653 

9.98921 

17 

7 

6.5 

6.4 

44 

9.34324 

56 

56 

9.35405 

58 

59  . 

0.64595 

9.98919 

16 

8 

7.5 

7.3 

45 

9.34380 

9.35464 

0.64536 

9.98916 

15 

9 

8.4 

8.3 

46 

9.34436 

56 

9.35523 

59 

0.64477 

9.98913 

14 

10 

9.3 

9.2 

47 

9.34491 

55 

9.35581 

58 

0.64419 

9.98910 

13 

20 

18.7 

18.3 

48 

9.34547 

56 

9.35640 

59 

0.64360 

9.98907 

12 

30 

28.0 

27.5 

49 

9.34602 

55 

9.35698 

58 

0,64302 

9.98904 

11 

40 

37.3 

36.7 

56 

59 

50 

45.8 

50 

9.34658 

9.35757 

0.64243 

9.98901 

10 

51 

9.34713 

55 

9.35815 

58 

0.64185 

9.98898 

9 

2 

52 

9.34769 

56 

9.35873 

58 

0.64127 

9.98896 

8 

6 

0.3 

0.2 

53 

9.34824 

55 

9.35931 

58 

0.64069 

9.98893 

7 

7 

0 4 

0 2 

54 

9.34879 

55 

55 

9.35989 

58 

58 

0.64011 

9.98890 

6 

8 

0.4 

0.3 

55 

9.34934 

9.36047 

0.63953 

9.98887 

5 

9 

0.5 

0.3 

56 

9.34989 

55 

9.36105 

58 

0.63895 

9.98884 

4 

10 

0.5 

0.3 

57 

9.35044 

55 

9.36163 

58 

0.63837 

9.98881 

3 

20 

1.0 

0.7 

58 

9.35099 

55 

9.36221 

58 

0.63779 

9.98878 

2 

30 

1.5 

1.0 

59 

9.35154 

55 

55 

9.36279 

58 

57 

0.63721 

9.98875 

1 

40 

2.0 

1.3 

60 

9.35209 

9.36336 

0.63664 

9.98872 

0 

50 

2.5 

1.7 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

f 

P.  P. 

77° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS,  505 


13° 


! 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

P.  P. 

0 

9.35209 

9.36336 

0.63664 

9.98872 

60 

1 

9.35263 

54 

9.36394 

58 

0.63606 

9.98869 

59 

QO 

57 

2 

9.35318 

55 

9.36452 

58 

0.63548 

9.98867 

58 

6 

5.8 

5.7 

3 

9.35373 

55 

9.36509 

57 

0.63491 

9.98864 

57 

7 

6.8 

6.7 

4 

9.35427 

54 

54 

9.36566 

57 

Pift 

0.63434 

9.98861 

56 

8 

9 

7.7 

8.7 

7.6 

8.6 

5 

9.35481 

9.36624 

0.63376 

9.98858 

55 

10 

9.7 

9.b 

6 

9.35536 

55 

9.36681 

57 

0.63319 

9.98855 

54 

20 

19.3 

19.0 

7 

9.35590 

54 

9.36738 

57 

0.63262 

9.98852 

53 

30 

29.0 

28.5 

8 

9.35644 

54 

9.36795 

57 

0.63205 

9.98849 

52 

40 

38.7 

38.0 

9 

9.35698 

54 

54 

9.36852 

57 

57 

0.63148 

9.98846 

51 

50 

48.3 

47.5 

10 

9.35752 

9.36909 

0.63091 

9.98843 

50 

11 

9.35806 

54 

9.36966 

57 

0.63034 

9.98840 

49 

56 

55 

12 

9.35860 

54 

9.37023 

57 

0.62977 

9.98837 

48 

6 

5.6 

5.5 

13 

9.35914 

54 

9.37080 

57 

0.62920 

9.98834 

47 

7 

6.5 

6.4 

14 

9.35968 

54 

9.37137 

57 

0.62863 

9.98831 

46 

8 

7.5 

7.3 

54 

56 

Q 

ft  A 

8.3 

9.2 

15 

9.36022 

9.37193 

0.62807 

9.98828 

45 

10 

o.A 

9.3 

16 

9.36075 

53 

9.37250 

57 

0.62750 

9.98825 

44 

20 

18.7 

18.3 

17 

9.36129 

54 

9.37306 

56 

0.62694 

9.98822 

43 

30 

28.0 

27.5 

18 

9.36182 

53 

9.37363 

57 

0.62637 

9.98819 

42 

40 

37.3 

36.7 

19 

9.36236 

54 

63 

9.37419 

56 

0.62581 

9.98816 

41 

60 

46!7 

45!8 

20 

9.36289 

9.37476 

0.62524 

9.98813 

40 

21 

9.36342 

53 

9.37532 

56 

0.62468 

9.98810 

39 

54 

22 

9.36395 

. 53 

9.37588 

56 

0.62412 

9.98807 

38 

6 

5.4 

23 

9.36449 

54 

9.37644 

56 

0.62356 

9.98804 

37 

7 

6.3 

24 

9.36502 

53 

53 

9.37700 

56 

0.62300 

9.98801 

36 

8 

7.2 

25 

9.36555 

9.37756 

0.62244 

9.98798 

35 

9 

8.1 

26 

9.36608 

53 

9.37812 

56 

0.62188 

9.98795 

34 

lU 

9.0 

27 

9.36660 

5l2 

9.37868 

56 

0.62132 

9.98792 

33 

20 

18.0 

28 

9.36713 

53 

9.37924 

56 

0.62076 

9.98789 

32 

30 

27.0 

29 

9.36766 

53 

53 

9.37980 

56 

55 

0.62020 

9.98786 

31 

40 

36.0 

0 

30 

9.36819 

9.38035 

0.61965 

9.98783 

30 

31 

9.36871 

52 

9.38091 

56 

0.61909 

9.98780 

29 

53 

52 

32 

9.36924 

53 

9.38147 

56- 

0.61853 

9.98777 

28 

6 

5.3 

5.2 

33 

9.36976 

52 

9.38202 

55 

0.61798 

9.98774 

27 

7 

6.2 

6.1 

34 

9.37028 

52 

53 

9.38257 

55 

56 

0.61743 

9.98771 

26 

8 

7.1 

6.9 

35 

9.37081 

9.38313 

0.61687 

9.98768 

25 

9 

8.0 

7.8 

36 

9.37133 

52 

9.38368 

55 

0.61632 

9.98765 

24 

10 

8.8 

8.7 

37 

9.37185 

52 

9.38423 

55 

0.61577 

9.98762 

23 

20 

17.7 

17.3 

38 

9.37237 

52 

9.38479 

56 

0.61521 

9.98759 

22 

30 

26.5 

26.0 

39 

9.37289 

52 

52 

9.38534 

55 

55 

0.61466 

9.98756 

21 

40 

60 

35.3 

AA  O 

34.7 

43.3 

40 

9.37341 

9.38589 

0.61411 

9.98753 

20 

•At 

41 

9.37393 

52 

9.38644 

55 

0.61356 

9.98750 

19 

51 

4 

42 

9.37445 

52 

9.38699 

55 

0.61301 

9.98746 

18 

6 

5.1 

0.4 

43 

9.37497 

52 

9.38754 

55 

0.61246 

9.987^. 

17 

7 

6.0 

o!5 

44 

9.37549 

52 

51 

9.38808 

54 

55 

0.61192 

9.98740 

16 

8 

6.8 

0.5 

45 

9.37600 

9.38863 

0.61137 

9.98737 

15 

9 

7.7 

0.6 

46 

9.37652 

52 

9.38918 

55 

0.61082 

9.98734 

14 

10 

8.5 

0.7 

47 

9.37703 

51 

9.38972 

54 

0.61028 

9.98731 

13 

20 

17.0 

1.3 

48 

9.37755 

52 

9.39027 

55 

0.60973 

9.98728 

12 

30 

25.5 

2.0 

49 

9.37806 

51 

52 

9.39082 

55 

54 

0.60918 

9.98725 

11 

40 

34.0 

2.7 

50 

9.37858 

9.39136 

0.60864 

9.98722 

10 

50 

42.5 

3.3 

51 

9.37909 

51 

9.39190 

54 

0.60810 

9.98719 

9 

a 

9 

52 

9.37960 

51 

9.39245 

55 

0.60755 

9.98715 

8 

6 

0.3 

0.2 

53 

9.38011 

51 

9.39299 

54 

0.60701 

9.98712 

7 

7 

0*4 

0*2 

54 

9.38062 

51 

51 

9.39353 

54 

54 

0.60647 

9.98709 

6 

8 

o!4 

o!3 

55 

9.38113 

9.39407 

0.60593 

9.98706 

5 

9 

0.5 

0.3 

56 

9.38164 

51 

9.39461 

54 

0.60539 

9.98703 

4 

10 

0.5 

0.3 

57 

9.38215 

51 

9.39515 

54 

0.60485 

9.98700 

3 

20 

1.0 

0.7 

58 

9.38266 

51 

9.39569 

54 

0.60431 

9.98697 

2 

30 

1.5 

1.0 

59 

9.38317 

51 

51 

9.39623 

54 

54 

0.60377 

9.98694 

1 

40 

2.0 

1.3 

60 

9.38368 

9.39677 

0.60323 

9.98690 

0 

50 

2.5 

1.7 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

/ 

P.  P. 

76' 


606 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

140 


' 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

9.38368 

9.39677 

0.60323 

9.98690 

60 

1 

9.38418 

50 

9.39731 

54 

0.60269 

9.98687 

3 

59 

2 

9.38469 

51 

9.39785 

54 

0.60215 

9.98684 

3 

58 

54 

3 

9.38519 

50 

9.39838 

53 

0.60162 

9.98681 

3 

57 

53 

4 

9.38570 

51 

50 

9.39892 

54 

53 

0.60108 

9.98678 

3 

g 

56 

6 

7 

5.4 

6.3 

5.3 

6.2 

h 

9.38620 

9.39945 

0.60055 

9.98675 

55 

8 

7.2 

7.1 

6 

9.38670 

50 

9.39999 

54 

0.60001 

9.98671 

4 

54 

9 

8.1 

8.0 

7 

9.38721 

51 

9.40052 

53 

0.59948 

9.98668 

3 

53 

10 

9 0 

8.8 

8 

9.38771 

50 

9.40106 

54 

0.59894 

9.98665 

3 

52 

20 

18.0 

17.7 

9 

9.38821 

50 

50 

9.40159 

53 

53 

0.59841 

9.98662 

3 

3 

51 

30 

27.0 

26.5 

10 

9.38871 

9.40212 

0.59788 

9.98659 

50 

40 

36.0 

35.3 

11 

9.38921 

50 

9.40266 

54 

0.59734 

9.98656 

3 

49 

50 

45.0 

44.2 

12 

9.38971 

50 

9.40319 

53 

0.59681 

9.98652 

4 

48 

13 

9.39021 

50 

9.40372 

53 

0.59628 

9.98649 

3 

47 

14 

9.39071 

50 

50 

9.40425 

53 

53 

0.59575 

9.98646 

3 

3 

46 

52 

51 

15 

9.39121 

9.40478 

0.59522 

9.98643 

45 

6 

5.2 

5.1 

16 

9.39170 

49 

9.40531 

53 

0.59469 

9.98640 

3 

44 

7 

6.1 

6.0 

17 

9.39220 

50 

9.40584 

53 

0.59416 

9.98636 

4 

43 

8 

6.9 

6.8 

18 

9.39270 

50 

9.40636 

0.59364 

9.98633 

3 

42 

9 

7.8 

7.7 

19 

9.39319 

49 

50 

9.40689 

. 53 

53 

0.59311 

9.98630 

3 

3 

41 

10 

8.7 

8.5 

20 

9.39369 

9.40742 

0.59258 

9.98627 

40 

20 

17.3 

17.0 

21 

9.39418 

49 

9.40795 

53 

0.59205 

9.98623 

4 

39 

30 

26.0 

25.5 

22 

9.39467 

49 

9.40847 

52 

0.59153 

9.98620 

3 

38 

40 

34.7 

34.0 

23 

9.39517 

50 

9.40900 

53 

0.59100 

9.98617 

3 

37 

50 

43.3 

42.5 

24 

9.39566 

49 

9.40952 

52 

0.59048 

9.98614 

3 

36 

49 

53 

25 

9.39615 

9.41005 

0.58995 

9.98610 

35 

26 

9.39664 

49 

9.41057 

5^ 

0.58943 

9.98607 

3 

34 

50 

49 

27 

9.39713 

49 

9.41109 

52 

0.58891 

9.98604 

3 

33 

6 

5.0 

4.9 

28 

9.39762 

49 

9.41161 

52 

0.58839 

9.98601 

3 

32 

7 

5.8 

5.7 

29 

9.39811 

49 

49 

9.41214 

53 

52 

0.58786 

9.98597 

4 

3 

31 

8 

6.7 

6.5 

30 

9.39860 

9.41266 

0.58734 

9.98594 

30 

9 

7.5 

/ .4 

31 

9.39909 

49 

9.41318 

52 

0.58682 

9.98591 

3 

29 

10 

8.3 

8.2 

32 

9.39958 

49 

9.41370 

52 

0.58630 

9:98588 

3 

28 

20 

16.7 

16.3 

33 

9.40006 

48 

9.41422 

52 

0.58578 

9.98584 

4 

27 

30 

25.0 

24.5 

34 

9.40055 

49 

48 

9.41474 

52 

52 

0.58526 

9.98581 

3 

3 

26 

40 

50 

33.3 

41.7 

32.7 

40.8 

35 

9.40103 

^1526 

0.58474 

9.98578 

25 

36 

9.40152 

49 

9.41578 

52 

0.58422 

9.98574 

4 

24 

37 

9.40200 

48 

9.41629 

51 

0.58371 

9.98571 

3 

23 

38 

9.40249 

49 

9.41681 

52 

0.58319 

9.98568 

3 

22 

48 

47 

39 

9.40297 

48 

9.41733 

52 

0.58267 

9.98565 

3 

21 

6 

4.8 

4.7 

49 

51 

n 

40 

9.40346 

9.41784 

0.58216 

9.98561 

20 

/ 

g 

0.0 

6.4 

0.0 

6.3 

41 

9.40394 

48 

9.41836 

52 

0.58164 

9.98558 

3 

19 

9 

7.2 

7.1 

42 

9.40442 

48 

9.41887 

51 

0.58113 

9.98555 

3 

18 

10 

8.0 

7.8 

43 

^.40490 

48 

9.41939 

52 

0.58061 

9.98551 

4 

17 

20 

16.0 

15]7 

44 

9.40538 

48 

48 

9.41990 

51 

51 

0.58010 

9.98548 

3 

3 

16 

30 

24!o 

23!5 

45 

9.40586 

9.42041 

0.57959 

9.98545 

15 

40 

32.0 

31.3 

46 

9.40634 

48 

9.42093 

52 

0.57907 

9.98541 

4 

14 

50 

40.0 

39.2 

47 

9.40682 

48 

9.42144 

51 

0.57856 

9.98538 

3 

13 

48 

9.40730 

48 

9.42195 

51 

0.57805 

9.98535 

3 

12 

49 

9.40778 

48 

47 

9.42246 

51 

51 

0.57754 

9.98531 

4 

3 

11 

4 

3 

50 

9.40825 

9.42297 

0.57703 

9.98528 

10 

6 

0.4 

0.3 

51 

9.40873 

48 

9.42348 

51 

0.57652 

9.98525 

3 

9 

7 

0.5 

0.4 

52 

9.40921 

48 

9.42399 

51 

0.57601 

9.98521 

4 

8 

8 

0.5 

0.4 

53 

9.40968 

47 

9.42450 

51 

0.57550 

9.98518 

3 

7 

9 

1 

0.6 

0.5 

54 

9.41016 

48 

47 

9.42501 

51 

51 

0.57499 

9.98515 

8 

4 

6 

10 

0.7 

0.5 

55 

9.41063 

9.42552 

0.57448 

9.98511 

5 

20 

1.3 

1.0 

56 

9.41111 

48 

9.42603 

51 

0.57397 

9.98508 

3 

4 

30 

2.0 

1.5 

57 

9.41158 

47 

9.42653 

50 

0.57347 

9.98505 

3 

3 

40 

2.7 

2.0 

58 

9.41205 

47 

9.42704 

51 

0.57296 

9.98501 

4 

2 

50 

3.3 

2.5 

59 

9.41252 

47 

48 

9.42755 

51 

50 

0.57245 

9.98498 

3 

4 

1 

60 

9.41300 

9.42805 

0.57195 

9.98494 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  g7 

L.Tang. 

L.  Sin. 

d. 

/ 

P.  P. 

75^^ 


507 


. LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


15° 


L.  Sin. 

d. 

L.Tang. 

d.  c. 

|L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

9.41300 

9.42805 

0.57195 

9.98494 

60 

1 

9.41347 

47 

9.42856 

51 

0.57144 

9.98491 

3 

59 

2 

9.41394 

47 

9.42906 

50 

0.57094 

9.98488 

3 

58 

3 

9.41441 

47 

9.42957 

51 

0.57043 

9.98484 

4 

57 

51 

50 

4 

9.41488 

47 

47 

9.43007 

50 

50 

0.56993 

9.98481 

3 

4 

56 

6 

7 

5.1 

6.0 

5.0 

5.8 

5 

9.41535 

9.43057 

0.56943 

9.98477 

55 

8 

6.8 

6.7 

6 

9.41582 

47 

9.43108 

51 

0.56892 

9.98474 

3 

54 

9 

7.7 

7.5 

7 

9.41628 

46 

9.43158 

50 

0.56842 

9.98471 

3 

53 

10 

8.5 

8.3 

8 

9.41675 

47 

9.43208 

50 

0.56792 

9.98467 

4 

52 

20 

17.0 

16.7 

9 

9.41722 

47 

9.43258 

50 

0.56742 

9.98464 

3 

4 

51 

30 

25.5 

25.0 

10 

9.41768 

9.43308 

0.56692 

9.98460 

50 

40 

34.0 

33.3 

11 

9.41815 

47 

9.43358 

50 

0.56642 

9.98457 

3 

49 

50 

42.5 

41.7 

12 

9.41861 

46 

9.43408 

50 

0.56592 

9.98453 

4 

48 

13 

9.41908 

47 

9.43458 

50 

0.56542 

9.98450 

3 

47 

14 

9.41954 

46 

47 

9.43508 

50 

50 

0.56492 

9.98447 

3 

4 

46 

49 

48 

15 

9.42001 

9.43558 

0.56442 

9.98443 

45 

6 

4.9 

4.8 

16 

9.42047 

46 

9.43607 

49 

0.56393 

9.98440 

3 

44 

7 

5.7 

5.6 

17 

9.42093 

46 

9.43657 

50 

0.56343 

9.98436 

4 

43 

8 

6.5 

6.4 

18 

9.42140 

47 

9.43707 

50 

0.56293 

9.98433 

3 

42 

9 

7.4 

7.2 

19 

9.42186 

46 

46 

9.43756 

49 

0.56244 

9.98429 

4 

3 

41 

10 

8.2 

8.0 

20 

9.42232 

9.43806 

0.56194 

9.98426 

40 

20 

16.3 

16.0 

21 

9.42278 

46 

9.43855 

49 

0.56145 

9.98422 

4 

39 

30 

24.5 

24.0 

22 

9.42324 

46 

9.43905 

50 

0.56095 

9.98419 

3 

38 

40 

32.7 

32.0 

23 

9.42370 

46 

9.43954 

49 

0.56046 

9.98415 

4 

37 

50 

40.8 

40.0 

24 

9.42416 

46 

45 

9.44004 

50 

49 

0.55996 

9.98412 

3 

3 

36 

25 

9.42461 

9.44053 

0.55947 

9.98409 

35 

26 

9.42507 

46 

9.44102 

49 

0.55898 

9.98405 

4 

34 

47 

46 

27 

9.42553 

46 

9.44151 

49 

0.55849 

9.98402 

3 

33 

6 

4.7 

4.6 

28 

9.42599 

46 

9.44201 

50 

0.55799 

9.98398 

4 

32 

7 

5.5 

5.4 

29 

9.42644 

45 

46 

9.44250 

49 

49 

0.55750 

9.98395 

3 

4 

31 

8 

6.3 

6.1 

30 

9.42690 

9.44299 

0.55701 

9.98391 

30 

9 

7.1 

6.9 

31 

9.42735 

45 

9.44348 

49 

0.55652 

9.98388 

3 

29 

10 

7.8 

7.7 

32 

9.42781 

46 

9.44397 

49 

0.55603 

9.98384 

4 

28 

20 

15.7 

15.3 

33 

9.42826 

45 

9.44446 

49 

0.55554 

9.98381 

3 

27 

30 

23.5 

23.0 

34 

9.42872 

46 

45 

9.44495 

49 

49 

0.55505 

9.98377 

4 

4 

26 

40 

50 

31.3 

39.2 

30.7 

38.3 

35 

9.42917 

9.44544 

0.55456 

9.98373 

25 

36 

9.42962 

45 

9.44592 

48 

0.55408 

9.98370 

3 

24 

37 

9.43008 

46 

9.44641 

49 

0.55359 

9.98366 

4 

23 

38 

9.43053 

45 

9.44690 

49 

0.55310 

9.98363 

3 

22 

45 

44 

39 

9.43098 

45 

45 

9.44738 

48 

49 

0.55262 

9.98359 

4 

3 

21 

6 

7 

4.5 

K Q 

4.4 

40 

9.43143 

9.44787 

0.55213 

9.98356 

20 

/ 

3 

0.0 

6.0 

0.1 

5.9 

41 

9.43188 

45 

9.44836 

49 

0.55164 

9.98352 

4 

19 

9 

6.8 

6.6 

42 

9.43233 

45 

9.44884 

48 

0.55116 

9.98349 

3 

18 

10 

7^5 

7.3 

43 

9.43278 

45 

9.44933 

49 

0.55067 

9.98345 

4 

17 

20 

15.0 

14.7 

44 

9.43323 

45 

44 

9.44981 

48 

48 

0.55019 

9.98342 

3 

4 

16 

so 

22.5 

22!o 

45 

9.43367 

9.45029 

0.54971 

9.98338 

15 

40 

30.0 

29.3 

46 

9.43412 

45 

9.45078 

49 

0.54922 

9.98334 

4 

14 

50 

37.5 

36.7 

47 

9.43457 

45 

9.45126 

48 

0.54874 

9.98331 

3 

13 

48 

9.43502 

45 

9.45174 

48 

0.54826 

9.98327 

4 

12 

49 

9.43546 

44 

45 

9.45222 

48 

49 

0.54778 

9.98324 

3 

4 

11 

4 

3 

50 

9.43591 

9.45271 

0.54729 

9.98320 

10 

6 

0.4 

0.3 

51 

9.43635 

44 

9.45319 

48 

0.54681 

9.98317 

3 

9 

7 

0.5 

0.4 

52 

9.43680 

45 

9.45367 

48 

0.54633 

9.98313 

4 

8 

8 

0.5 

0.4 

53 

9.43724 

44 

9.45415 

48 

0.54585 

9.98309 

4 

7 

9 

0.6 

0.5 

54 

9.43769 

45 

44 

9.45463 

48 

48 

0.54537 

9.98306 

3 

4 

6 

10 

0.7 

0.5 

55 

9.43813 

9.45511 

0.54489 

9.98302 

5 

20 

1.3 

1.0 

56 

9.43857 

44 

9.45559 

48 

0.54441 

9.98299 

3 

4 

30 

2.0 

1.5 

57 

9.43901 

44 

9.45606 

47 

0.54394 

9.98295 

4 

3 

40 

2.7 

2.0 

58 

9.43946 

45 

9.45654 

48 

0.54346 

9.98291 

4 

2 

50 

3.3 

2.5 

59 

9.43990 

44 

44 

9.45702 

48 

48 

0.54298 

9.98288 

3 

4 

1 

60 

9.44034 

9.45750 

0.54250 

9.98284 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

' 

P.  P. 

74° 


508  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


16° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

9.44034 

9.45750 

0.54250 

9.98284 

60 

1 

9.44078 

44 

9.45797 

47 

0.54203 

9.98281 

3 

59 

2 

9.44122 

44 

9.45845 

48 

0.54155 

9.98277 

4 

58 

3 

9.44166 

44 

9.45892 

47 

0.54108 

9.98273 

4 

57 

48 

47 

4 

9.44210 

44 

43 

9.45940 

48 

0.54060 

9.98270 

3 

56 

6 

7 

4.8 

5.6 

4.7 

5.5 

5 

9.44253 

9.45987 

0.54013 

9.98266 

55 

8 

6!4 

6!3 

6 

9.44297 

44 

9.46035 

48 

0.53965 

9.98262 

4 

54 

9 

7.2 

7.1 

7 

9.44341 

44 

9.46082 

47 

0.53918 

9.98259 

3 

53 

10 

8.0 

7.8 

8 

9.44385 

44 

9.46130 

48 

0.53870 

9.98255 

4 

52 

20 

16.0 

15.7 

9 

9.44428 

43 

44 

9.46177 

47 

0.53823 

9.98251 

4 

3 

51 

30 

24.0 

23.5 

10 

9.44472 

9.46224 

0.53776 

9.98248 

50 

40 

32.0 

31.3 

11 

9.44516 

44 

9.46271 

47 

0.53729 

9.98244 

4 

49 

50 

40.0 

39.2 

12 

9.44559 

43 

9.46319 

48 

0.53681 

9.98240 

4 

48 

13 

9.44602 

43 

9.46366 

47 

0.53634 

9.98237 

3 

47 

14 

9.44646 

44 

43 

9.46413 

47 

0.53587 

9.98233 

4 

4 

46 

46 

45 

15 

9.44689 

9.46460 

0.53540 

9.98229 

45 

6 

4.6 

4.5 

16 

9.44733 

44 

9.46507 

47 

0.53493 

9.98226 

3 

44 

7 

5.4 

5.3 

17 

9.44776 

43 

9.46554 

47 

0.53446 

9.98222 

4 

43 

8 

6.1 

6.0 

18 

9.44819 

43 

9.46601 

47 

0.53399 

9.98218 

4 

42 

9 

6.9 

6.8 

19 

9.44862 

43 

9.46648 

47 

0.53352 

9.98215 

3 

4 

41 

10 

7.7 

7.5 

20 

9.44905 

9.46694 

0.53306 

9.98211 

40 

20 

15.3 

15.0 

21 

9.44948 

43 

9.46741 

47 

0.53259 

9.98207 

4 

39 

30 

23.0 

22.5 

22 

9.44992 

44 

9.46788 

47 

0.53212 

9.98204 

3 

38 

40 

30.7 

30.0 

23 

9.45035 

43 

9.46835 

47 

0.53165 

9.98200 

4 

37 

50 

38.3 

37.5 

24 

9.45077 

42 

9.46881 

46 

0.53119 

9.98196 

4 

36 

43 

47 

A 

25 

9.45120 

9.46928 

0.53072 

9.98192 

35 

26 

9.45163 

43 

9.46975 

47 

0.53025 

9.98189 

3 

34 

44 

43 

27 

9.45206 

43 

9.47021 

46 

0.52979 

9.98185 

4 

33 

6 

4.4 

4.3 

28 

9.45249 

43 

9.47068 

47 

0.52932 

9.98181 

4 

32 

7 

5.1 

5.0 

29 

9.45292 

43 

9.47114 

46 

0.52886 

9.98177 

4 

31 

8 

5.9 

5.7 

AO 

46 

o 

6.6 

6.5 

30 

9.45334 

9.47160 

0.52840 

9.98174 

o 

30 

9 

31 

9.45377 

43 

9.47207 

47 

0.52793 

9.98170 

4 

29 

10 

7.3 

7.2 

32 

9.45419 

42 

9.47253 

46 

0.52747 

9.98166 

4 

28 

20 

14.7 

14.3 

33 

9.45462 

43 

9.47299 

46 

0.52701 

9.98162 

4 

27 

30 

22.0 

21.5 

34 

9.45504 

42 

43 

9.47346 

47 

0.52654 

9.98159 

3 

4 

26 

40 

50 

29.3 

36.7 

28.7 

35.8 

35 

9.45547 

9.47392 

4o 

0.52608 

9.98155 

25 

36 

9.45589 

42 

9.47438 

46 

0.52562 

9.98151 

4 

24 

37 

9.45632 

43 

9.47484 

46 

0.52516 

9.98147 

4 

23 

38 

9.45674 

42 

9.47530 

46 

0.52470 

9.98144 

3 

22 

42 

41 

39 

9.45716 

42 

9.47576 

46 

0.52424 

9.98140 

4 

21 

6 

4.2 

4.1 

42 

A 

7 

A Q 

A S 

40 

9.45758 

9.47622 

4;0 

0.52378 

9.98136 

20 

/ 

3 

5.6 

5.5 

41 

9.45801 

43 

9.47668 

46 

0.52332 

9.98132 

4 

19 

g 

6.3 

6.2 

42 

9.45843 

42 

9.47714 

• 46 

0.52286 

9.98129 

3 

18 

10 

7!o 

6^8 

43 

9.45885 

42 

9.47760 

46 

0.52240 

9.98125 

4 

17 

20 

14!o 

13]  7 

44 

9.45927 

42 

AO 

9.47806 

46 

0.52194 

9.98121 

4 

4 

16 

30 

21.0 

2o!5 

45 

9.45969 

9.47852 

0.52148 

9.98117 

15 

40 

28.0 

27.3 

46 

9.46011 

42 

9.47897 

45 

0.52103 

9.98113 

4 

14 

50 

35.0 

34.2 

47 

9.46053 

42 

9.47943 

46 

0.52057 

9.98110 

3 

13 

48 

9.46095 

42 

9.47989 

46 

0.52011 

9.98106 

4 

12 

49 

9.46136 

41 

42 

9.48035 

46 

45 

0.51965 

9.98102 

4 

4 

11 

4 

3 

50 

9.46178 

9.48080 

0.51920 

9.98098 

10 

6 

0.4 

0.3 

51 

9.46220 

42 

9.48126 

46 

0.51874 

9.98094 

4 

9 

7 

0^5 

0.4 

52 

9.46262 

42 

9.48171 

45 

0.51829 

9.98090 

4 

8 

8 

0.5 

0.4 

53 

9.46303 

41 

9.48217 

46 

0.51783 

9.98087 

3 

7 

9 

0.6 

0.5 

54 

9.46345 

42 

41 

9.48262 

45 

45 

0.51738 

9.98083 

4 

4 

6 

10 

0.7 

0.5 

55 

9.46386 

9.48307 

0.51693 

9.98079 

5 

20 

1.3 

1.0 

56 

9.46428 

42 

8.48353 

46 

0.51(>47 

9.98075 

4 

4 

30 

2.0 

1.5 

57 

9.46469 

41 

9.48398 

45 

0.51602 

9.98071 

4 

3 

40 

2.7 

2.0 

58 

9.46511 

42 

9.48443 

45 

0.51557 

9.98067 

4 

2 

50 

3.3 

2.5 

59 

9.46552 

41 

42 

9.48489 

46 

45 

0.51511 

9.98063 

4 

3 

1 

60 

9.46594 

9.48534 

0.51466 

9.98060 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.  P. 

73' 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

170 


509 


/ 

L.  Sin. 

0 

9.46594 

1 

9.46635 

2 

9.46676 

3 

9.46717 

4 

9.46758 

5 

9.46800 

6 

9.46841 

7 

9.46882 

8 

9.46923 

9 

9.46964 

10 

9.47005 

11 

9.47045 

12 

9.47086 

13 

9.47127 

14 

9.47168 

15 

9.47209 

16 

9.47249 

17 

9.47290 

18 

9.47330 

19 

9.47371 

20 

9.47411 

21 

9.47452 

22 

9.47492 

23 

9.47533 

24 

9.47573 

25 

9.47613 

26 

9.47654 

27 

9.47694 

28 

9.47734 

29 

9.47774 

30 

9.47814 

31 

9.47854 

32 

9.47894 

33 

9.47934 

34 

9.47974 

35 

9.48014 

36 

9.48054 

37 

9.48094 

38 

9.48133 

39 

9.48173 

40 

9.48213 

41 

9.48252 

42 

9.48292 

43 

9.48332 

44 

9.48371 

45 

9.48411 

46 

9.48450 

47 

9.48490 

48 

9.48529 

49 

9.48568 

50 

9.48607 

51 

9.48647 

52 

9.48686 

53 

9.48725 

54 

9.48764 

55 

9.48803 

56 

9.48842 

57 

9.48881 

58 

9.48920 

59 

9.48959 

60 

9.48998 

L.  Cos. 

L.Tang. 

9.48534 

9.48579 

9.48624 

9.48669 

9.48714 

9.48759 

9.48804 

9.48849 

9.48894 

9.48939 

9.48984 

9.49029 

9.49073 

9.49118 

9.49163 

9.49207 

9.49252 

9.49296 

9.49341 

9.49385 

9.49430 

9.49474 

9.49519 

9.49563 

9.49607 

9.49652 

9.49696 

9.49740 

9.49784 

9.49828 

9.49872 

9.49916 

9.49960 

9.50004 

9.50048 

9.50092- 

9.50136 

9.50180 

9.50223 

9.50267 

9.50311 

9.50355 

9.50398 

9.50442 

9.50485 

9.50529 

9.50572 

9.50616 

9.50659 

9.50703 

9.50746 

9.50789 

9.50833 

9.50876 

9.50919 

9.50962 

9.51005 

9.51048 

9.51092 

9.51135 

9.51178 

Cotg; 

d.  c. 


L.  Cotg. 


L.  Cos. 


P.  P. 


45 

45 

45 

45 

45 

45 

45 

45 

45 

45 

45 

44 

45 
45 

44 

45 

44 

45 

44 

45 

44 

45 
44 

44 

45 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 

43 

44 
44 
44 

43 

44 

43 

44 

43 

44 

43 

44 
43 

43 

44 
43 
43 
43 
43 

43 

44 
43 
43 

d.  c. 


0.51466 

0.51421 

0.51376 

0.51331 

0.51286 

0.51241 

0.51196 

0.51151 

0.51106 

0.51061 


9.98060 

9.98056 

9.98052 

9.98048 

9.98044 

9.98040 

9.98036 

9.98032 

9.98029 

9.98025 


0.51016 

0.50971 

0.50927 

0.50882 

0.50837 


9.98021 

9.98017 

9.98013 

9.98009 

9.98005 


0.50793 

0.50748 

0.50704 

0.50659 

0.50615 


9.98001 

9.97997 

9.97993 

9.97989 

9.97986 


0.50570 

0.50526 

0.50481 

0.50437 

0.50393 


9.97982 

9.97978 

9.97974 

9.97970 

9.97966 


0.50348 

0.50304 

0.50260 

0.50216 

0.50172 


9.97962 

9.97958 

9.97954 

9.97950 

9.97946 


0.50128 

0.50084 

0.50040 

0.49996 

0.49952 


9.97942 

9.97938 

9.97934 

9.97930 

9.97926 


0.49908 

0.49864 

0.49820 

0.49777 

0.49733 


9.97922 

9.97918 

9.97914 

9.97910 

9.97906 


0.49689 

0.49645 

0.49602 

0.49558 

0.49515 


9.97902 

9.97898 

9.97894 

9.97890 

9.97886 


0.49471 

0.49428 

0.49384 

0.49341 

0.49297 


9.97882 

9.97878 

9.97874 

9.97870 

9.97866 


0.49254 

0.49211 

0.49167 

0.49124 

0.49081 


9.97861 

9.97857 

9.97853 

9.97849 

9.97845 


0.49038 

0.48995 

0.48952 

0.48908 

0.48865 


9.97841 

9.97837 

9.97833 

9.97829 

9.97825 


0.48822 

L.Tang. 


L.  Sin. 


45 

4.5 
5.3 
6.0 
6.8 

7.5 

15.0 

22.5 

30.0 

37.5 


4.4 

5.1 

5.9 

6.6 

7.3 

14.7 
22.0 
29.3 

36.7 


43 

4.3 

5.0 

5.7 

6.5 

7.2 

14.3 

21.5 

28.7 

35.8 


42 

4.2 
4.9 
5.6 

6.3 
7.0 

14.0 

21.0 
28.0 
35.0 


40 

4.0 

4.7 
5.3 

6.0 

6.7 

13.3 
20.0 
26.7 

83.3 


41 

4.1 

4.8 
5.5 

6.2 

6.8 
13.7 

20.5. 

27.3 

34.2 


39 

3.9 
4.6 
5.2 

5.9 
6.5 

13.0 

19.5 

26.0 

32.5 


11 

5 

4 

3 

10 

6 

0.5 

0.4 

0.3 

9 

7 

0.6 

0.5 

0.4 

8 

8 

0.7 

0.5 

0.4 

7 

9 

0.8 

0.6 

0.5 

6 

10 

0.8 

0.7 

0.5 

5 

20 

1.7 

1.3 

1.0 

4 

30 

2.5 

2.0 

1.5 

3 

40 

3.3 

2.7 

2.0 

2 

50 

4.2 

3.3 

2.5 

1 

0 

' 

P.  P. 

7r 


510 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

18° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

0 

9.48998 

9.51178 

0.48822 

9.97821 

1 

9.49037 

39 

9.51221 

43 

0.48779 

9.97817 

2 

9.49076 

39 

9.51264 

43 

0.48736 

9.97812 

3 

9.49115 

39 

9.51306 

42 

0.48694 

9.97808 

4 

9.49153 

38 

39 

9.51349 

43 

43 

0.48651 

9.97804 

5 

9.49192 

9.51392 

0.48608 

9.97800 

6 

9.49231 

39 

9.51435 

43 

0.48565 

9.97796 

7 

9.49269 

38 

9.51478 

43 

0.48522 

9.97792 

8 

9.49308 

39 

9.51520 

42 

0.48480 

9.97788 

9 

9.49347 

39 

38 

9.51563 

43 

43 

0.48437 

9.97784 

10 

9.49385 

9.51606 

0.48394 

9.97779 

11 

9.49424 

39 

9.51648 

42 

0.48352 

9.97775 

12 

9.49462 

38 

9.51691 

43 

0.48309 

9.97771 

13 

9.49500 

38 

9.51734 

43 

0.48266 

9.97767 

14 

9.49539 

39 

38 

9.51776 

42 

43 

0.48224 

9.97763 

15 

9.49577 

9.51819 

0.48181 

9.97759 

16 

9.49615 

38 

9.51861 

42 

0.48139 

9.97754 

17 

9.49654 

39 

9.51903 

42 

0.48097 

9.97750 

18 

9.49692 

38 

9.51946 

43 

0.48054 

9.97746 

19 

9.49730 

38 

38 

9.51988 

42 

43 

0.48012 

9.97742 

20 

9.49768 

9.52031 

0.47969 

9.97738 

21 

9.49806 

38 

9.52073 

42 

0.47927 

9.97734 

22 

9.49844 

38 

9.52115 

42 

0.47885 

9.97729 

23 

9.49882 

38 

9.52157 

42 

0.47843 

9.97725 

24 

9.49920 

38 

38 

9.52200 

43 

42 

0.47800 

9.97721 

25 

9.49958 

9.52242 

0.47758 

9.97717 

26 

9.49996 

38 

9.52284 

42 

0.47716 

9.97713 

27 

9.50034 

38 

9.52326 

42 

0.47674 

9.97708 

28 

9.50072 

38 

9.52368 

42 

0.47632 

9.97704 

29 

9.50110 

38 

38 

9.52410 

42 

42 

0.47590 

9.97700 

30 

9.50148 

9.52452 

0.47548 

9.97696 

31 

9.50185 

37 

9.52494 

42 

0.47506 

9.97691 

32 

9.50223 

38 

9.52536 

42 

0.47464 

9.97687 

33 

9.50261 

38 

9.52578 

42 

0.47422 

9.97683 

34 

9.50298 

37 

38 

9.52620 

42 

41 

0.47380 

9.97679 

35 

9.50336 

9.52661 

0.47339 

9.97674 

36 

9.50374 

38 

9.52703 

42 

0.47297 

9.97670 

37 

9.50411 

37 

9.52745 

42 

0.47255 

9.97666 

38 

9.50449 

38 

9.52787 

42 

0.47213 

9.97662 

39 

9.50486 

37 

37 

9.52829 

42 

41 

0.47171 

9.97657 

40 

9.50523 

9.52870 

0.47130 

9.97653 

41 

9.50561 

38 

9.52912 

42 

0.47088 

9.97649 

42 

9.50598 

37 

9.52953 

41 

0.47047 

9.97645 

43 

9.50635 

37 

9.52995 

42 

0.47005 

9.97640 

44 

9.50673 

38 

37 

9.53037 

42 

41 

0.46963 

9.97636 

45 

9.50710 

9.53078 

0.46922 

9.97632 

46 

9.50747 

37 

9.53120 

42 

0.46880 

9.97628 

47 

9.50784 

37 

9.53161 

41 

0.46839 

9.97623 

48 

9.50821 

37 

9.53202 

41 

0.46798 

9.97619 

49 

9.50858 

37 

38 

9.53244 

42 

41 

0.46756 

9.97615 

50 

9.50896 

9.53285 

0.46715 

9.97610 

51 

9.50933 

37 

9.53327 

42 

0.46673 

9.97606 

52 

9.50970 

37 

9.53368 

41 

0.46632 

9.97602 

53 

9.51007 

37 

9.53409 

41 

0.46591 

9.97597 

54 

9.51043 

36 

37 

9.53450 

41 

42 

0.46550 

9.97593 

55 

9.51080 

9.53492 

0.46508 

9.97589 

56 

9.51117 

37 

9.53533 

41 

0.46467 

9.97584 

57 

9.51154 

37 

9.53574 

41 

0.46426 

9.97580 

58 

9.51191 

37 

9.53615 

41 

0.46385 

9.97576 

59 

9.51227 

36 

37 

9.53656 

41 

41 

0.46344 

9.97571 

60 

9.51264 

9.53697 

0.46303 

9.97567 

Cos. 

d. 

L.  Cotg. 

d.  e. 

'L.Tang. 

L.  Sin. 

P.  P. 


43 

4.3 

5.0 

5.7 

6.5 

7.2 

14.3 

21.5 

28.7 

35.8 


42 

4.2 
4.9 
5.6 

6.3 
7.0 

14.0 

21.0 
28.0 
35.0 


4f 

4.1 

4.8 
5.5 

6.2 

6.8 
13.7 
20.5 
27.3 
34.2 


39 

3.9 
4.6 
5.2 

5.9 
6.5 

13.0 

19.5 

26.0 

32.5 


37 

3.7 

4.3 

4.9 

5.6 

6.2 

12.3 

18.5 

24.7 

30.8 


5 

6 0.5 

7 0.6 

8 0.7 

9 0.8 
10  0.8 
20  I 1.7 
30  I 2.5 
40  i 3.3 
50  I 4.2 


38 

3.8 

4.4 

5.1 

5.7 

6.3 

12.7 
19.0 
25.3 

31.7 


36 

3.6 

4.2 

4.8 

5.4 

6.0 

12.0 

18.0 

24.0 

30.0 


4 

0.4 

0.5 

0.5 

0.6 

0.7 

1.3 
2.0 
2.7 

3.3 


P.  P. 


71° 


LOGARITUm  OF  TRIGONOMETRIC  FUNCTIONS.  511 


19° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P 

.P, 

0 

9.51264 

9.53697 

0.46303 

9.97567 

60 

1 

9.51301 

37 

9.53738 

41 

0.46262 

9.97563 

4 

59 

2 

9.51338 

37 

9.53779 

41 

0.46221 

9.97558 

5 

58 

3 

9.51374 

36 

9.53820 

41 

0.46180 

9.97554 

4 

57 

41 

40 

4 

9.51411 

37 

36 

9.53861 

41 

41 

0.46139 

9.97550 

4 

56 

6 

7 

4.1 

4.8 

4.0 

4.7 

5 

9.51447 

9.53902 

0.46098 

9.97545 

D 

55 

8 

5!5 

6 

9.51484 

37 

9.53943 

41 

0.46057 

9.97541 

4 

54 

9 

6.2 

6.0 

7 

9.51520 

36 

9.53984 

41 

0.46016 

9.97536 

5 

53 

10 

6.8 

6.7 

8 

9.51557 

37 

9.54025 

41 

0.45975 

9.97532 

4 

52 

20 

13.7 

13.3 

9 

9.51593 

36 

36 

9.54065 

40 

41 

0.45935 

9.97528 

4 

51 

30 

20.5 

20.0 

10 

9.51629 

9.54106 

0.45894 

9.97523 

O 

50 

40 

27.3 

26.7 

11 

9.51666 

37 

9.54147 

41 

0.45853 

9.97519 

4 

49 

50 

34.2 

33.3 

12 

9.51702 

36 

9.54187 

40 

0.45813 

9.97515 

4 

48 

13 

9.51738 

36 

9.54228 

41 

0.45772 

9 97510 

5 

47 

14 

9.51774 

36 

37 

9.54269 

41 

40 

0.45731 

9.97506 

4 

46 

39 

15 

9.51811 

9.54309 

0.45691 

9.97501 

0 

45 

6 

3.9 

16 

9.51847 

36 

9.54350 

41 

0.45650 

9.97497 

4 

44 

7 

4.6 

17 

9.51883 

36 

9.54390 

40 

0.45610 

9.97492 

5 

43 

8 

6.2 

18 

9.51919 

36 

9.54431 

41 

0.45569 

9.97488 

4 

42 

9 

5.9 

19 

9.51955 

36 

36 

9.54471 

40 

41 

0.45529 

9.97484 

4 

41 

10 

6.5 

20 

9.51991 

9.54512 

0.45488 

9.97479 

D 

40 

20 

13.0 

21 

9.52027 

36 

9.54552 

40 

0.45448 

9.97475 

4 

39 

30 

19.5 

22 

9.52063 

36 

9.54593 

41 

0.45407 

9.97470 

5 

38 

40 

26.0 

23 

9.52099 

36 

9.54633 

40 

0.45367 

9.97466 

4 

37 

60 

32.5 

24 

9.52135 

36 

36 

9.54673 

40 

41 

0.45327 

9.97461 

5 

A 

36 

25 

9.52171 

9.54714 

0.45286 

9.97457 

35 

26 

9.52207 

36 

9.54754 

40 

0.45246 

9.97453 

4 

84 

37 

36 

27 

9.52242 

35 

9.54794 

40 

0.45206 

9.97448 

5 

33 

6 

3.7 

3.6 

28 

9.52278 

36 

9.54835 

41 

0.45165 

9.97444 

4 

32 

7 

4.3 

4.2 

29 

9.52314 

36 

9.54875 

40 

0.45125 

9.97439 

5 

31 

8 

4.9 

4.8 

36 

40 

A 

5.4 

A A 

9.52350 

9.54915 

0.45085 

9.97435 

30 

y 

1 A 

u.o 
A 0 

31 

9.52385 

35 

9.54955 

40 

0.45045 

9.97430 

5 

29 

lU 

9A 

o.z 

19  ^ 

O.U 

19  A 

32 

9.52421 

36 

9.54995 

40 

0.45005 

9.97426 

4 

28 

QA 

i-Z.O 

1 ft 

jLZ.U 

1 ft  A 

33 

9.52456 

35 

9.55035 

40 

0.44965 

9.97421 

5 

27 

oU 

A(\ 

±0.0 
24  7 

lo.U 
OA  A 

34 

9.52492 

36 

35 

9.55075 

40 

40 

0.44925 

9.97417 

4 

5 

26 

4:U 

60 

3o!8 

30.0 

35 

9.52527 

9.55115 

0.44885 

9.97412 

25 

36 

9.52563 

36 

9.55155 

40 

0.44845 

9.97408 

4 

24 

37 

9.52598 

35 

9.55195 

40 

0.44805 

9.97403 

5 

23 

38 

9.52634 

36 

9 55235 

40 

0.44765 

9.97399 

4 

22 

69 

34 

39 

9.52669 

35 

36 

9.55275 

40 

0.44725 

9.97394 

5 

4 

21 

6 

7 

3.5 

4.1 

3.4 

4.0 

40 

9.52705 

9.55315 

0.44685 

9.97390 

20 

8 

4!7 

4!5 

41 

9.52740 

35 

9.55355 

40 

0.44645 

9.97385 

5 

19 

9 

5.3 

5.1 

42 

9.52775 

35 

9.55395 

40 

0.44605 

9.97381 

4 

18 

10 

5.8 

5.7 

43 

9.52811 

36 

9.55434 

39 

0.44566 

9.97376 

5 

17 

20 

11  7 

11.3 

44 

9.52846 

35 

35 

9.55474 

40 

40 

0.44526 

9.97372 

4 

5 

16 

30 

17.5 

17.0 

45 

9.52881 

9.55514 

0.44486 

9.97367 

15 

40 

23.3 

22.7 

46 

9.52916 

35 

9.55554 

40 

0.44446 

9.97363 

4 

14 

50 

29.2 

28.3 

47 

9.52951 

35 

9.55593 

39 

0.44407 

9.97358 

5 

13 

48 

9.52986 

35 

9.55633 

40 

0.44367 

9.97353 

5 

12 

49 

9.53021 

35 

35 

9.55673 

40 

0.44327 

9.97349 

4 

5 

11 

5 

4 

50 

9.53056 

9.55712 

0.44288 

9.97344 

SO 

6 

0.5 

0.4 

51 

9.53092 

36 

9.55752 

40 

0.44248 

9.97340 

4 

9 

7 

0.6 

0.5 

52 

9.53126 

34 

9.55791 

39 

0.44209 

9.97335 

5 

8 

8 

0.7 

0.5 

53 

9.53161 

35 

9.55831 

40 

0.44169 

9.97331 

4 

7 

9 

0.8 

0.6 

54 

9.53196 

35 

35 

9.55870 

39 

40 

0.44130 

9.97326 

5 

4 

6 

10 

0.8 

0.7 

55 

9.53231 

9.55910 

0.44090 

9.97322 

5 

20 

1.7 

1.3 

56 

9.53266 

35 

9.55949 

39 

0.44051 

9.97317 

5 

4 

30 

2.5 

2.0 

57 

9.53301 

35 

9.55989 

40 

0.44011 

9.97312 

5 

3 

40 

3.3 

2.7 

58 

9.53336 

35 

9.56028 

39 

0.43972 

9.97308 

4 

2 

50 

4.2 

3.3 

59 

9.53370 

34 

35 

9.56067 

39 

40 

0.43933 

9.97303 

5 

4 

1 

60 

9.53405 

9.56107 

0.43893 

9.97299 

0 

L.  Cos. 

~d.' 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

' 

P.  P. 

70^ 


512 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

200 


/ 

L.  Sin. 

0 

9.53405 

1 

9.53440 

2 

9.53475 

3 

9.53509 

4 

9.63544 

5 

9.53578 

6 

9.53613 

7 

9.53647 

8 

9.53682 

9 

9.53716 

10 

9.53751 

11 

9.53785 

12 

9.53819 

13 

9.53854 

14 

9.53888 

15 

9.53922 

16 

9.53957 

17 

9.53991 

18 

9.54025 

19 

9.54059 

20 

9.54093 

21 

9.54127 

22 

9.54161 

23 

9.54195 

24 

9.54229 

25 

9.54263 

26 

9.54297 

27 

9.54331 

28 

9.54365 

29 

9.54399 

30 

9.54433 

31 

9.54466 

32 

9.54500 

33 

9.54534 

34 

9.54567 

35 

9.54601 

36 

9.54635 

37 

9.54668 

38 

9.54702 

39 

9.54735 

40 

9.54769 

41 

9.54802 

42 

9.54836 

43 

9.54869 

44 

9.54903 

45 

9.54936 

46 

9.54969 

47 

9.55003 

48 

9.55036 

49 

9.55069 

50 

9.55102 

51 

9.55136 

52 

9.55169 

53 

9.55202 

54 

9.55235 

55 

9.55268 

56 

9.55301 

57 

9.55334 

58 

9.55367 

59 

9.55100 

60 

9.55433 

L.  Cos. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

9.56107 

0.43893 

9.97299 

60 

9.56146 

39 

0.43854 

9.97294 

5 

59 

9.56185 

39 

0.43815 

9.97289 

5 

58 

9.56224 

39 

0.43776 

9.97285 

4 

57 

4U 

39 

9.56264 

40 

0.43736 

9.97280 

5 

A 

56 

6 

7 

4.0 

4.7 

3.9 

4.6 

9.56303 

0.43697 

9.97276 

55 

8 

5^3 

5.2 

9.56342 

39 

0.43658 

9.97271 

5 

54 

9 

6.0 

5.9 

9.56381 

39 

0.43619 

9.97266 

5 

53 

To 

6.7 

6.5 

9.56420 

39 

0.43580 

9.97262 

4 

52 

‘JO 

13.3 

13.0 

9.56459 

39 

39 

0.43541 

9.97257 

5 

51 

30 

20.0 

19.5 

9.56498 

0.43502 

"9.97252 

o 

50 

40 

26.7 

26.0 

9.56537 

39 

0.43463 

9.97248 

4 

49 

50 

33.3 

32.5 

9.56576 

39 

0.43424 

9.97243 

6 

48 

9.56615 

39 

0.43385 

9.97238 

5 

47 

9.56654 

39 

39 

0.43346 

9.97234 

4 

PL 

46 

38 

37 

9.56693 

0.43307 

9.97229 

O 

45 

6 

3.8 

3.7 

9.56732 

39 

0.43268 

9.97224 

5 

44 

7 

4.4 

4.3 

9.56771 

39 

0.43229 

9.97220 

4 

43 

8 

5.1 

4.9 

9.56810 

39 

0.43190 

9.97215 

5 

42 

9 

5.7 

5.6 

9.56849 

39 

0.43151 

9.97210 

5 

A 

41 

10 

6.3 

6.2 

9.5^887 

0.43113 

9.97206 

'± 

40 

20 

12.7 

12.3 

9.56926 

39 

0.43074 

9.97201 

5 

39 

30 

19.0 

18.5 

9.56965 

39 

0.43035 

9.97196 

5 

38 

40 

25.3 

24.7 

9.57004 

39 

0.42996 

9.97192 

4 

37 

50 

31.7 

30.8 

9.57042 

38 

39 

0.42958 

9.97187 

6 

36 

9.57081 

0.42919 

9.97182 

o 

35 

9.57120 

39 

0.42880 

9.97178 

4 

34 

35 

9.57158 

38 

0.42842 

9.97173 

5 

33 

6 

3.5 

9.57197 

39 

0.42803 

9.97168 

5 

32 

7 

4.1 

9.57235 

38 

39 

0.42765 

9.97163 

5 

A 

31 

8 

4.7 

9.57274 

0.42726 

9.97159 

30 

y 

in 

5.3 

K Q 

9.57312 

38 

0.42688 

9.97154 

5 

29 

lU 

on 

O.o 

117 

9.57351 

39 

0.42649 

9.97149 

5 

28 

on 

11.  / 

17 

9.57389 

38 

0.42611 

9.97145 

4 

27 

ou 

An 

1/ .D 

OQ  Q 

9.57428 

39 

QQ 

0.42572 

9.97140 

5 

r; 

26 

Zo.o 

90  9 

9.57466 

OO 

0.42534 

9.97135 

0 

25 

9.57504 

38 

0.42496 

9.97130 

6 

24 

9.57543 

39 

0.42457 

9.97126 

4 

23 

9.57581 

38 

0.42419 

9.9712] 

5 

22 

34 

33 

9.57619 

38 

0.42381 

9.97116 

5 

5 

21 

6 

7 

3.4 

4.0 

3.3 

3.9 

9.57658 

oy 

0.42342 

9.97111 

20 

8 

4!5 

4^4 

9.57696 

38 

0.42304 

9.97107 

4 

19 

9 

5.1 

5.0 

9.57734 

38 

0.42266 

9.97102 

6 

18 

10 

5.7 

5.5 

9.57772 

38- 

0.42228 

9.97097 

5 

17 

20 

11.3 

11.0 

9.57810 

38 

QQ 

0.42190 

9.97092 

5 

5 

16 

30 

17.0 

16.5 

9.57849 

Oif 

0.42151 

9.97087 

15 

40 

22.7 

22.0 

9.57887 

38 

0.42113 

9.97083 

4 

14 

60 

28.3 

27.5 

9.57925 

38 

0.42075 

9.97078 

5 

13 

9.57963 

38 

0.42037 

9.97073 

5 

12 

9.58001 

38 

0.41999 

9.97068 

5 

5 

11 

1 

4 

9.58039 

OO 

0.41961 

9.97063 

10 

6 

0.5 

0.4 

9.58077 

38 

0.41923 

9.97059 

4 

9 

7 

0.6 

0.5 

9.58115 

38 

0.41885 

9.97054 

5 

8 

8 

0.7 

0.5 

9.58153 

38 

0.41847 

9.97049 

6 

7 

9 

0.8 

0.6 

9.58191 

38 

0.41809 

9.97044 

6 

5 

6 

10 

0.8 

0.7 

9.58229 

OO 

0.41771' 

9.97039- 

5 

20 

1.7 

1.3 

9.58267 

38 

0.41733 

9.97035 

4 

4 

30 

2.5 

2.0 

9.58304 

37 

0.41696 

9.97030 

5 

3 

40 

3.3 

2.7 

9.58342 

38 

0.41658 

9.97025 

5 

2 

50 

4.2 

3.3 

9.58380 

38 

38 

0.41620 

9.97020 

5 

5 

1 

9.58418 

0.41582 

9.97015 

0 

L.  Cotg. 

L.Tang. 

I..  Sin. 

“dr 

' 

P, 

. P. 

d. 


d. 


^9° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

21° 


518 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

0 

9.55433 

9.58418 

0.41582 

9.97015 

60 

1 

9.55466 

33 

9.58455 

37 

0.41545 

9.97010 

5 

59 

2 

9.55499 

33 

9.58493 

38 

0.41507 

9.97005 

5 

58 

3 

9.55532 

33 

9.58531 

38 

0.41469 

9.97001 

4 

57 

4 

9.55564 

32 

9.58569 

38 

37 

0.41431 

9.96996 

5 

5 

56 

5 

9.55597 

9.58606 

0.41394 

9.96991 

55 

6 

9.55630 

33 

9.58644 

38 

0.41356 

9.96986 

5 

54 

7 

9.55663 

33 

9.58681 

37 

0.41319 

9.96981 

5 

53 

8 

9.15695 

32 

9.58719 

o8 

0.41281 

9.96976 

5 

52 

9 

9.55728 

33 

33 

9.58757 

38 

37 

0.41243 

9.96971 

5 

5 

51 

10 

9.55761 

9.58794 

0.41206 

9.96966 

50 

11 

9.55793 

32 

9.58832 

38 

0.41168 

9.96962 

4 

49 

12 

9.55826 

33 

9.58869 

37 

0.41131 

9.96957 

5 

48 

13 

9.55858 

32 

9.58907 

38 

0.41093 

9.96952 

5 

47 

14 

9.55891 

33 

9.58944 

37 

37 

0.41056 

9.96947 

5 

5 

46 

15 

9.55923 

9.58981 

0.41019 

9.96942 

45 

16 

9.55956 

33 

9.59019 

38 

0.40981 

9.96937 

5 

44 

17 

9.55988 

32 

9.59056 

37 

0.40944 

9.96932 

5 

43 

18 

9.56021 

33 

9.59094 

38 

0.40906 

9.96927 

5 

42 

19 

9.56053 

32 

32 

9.59131 

37 

37 

0.40869 

9.96922 

5 

5 

41 

20 

9.56085 

9.59168 

0.40832 

9.96917 

40 

21 

9.56118 

33 

9.59205 

37 

0.40795 

9.96912 

5 

39 

22 

9.56150 

32 

9.59243 

38 

0.40757 

9.96907 

5 

38 

23 

9.56182 

32 

9.59280 

37 

0.40720 

9.96903 

4 

37 

24 

9.56215 

33 

32 

9.59317 

37 

37 

0.40683 

9.96898 

5 

5 

36 

25 

9.56247 

9.59354 

0.40646 

9.96893 

35 

26 

9.56279 

32 

9.59391 

37 

0.40609 

9.96888 

5 

34 

27 

9.56311 

32 

9.59429 

38 

0.40571 

9.96883 

5 

33 

28 

9.56343 

32 

9.59466 

37 

0.40534 

9.96878 

5 

32 

29 

9.56375 

32 

9.59503 

37 

37 

0.40497 

9.96873 

5 

5 

31 

30 

9.56408 

oo 

9.59540 

0.40460 

9.96868 

30 

31 

9.56440 

32 

9.59577 

37 

0.40423 

9.96863 

5 

29 

32 

9.56472 

32 

9.59614 

37 

0.40386 

9.96858 

5 

28 

33 

9.56504 

32 

9.59651 

37 

0.40349 

9.96853 

5 

27 

34 

9.56536 

32 

Q9 

9.59688 

37 

37 

0.40312 

9.96848 

5 

5 

26 

35 

9.56568 

Oii 

9.59725 

0.40275 

9.96843 

25 

36 

9.56599 

31 

9.59762 

37 

0.40238 

9.96838 

5 

24 

37 

9.56631 

32 

9.59799 

37 

0.40201 

9.96833 

5 

23 

38 

9.56663 

32 

9.59835 

36 

0.40165 

9.96828 

5 

22 

39 

9.56695 

32 

32 

9.59872 

37 

37 

0.40128 

9.96823 

5 

5 

21 

40 

9.56727 

9.59909 

0.40091 

9.96818 

20 

41 

9.56759 

32 

9.59946 

37 

0.40054 

9.96813 

5 

19 

42 

9.56790 

31 

9.59983 

37 

0.40017 

9.96808 

5 

18 

43 

9.56822 

32 

9.60019 

36 

0.39981 

9.96803 

5 

17 

44 

9.56854 

32 

32 

9.60056 

37 

37 

0.39944 

9.96798 

5 

5 

16 

45 

9.56886 

9.60093 

0.39907 

9.96793 

15 

46 

9.56917 

31 

9.60130 

37 

0.39870 

9.96788 

5 

14 

47 

9.56949 

32 

9.60166 

36 

0.39834 

9.96783 

5 

13 

48 

9.56980 

31 

9.60203 

37 

0.39797 

9.96778 

5 

12 

49 

9.57012 

32 

32 

9.60240 

37 

36 

0.39760 

9.96772 

6 

5 

11 

50 

9.57044 

9.60276 

0.39724 

9.96767 

10 

51 

9.57075 

31 

9.60313 

37 

0.39687 

9.96762 

5 

9 

52 

9.57107 

32 

9.60349 

36 

0.39651 

9.96757 

5 

8 

53 

9.57138 

31 

9.60386 

37 

0.39614 

9.96752 

5 

7 

54 

9.57169 

31 

32 

9.60422 

36 

37 

0.39578 

9.96747 

5- 

5 

6 

55 

9.57201 

9.60459 

0.39541 

9.96742 

5 

56 

9.57232 

31 

9.60495 

36 

0.39505 

9.96737 

5 

4 

57 

9.57264 

32 

9.60532 

37 

0.39468 

9.96732 

5 

3 

58 

9.57295 

31 

9.60568 

36 

0.39432 

9.96727 

5 

2 

59 

9.57326 

31 

32 

9.60605 

37 

36 

0.39395 

9.96722 

5 

5 

1 

80 

9.57358 

9.60641 

0.39359 

9.96717 

0 

L.  Cos, 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.  P. 


38 

3.8 

4.4 

5.1 

5.7 

6.3 

12.7 
19.0 
25.3 

31.7 


36 

3.6 

4.2 

4.8 

5.4 

6.0 

12.0 

18.0 

24.0 

30.0 


37 

3.7 

4.3 

4.9 

5.6 

6.2 

12.3 

18.5 

24.7 

30.8 


33 

3.3 
3.9 

4.4 
5.0 

5.5 

11.0 

16.5 

22.0 

27.5 


32 

3.2 

3.7 

4.3 

4.8 

5.3 

10.7 
16.0 
21.3 

26.7 


31 

3.1 

3.6 

4.1 

4.7 

5.2 
10.3 
15.5 

20.7 

25.8 


0.4 

0.5 

0.5 

0.6 

0.7 

1.3 
2.0 
2.7 

3.3 


P.  P. 


68° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

22° 


5U 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

0 

9.57358 

9.60641 

0.39359 

9.96717 

60 

1 

9.57389 

31 

9.60677 

36 

0.39323 

9.96711 

6 

59 

2 

9.57420 

31 

9.60714 

3 / 

0.39286 

9.96706 

5 

58 

3 

9.57451 

31 

9.60750 

36 

0.39250 

9.96701 

5 

57 

4 

9.57482 

31 

32 

9.60786 

36 

37 

0.39214 

9.96696 

5 

56 

5 

9.57514 

9.60823 

0.39177 

9.96691 

0 

'55 

6 

9.57545 

31 

9.60859 

36 

0.39141 

9.96686 

5 

54 

7 

■9.57576 

31 

9.60895 

36 

0.39105 

9.96681 

5 

53 

8 

9.57607 

31 

9.60931 

36 

0.39069 

9.96676 

5 

52 

9 

9.57638 

31 

31 

9.60967 

36 

37 

0.39033 

9.96670 

6 

51 

10 

9.57669 

9.61004 

0.38996 

9.96665 

0 

50 

11 

9.57700 

31 

9.61040 

36 

0.38960 

9.96660 

5 

49 

12 

9.57731 

31 

9.61076 

36 

0.38924 

9.96655 

5 

48 

13 

9.57762 

31 

9.61112 

36 

0.38888 

9.96650 

5 

47 

14 

9.57793 

31 

31 

9.61148 

36 

36 

0.38852 

9.96645 

5 

c 

46 

15 

9.57824 

9.61184 

0.38816 

9.96640 

0 

45 

16 

9.57855 

31 

9.61220 

36 

0.38780 

9.96634 

6 

44 

17 

9.57885 

30 

9.61256 

36 

0.38744 

9.96629 

5 

43 

18 

9.57916 

31 

9.61292 

36 

0.38708 

9.96624 

5 

42 

19 

9.57947 

31 

9.61328 

36 

36 

0.38672 

9.96619 

5 

c 

41 

20 

9.57978 

9.61364 

0.38636 

9.96614 

0 

40 

21 

9.58008 

30 

9.61400 

36 

0.38600 

9.96608 

6 

39 

22 

9.58039 

31 

9.61436 

36 

0.38564 

9.96603 

5 

38 

23 

9.58070 

31 

9.61472 

36 

0.38528 

9.96598 

5 

37 

24 

9.58101 

31 

30 

9.61508 

36 

36 

0.38492 

9.96593 

5 

36 

25 

9.58131 

9.61544 

0.38456 

9.96588 

5 

35 

26 

9.58162 

31 

9.61579 

35 

0.38421 

9.96582 

6 

34 

27 

9.58192 

30 

9.61615 

36 

0.38385 

9.96577 

5 

33 

28 

9.58223 

31 

9.61651 

36 

0.38349 

9.96572 

5 

32 

29 

9.58253 

30 

31 

9.61687 

36 

35 

0.38313 

9.96567 

5 

31 

30 

9.58284 

9.61722 

0.38278 

9.96562 

0 

30 

31 

9.58314 

30 

9.61758 

36 

0.38242 

9.96556 

6 

29 

32 

9.58345 

31 

9.61794 

36 

0.38206 

9.96551 

5 

28 

33 

9.58375 

30 

9.61830 

36 

0.38170 

9.96546 

5 

27 

34 

9.58406 

31 

30 

9.61865 

35 

36 

0.38135 

9.96541 

5 

a 

26 

35 

9.58436 

9.61901 

0.38099 

9.96535 

0 

2.5 

36 

9.58467 

31 

9.61936 

35 

0.38064 

9.96530 

5 

24 

37 

9.58497 

30 

9.61972 

36 

0.38028 

9.96525 

5 

23 

38 

9.58527 

30 

9.62008 

36 

0.37992 

9.96520 

5 

22 

39 

9.58557 

30 

31 

9.62043 

35 

36 

0.37957 

9.96514 

6 

c 

21 

40 

9.58588 

9.62079 

0.37921 

9.96509 

o 

20 

41 

9.58618 

30 

9.62114 

35 

0.37886 

9.96504 

5 

19 

42 

9.58648 

30 

9.62150 

36 

0.37850 

9.96498 

6 

18 

43 

9.58678 

30 

9.62185 

35 

0.37815 

9.96493 

5 

17 

44 

9.58709 

31 

30 

9.62221 

36 

35 

0.37779 

9.96488 

5 

K 

16 

45 

9.58739 

9.62256 

0.37744 

9.96483 

0 

15 

46 

9.58769 

30 

9.62292 

36 

0.37708 

9.96477 

6 

14 

47 

9.58799 

30 

9.62327 

35 

0.37673 

9.96472 

5 

13 

48 

9.58829 

30 

9.62362 

35 

0.37638 

9.96467 

5 

12 

49 

9.58859 

30 

30 

9.62398 

36 

35 

0.37602 

9.96161 

6 

5 

11 

50 

9.58889 

9.62433 

0.37567 

9.96456 

10 

51 

9.58919 

30 

9.62468 

35 

0.37532 

9.96451 

5 

9 

52 

9.58949 

30 

9.62504 

36 

0.37496 

9.96445 

6 

8 

53 

9.58979 

30 

9.62539 

3o 

0.37461 

9.96440 

5 

7 

54 

9.59009 

30 

30 

9.62574 

35 

35 

0.37426 

9.96435 

5 

6 

55 

9.59039 

9.62609 

0.37391 

9.9(>429 

5 

56 

9.59069 

30 

9.62645 

36 

0.37355 

9.96424 

5 

4 

57 

9.59098 

29 

9.62680 

35 

0.37320 

9.96419 

5 

3 

58 

9.59128 

30 

9.62715 

35 

0.37285 

9.96413 

6 

2 

59 

9.59158 

30 

30 

9.62750 

35 

35 

0.372^50 

9.96408 

5 

5 

1 

60 

9.59188 

9.62785 

0.37215 

9.96403 

0 

L.  Cos. 

1 d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

/ 

67° 


P.  P. 


37  36 

6 3.7  3.6 

7 4.3  4.2 

8 4.9  4.8 

9 5.6  5.4 

10  6.2  6.0 
20  12.3  12.0 
30  18.5  18.0 
40  24.7  24.0 
50  30.8  30.0 


35 

6 3.5 

7 4.1 

8 4.7 

9 5.3 

10  5.8 

20  11.7 
30  17.5 
40  23.3 
50  29.2 


32  31 

6 3.2  3.1 

7 3.7  3.6 

8 4.3  4.1 

9 4.8  4.7 

10  5.3  5.2 

20  10.7  10.3 
30  16.0  15.5 
40  21.3  20.7 
50  26.7  25.8 


30  29 

6 3.0  2.9 

7 3.5  3.4 

8 4.0  3.9 

9 4.5  4.4 

10  5.0  4.8 

20  10.0  9.7 

30  15.0  14.5 
40  20.0  19.3 
50  25.0  24.2 


6 5 

6 ' 0.6  0.5 

7 I 0.7  0.6 

8 0.8  0.7 

9 0.9  0.8 
10  1.0  0.8 
20  2.0  1.7 
30  3.0  2.5 
40  I 4.0  3.3 
50  I 5.0  4.2 


P.  P. 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS, 

23^ 


515 


/ 

L.  Sin.'. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

0 

9.59188 

9.62785 

0.37215 

9.96403 

60 

1 

9.59218 

30 

9.62820 

35 

0.37180 

9.96397 

6 

59 

2 

9.59247 

29 

9.62855 

35 

0.37145 

9.96392 

5 

58 

3 

9.59277 

30 

9.62890 

35 

0.37110 

9.96387 

5 

57 

4 

9.59307 

30 

29 

9.62926 

36 

35 

0.37074 

9.96381 

6 

K 

56 

5 

9.59336 

9.62961 

0.37039 

9.96376 

o 

55 

6 

9.59366 

30 

9.62996 

35 

0.37004 

9.96370 

6 

54 

7 

9.59396 

30 

9.63031 

35 

0.36969 

9.96365 

5 

53 

8 

9.59425 

29 

9.63066 

35 

0.36934 

9.96360 

5 

52 

9 

9.59455 

30 

29 

9.63101 

35 

34 

0.36899 

9.96354 

6 

51 

10 

9.59484 

9.63135 

0.36865 

9.96349 

O 

50 

11 

9.59514 

30 

9.63170 

35 

0.36830 

9.96343 

6 

49 

12 

9.59543 

29 

9.63205 

35 

0.36795 

9.96338 

5 

48 

13 

9.59573 

30 

9.63240 

35 

0.36760 

9.96333 

5 

47 

14 

9.59602 

29 

30 

9.63275 

35 

35 

0.36725 

9.96327 

6 

46 

15 

9.59632 

9.63310 

0.36690 

9.96322 

O 

45 

16 

9.59661 

29 

9.63345 

35 

0.36655 

9.96316 

6 

44 

17 

9.59690 

29 

9.63379 

34 

0.36621 

9.96311 

5 

43 

18 

9.59720 

30 

9.63414 

35 

0.36586 

9.96305 

6 

42 

19 

9.59749 

29 

29 

9.63449 

35 

35 

0.36551 

9.96300 

5 

41 

20 

9.59778 

9.63484 

0.36516 

9.96294 

0 

40 

21 

9.59808 

30 

9.63519 

35 

0.36481 

9.96289 

5 

39 

22 

9.59837 

29 

9.63553 

34 

0.36447 

9.96284 

5 

38 

23 

9.59866 

29 

9.63588 

35 

0.36412 

9.96278 

6 

37 

24 

9.59895 

29 

29 

9.63623 

35 

34 

0.36377 

9.96273 

5 

a 

36 

25 

9.59924 

9.63657 

0.36343 

9.96267 

0 

35 

26 

9.59954 

30 

9.63692 

35 

0.36308 

9.96262 

5 

34 

27 

9.59983 

29 

9.63726 

34 

0.36274 

9.96256 

6 

33 

28 

9.60012 

29 

9.63761 

35 

0.36239 

9.96251 

5 

32 

29 

9.60041 

29 

29 

9.63796 

35 

34 

0.36204 

9.96245 

6 

31 

30 

9.60070 

9.63830 

0.36170 

9.96240 

O 

30 

31 

9.60099 

29 

9.63865 

35 

0.36135 

9.96234 

6 

29 

32 

9.60128 

29 

9.63899 

34 

0.36101 

9.96229 

5 

28 

33 

9.60157 

29 

9.63934 

35 

0.36066 

9.96223 

6 

27 

34 

9.60186 

29 

29 

9.63968 

34 

35 

0.36032 

9.96218 

5 

g 

26 

35 

9.60215 

9.64003 

0.35997 

9.96212 

25 

36 

9.60244 

29 

9.64037 

34 

0.35963 

9.96207 

5 

24 

37 

9.60273 

29 

9.64072 

35 

0.35928 

9.96201 

6 

23 

38 

9.60302 

29 

9.64106 

34 

0.35894 

9.96196 

5 

22 

39 

9.60331 

29 

28 

9.64140 

34 

35 

0.35860 

9.96190 

6 

5 

21 

40 

9.60359 

9.64175 

0.35825 

9.96185 

20 

41 

9.60388 

29 

9.64209 

34 

0.35791 

9.96179 

6 

19 

42 

9.60417 

29 

9.64243 

34 

0.35757 

9.96174 

5 

18 

43 

9.60446 

29 

9.64278 

35 

0.35722 

9.96168 

6 

17 

44 

9.60474 

28 

29 

9.64312 

34 

34 

0.35688 

9.96162 

6 

5 

16 

45 

9.60503 

9.64346 

0.35654 

9.96157 

15 

46 

9.60532 

29 

9.64381 

35 

0.35619 

9.96151 

6 

14 

47 

9.60561 

29 

9.64415 

34 

0.35585 

9.96146 

5 

13 

48 

9.60589 

28 

9.64449 

34 

0.35551 

9.96140 

6 

12 

49 

9.60618 

29 

28 

9.64483 

34 

34 

0.35517 

9.96135 

5 

6 

11 

50 

9.60646 

9.64517 

0.35483 

9.96129 

10 

51 

9.60675 

29 

9.64552 

35 

0.35448 

9.96123 

6 

9 

52 

9.60704 

29 

9.64586 

34 

0.35414 

9.96118 

5 

8 

53 

9.60732 

28 

9.64620 

34 

0.35380 

9.96112 

6 

7 

54 

9.60761 

29 

28 

9.64654 

34 

34 

0.35346 

9.96107 

5 

Q 

6 

55 

9.60789 

9.64688 

0.35312 

9.96101 

5 

56 

9.60818 

29 

9.64722 

34 

0.35278 

9.96095 

6 

4 

57 

9.60846 

28 

9.64756 

34 

0.35244 

9.96090 

5 

3 

58 

9.60875 

29 

9.64790 

34 

0.35210 

9.96084 

6 

2 

59 

9.60903 

28 

28 

9.64824 

34 

34 

0.35176 

9.96079 

5 

g 

1 

60 

9.60931 

9.64858 

0.35142 

9.96073 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.  P. 


36 

3.6 

4.2 

4.8 

5.4 

6.0 

12.0 

18.0 

24.0 

30.0 


35 

3.5 

4.1 

4.7 
5.3 

5.8 
11.7 
17.5 
23.3 
29.2 


34 

3.4 

4.0 

4.5 

5.1 
5.7 

11.3 
17.0 
22.7 

28.3 


30 

3.0 

3.5 

4.0 

4.5 

5.0 
10.0 

15.0 

20.0 
25.0 


29 

2.9 

3.4 

3.9 

4.4 
4.8 
9.7 

14.5 

]9.3 

24.2 


28 

2.8 

3.3 

3.7 

4.2 

4.7 

9.3 
14.0 
18.7 
23.3 


6 

5 

6 

0.6 

0.5 

7 

0.7 

0.6 

8 

0.8 

0.7 

9 

0.9 

0.8 

10 

1.0 

0.8 

20 

2.0 

L7 

30 

3.0 

2.5 

40 

4.0 

3.3 

50 

5.0 

4.2 

P.  P. 

66° 


516  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

24° 


/ 

L.  Sin. 

0 

9.60931 

1 

9.60960 

2 

9.60988 

3 

9.61016 

4 

9.61045 

5 

9.61073 

6 

9.61101 

7 

9.61129 

8 

9.61158 

9 

9.61186 

10 

9.61214 

11 

9.61242 

12 

9.61270 

13 

9.61298 

14 

9.61326 

15 

9.61354 

16 

9.61382 

17 

9.61411 

18 

9.61438 

19 

9.61466 

20 

9.61494 

21 

9.61522 

22 

9.61550 

23 

9.61578 

24 

9.61606 

25 

9.61634 

26 

9.61662 

27 

9.61689 

28 

9.61717 

29 

9.61745 

30 

9.61773 

31 

9.61800 

32 

9.61828 

33 

9.61856 

34 

9.61883 

35 

9.61911 

36 

9.61939 

37 

9.61966 

38 

9.61994 

39 

9.62021 

40 

9.62049 

41 

9.62076 

42 

9.62104 

43 

9.62131 

44 

9.62159 

45 

9.62186 

46 

9.62214 

47 

9.62241 

48 

9.62268 

49 

9.62296 

50 

9.62323 

51 

9.62350 

52 

9.62377 

53 

9.62405 

54 

9.62432 

55 

9.62459 

56 

9.62486 

57 

9.62513 

58 

9.62541 

59 

9.62568 

60 

'9.62595 

L.  Cos. 

d. 


L.Tang. 


29 

28 

28 

29 

28 

28 

28 

29 

28 

28 

28 

28 

28 

28 

28 

28 

29 

27 

28 
28 
28 
28 
28 
28 
28 
28 

27 

28 
28 
28 

27 

28 
28 

27 

28 
28 

27 

28 

27 

28 

27 

28 

27 

28 

27 

28 
27 

27 

28 
27 
27 

27 

28 
27 
27 
27 

27 

28 
27 
27 


9.64858 

9.64892 

9.64926 

9.64960 

9.64994 

9.65028 

9.65062 

9.65096 

9.65130 

9.65164 

9.65197 

9.65231 

9.65265 

9.65299 

9.65333 

9.65366 

9.65400 

9.65434 

9.65467 

9.65501 


9.65535 

9.65568 

9.65602 

9.65636 

9.65669 


9.65703 

9.65736 

9-65770 

9.65803 

9.65837 


9.65870 

9.65904 

9.65937 

9.65971 

9.66004 


9.66038 

9.66071 

9.66104 

9.66138 

9.66171 

9.66204 

9.66238 

9.66271 

9.66301 

9.66337 


9.66371 

9.66404 

9.66437 

9.66470 

9.66503 


9.66537 

9.66570 

9.66603 

9.66636 

9.66669 


9.66702 
9.66735 
9.66768 
9.66801 
9^6^ 
9.66867 
L-  C(^ 


d.  c. 


34 

34 

34 

34 

34 

34 

34 

34 

34 

33 

34 
34 
34 
34 

33 

34 
34 

33 

34 
34 

33 

34 
34 

33 

34 

33 

34 

33 

34 

33 

34 

33 

34 

33 

34 
33 

33 

34 
33 

33 

34 
33 
33 

33 

34 
33 
33 
33 

33 

34 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 

d.^cT 


L.  Cotg. 

L.  Cos. 

d. 

] 

P. 

P. 

0.35142 

9.96073 

60 

0.35108 

9.96067 

6 

59 

0.35074 

9.96062 

5 

58 

0.35040 

9.96056 

6 

57 

A 

04 

Q A 

00 

Q Q 

0.35006 

9.96050 

6 

5 

56 

O 

7 

O.'l 

4.0 

0.0 

3.9 

0.34972 

9.96045 

55 

8 

4.5 

4.4 

0.34938 

9.96039 

6 

54 

9 

5.1 

5.0 

0.34904 

9.96034 

5 

53 

10 

5.7 

5.5 

0.34870 

9.96028 

6 

52 

20 

11.3 

11.0 

0.34836 

9.96022 

6 

5 

51 

30 

17.0 

16.5 

0.34803 

9.96017 

50 

40 

22.7 

22.0 

0.34769 

9.96011 

6 

49 

50 

28.3 

27.5 

0.34735 

9.96005 

6 

48 

0.34701 

9.96000 

5 

47 

0.34667 

9.95994 

6 

6 

46 

29 

0.34634 

9.95988 

45 

6 

2.9 

0.34600 

9.95982 

6 

44 

7 

3.4 

0.34566 

9.95977 

5 

43 

8 

3.9 

0.34533 

9.95971 

6 

42 

9 

4.4 

0.34499 

9.95965 

6 

5 

41 

10 

4.8 

0.34465 

9.95960 

40 

20 

9.7 

0.34432 

9.95954 

6 

39 

30 

14.5 

0.34398 

9.95948 

6 

38 

40 

19.3 

0.34364 

9.95942 

6 

37 

50 

24.2 

0.34331 

9.95937 

5 

a 

36 

0.34297 

9.95931 

O 

35 

0.34264 

9.95925 

6 

34 

28 

0.34230 

9.95920 

5 

33 

6 

2.8 

0.34197 

9.95914 

6 

32 

J 

3.3 

0.34163 

9.95908 

6 

31 

8 

3.7 

0.34130 

9.95902 

6 

30 

9 

in 

4.2 

A 7 

0.34096 

9.95897 

5 

29 

lU 

on 

Q Q 

0.34063 

9.95891 

6 

28 

on 

M n 

0.34029 

9.95885 

6 

27 

OU 

An 

1ft  7 

0.33996 

9.95879 

6 

Q 

26 

50 

lo.  / 

23.3 

0.33962 

9.95873 

25 

0.33929 

9.95868 

5 

24 

0.33896 

9.95862 

6 

23 

0.33862 

9.95856 

6 

22 

C! 

0.33829 

9.95850 

6 

(j 

21 

t) 

7 

2.7 

3.2 

0.33796 

9.95844 

20 

3!6 

0.33762 

9.95839 

5 

19 

t 

5 

4.1 

0.33729 

9.95833 

6 

18 

10 

4.5 

0.33696 

9.95827 

6 

17 

20 

9.0 

0.33663 

9.95821 

6 

6 

16 

30 

13.5 

0.33629 

9.95815 

15 

40 

18.0 

0.33596 

9.95810 

5 

14 

50 

22.5 

0.33563 

9.95804 

6 

13 

0.33530 

9.95798 

6 

12 

0.33497 

9.95792 

6 

g 

11 

6 

5 

0.33463 

9.95786 

10 

6 

0.6 

0.5 

0.33430 

9.95780 

6 

9 

7 

0.7 

0.6 

0.33397 

9.95775 

6 

8 

8 

0.8 

0.7 

0.33364 

9.95769 

6 

7 

9 

0.9 

0.8 

0.33331 

9.95763 

6 

6 

6 

10 

1.0 

0.8 

0.33298 

9.95757 

5 

20 

2.0 

1.7 

0.33265 

9.95751 

6 

4 

30 

3.0 

2*5 

0.33232 

9.95745 

6 

3 

40 

4.0 

3.3 

0.33199 

9.95739 

6 

2 

60 

5.0 

4.2 

0.33166 

9.95733 

6 

5 

1 

0.33133 

9.95728 

0 

1 L.Tang. 

L.  Sin. 

/ 

P.  P. 

65° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS, 

25° 


517 


/ 

L.  Sin. 

d. 

L.Tanff. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

0 

9.62595 

9.66867 

0.33133 

9.95728 

60 

1 

9.62622 

27 

9.66900 

33 

0.33100 

9.95722 

6 

59 

2 

9.62649 

27 

9.66933 

33 

0.33067 

9.95716 

6 

58 

3 

9.62676 

27 

9.66966 

33 

0.33034 

9.95710 

6 

57 

4 

9.62703 

27 

27 

9.66999 

33 

33 

0.33001 

9.95704 

6 

56 

5 

9.62730 

9.67032 

0.32968 

9.95698 

O 

55 

6 

9.62757 

27 

9.67065 

33 

0.32935 

9.95692 

6 

54 

7 

9.62784 

27 

9.67098 

33 

0.32902 

9.95686^ 

^ 6 

53 

8 

9.62811 

27 

9.67131 

33 

0.32869 

9.95680 

6 

52 

9 

9.62838 

27 

27 

9.67163 

32 

33 

0.32837 

9.95674 

6 

51 

10 

9.62865 

9.67196 

0.32804 

9.95668 

D 

50 

11 

9.62892 

27 

9.67229 

33 

0.32771 

9.95663 

5 

49 

12 

9.62918 

26 

9.67262 

33 

0.32738 

9.95657 

6 

48 

13 

9.62945 

27 

9.67295 

33 

0.32705 

9.95651 

6 

47 

14 

9.62972 

27 

27 

9.67327 

32 

33 

0.32673 

9.95645 

6 

46 

15 

9.62999 

9.67360 

0.32640 

9.95639 

o 

45 

16 

9.63026 

27 

9.67393 

33 

0.32607 

9.95633 

6 

44 

17 

9.63052 

26 

9.67426 

33 

0.32574 

9.95627 

6 

43 

18 

9.63079 

27 

9.67458 

32 

0.32542 

9.95621 

6 

42 

19 

9.63106 

27 

27 

9.67491 

33 

33 

0.32509 

9.95615 

6 

41 

20 

9.63133 

9.67524 

0.32476 

9.95609 

6 

40 

21 

9.63159 

26 

9.67556 

32 

0.32444 

9.95603 

6 

39 

22 

9.63186 

27 

9.67589 

33 

0.32411 

9.95597 

6 

38 

23 

9.63213 

27 

9.67622 

33 

0.32378 

9.95591 

6 

37 

24 

9.63239 

26 

27 

9.67654 

32 

33 

0.32346 

9.95585 

6 

36 

25 

9.63266 

9.67687 

0.32313 

9.95579 

6 

35 

26 

9.63292 

26 

9.67719 

32 

0.32281 

9.95573 

6 

34 

27 

9.63319 

27 

9.67752 

33 

0.32248 

9.95567 

6 

33 

28 

9.63345 

26 

9.67785 

33 

0.32215 

9.95561 

6 

32 

29 

9.63372 

27 

26 

9.67817 

32 

33 

0.32183 

9.95555 

6 

R 

31 

30 

9.63398 

9.67850 

0.32150 

9.95549 

0 

30 

31 

9.63425 

27 

9.67882 

32 

0.32118 

9.95543 

6 

29 

32 

9.63451 

26 

9.67915 

33 

0.32085 

9.95537 

6 

28 

33 

9.63478 

27 

9.67947 

32 

0.32053 

9.95531 

6 

.27 

34 

9.63504 

26 

27 

9.67980 

33 

32 

0.32020 

9.95525 

6 

£* 

26 

35 

9.63531 

9.68012 

0.31988 

9.95519 

O 

25 

36 

9.63557 

26 

9.68044 

32 

0.31956 

9.95513 

6 

24 

37 

9.63583 

26 

9.68077 

33 

0.31923 

9.95507 

6 

23 

38 

9.63610 

27 

9.68109 

32 

0.31891 

9.95500 

7 

22 

39 

9.63636 

26 

26 

9.68142 

33 

32 

0.31858 

9.95494 

6 

R 

21 

40 

9.63662 

9.68174 

0.31826 

9.95488 

O 

20 

41 

9.63689 

27 

9.68206 

32 

0.31794 

9.95482 

6 

19 

42 

9.63715 

26 

9.68239 

33 

0.31761 

9.95476 

6 

18 

43 

9.63741 

26 

9.68271 

32 

0.31729 

9.95470 

6 

17 

44 

9.63767 

26 

27 

9.68303 

32 

33 

0.31697 

9.95464 

6 

6 

16 

45 

9.63794 

9.68336 

0.31664 

9.95458 

15 

46 

9.63820 

26 

9.68368 

32 

0.31632 

9.95452 

6 

14 

47 

9.63846 

26 

9.68400 

32 

0.31600 

9.95446 

6 

13 

48 

9.63872 

26 

9.68432 

32 

0.31568 

9.95440 

6 

12 

49 

9.63898 

26 

26 

9.68465 

33 

32 

0.31535 

9.95434 

6 

rj 

11 

50 

9.63924 

9.68497 

0.31503 

9.95427 

4 

10 

51 

9.63950 

26 

9.68529 

32 

0.31471 

9.95421 

6 

9 

52 

9.63976 

26 

9.68561 

32 

0.31439 

9.95415 

6 

8 

53 

9.64002 

26 

9.68593 

32 

0.31407 

9.95409 

6 

7 

54 

9.64028 

26 

26 

9.68626 

33 

32 

0.31374 

9.95403 

6 

R 

6 

55 

9.64054 

9.68658 

0.31342 

9.95397 

O 

5 

56 

9.64080 

26 

9.68690 

82 

0.31310 

9.95391 

6 

4 

57 

9.64106 

26 

9.68722 

32 

0.31278 

9.95384 

7 

3 

58 

9.64132 

26 

9.68754 

32 

0.31246 

9.95378 

6 

2 

59 

9.64158 

26 

26 

9.68786 

32 

32 

0.31214 

9.95372 

6 

6 

1 

60 

9.64184 

9.68818 

0.31182 

9.95366 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.  P. 


33 

32 

6 

3.3 

3.2 

7 

3.9 

3.7 

8 

4.4 

4.3 

9 

5.0 

4.8 

10 

5.5 

5.3 

20 

11.0 

10.7 

30 

16.5 

16.0 

40 

22.0 

21.3 

50 

27.5 

26.7 

27 

6 

2.7 

7 

3.2 

8 

3.6 

9 

4.1 

10 

4.5 

20 

9.0 

30 

13.5 

40 

18.0 

50 

22.5 

26 

6 

2.6 

7 

3.0 

8 

3.5 

9 

3.9 

10 

4.3 

20 

8.7 

30 

13.0 

40 

17.3 

50 

21.7 

6 

0.7 

7 

0.8 

8 

0.9 

9 

1.1 

10 

1.2 

20 

2.3 

30 

3.5 

40 

4.7 

50 

5.8 

6 

5 

6 

0.6 

0.5 

7 

0.7 

0.6 

8 

0.8 

0.7 

9 

0.9 

0.8 

10 

1.0 

0.8 

20 

2.0 

1.7 

30 

3.0 

2.5 

40 

4.0 

3.3 

50 

5.0 

4.2 

P.  P. 

64° 


518  ' LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS, 

26° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

0 

9.64184 

9.68818 

0.31182 

9.95366 

60 

1 

9.64210 

26 

9.68850 

32 

0.31150 

9.95360 

6 

59 

2 

9.64236 

26 

9.68882 

32 

0.31118 

9.95354 

6 

58 

3 

9.64262 

26 

9.68914 

32 

0.31086 

9.95348 

6 

57 

4 

9.64288 

26 

25 

9.68946 

32 

32 

0.31054 

9.95341 

7 

8 

56 

6 

9.64313 

9.68978 

0.31022 

9.95335 

55 

6 

9.64339 

26 

9.690m 

32 

0.30990 

9.95329 

6 

54 

7 

9.64365 

26 

9.690^ 

32 

0.30958 

9.95323 

6 

53 

8 

9.64391 

26 

9.69074 

32 

0.30926 

9.95317 

6 

52 

9 

9.64417 

26 

25 

9.69106 

32 

32 

0.30894 

9.95310 

7 

51 

10 

9.64442 

9.69138 

0.30862 

9.95304 

D 

50 

11 

9.64468 

26 

9.69170 

32 

0.30830 

9.95298 

6 

49 

12 

9.64494 

26 

9.69202 

32 

0.30798 

9.95292 

6 

48 

13 

9.64519 

^5 

9.69234 

32 

0.30766 

9.95286 

6 

47 

14 

9.64545 

26 

9.69266 

32 

0.30734 

9.95279 

7 

46 

15 

9.64571 

26 

9.69298 

32 

0.30702 

9.95273 

6 

45 

16 

9.64596 

25 

9.69329 

31 

0.30671 

9.95267 

6 

44 

17 

9.64622 

26 

9.69361 

32 

0.30639 

9.95261 

6 

43 

18 

9.64647 

25 

9.69393 

32 

0.30607 

9.95254 

7 

42 

19 

9.64673 

26 

25 

9.69425 

32 

32 

0.30575 

9.95248 

6 

41 

20 

9.64698 

9.69457 

0.30543 

9.95242 

0 

40 

21 

9.64724 

26 

9.69488 

31 

0.30512 

9.95236 

6 

39 

22 

9.64749 

25 

9.69520 

32 

0.30480 

9.95229 

7 

38 

23 

9.64775 

26 

9.69552 

32 

0.30448 

9.95223 

6 

37 

24 

9.64800 

25 

96 

9.69584 

32 

31 

0.30416 

9.95217 

6 

36 

25 

9.64826 

9.69615 

0.30385 

9.95211 

D 

35 

26 

9.64851 

25 

9.69647 

32 

0.30353 

9.95204 

7 

34 

27 

9.64877 

26 

9.69679 

32 

0.30321 

9.95198 

6 

33 

28 

9.64902 

25 

9.69710 

31 

0.30290 

9.95192 

6 

32 

29 

9.64927 

25 

26 

9.69742 

32 

0.30258 

9.95185 

7 

a 

31 

30 

9.64953 

9.69774 

OZi 

0.30226 

9.95179 

0 

30 

31 

9.64978 

25 

9.69805 

31 

0.30195 

9.95173 

6 

29 

32 

9.65003 

25 

9.69837 

32 

0.30163 

9.95167 

6 

28 

33 

9.65029 

26 

9.69868 

31 

0.30132 

9.95160 

7 

27 

34 

9.65054 

25 

25 

9.69900 

32 

32 

0.30100 

9.95154 

6 

6 

26 

35 

9.65079 

9.69932 

0.30068 

9.95148 

25 

36 

9.65104 

25 

9.69963 

31 

0.30037 

9.95141 

7 

24 

37 

9.65130 

26 

9.69995 

32 

0.30005 

9.95135 

6 

23 

38 

9.65155 

25 

9.70026 

31 

0.29974 

9.95129 

6 

22 

39 

9.65180 

25 

25 

9.70058 

32 

31 

0.29942 

9.95122 

7 

21 

40 

9.65205 

9.70089 

0.29911 

9.95116 

o 

20 

41 

9.65230 

25 

9.70121 

32 

0.29879 

9.95110 

6 

19 

42 

9.65255 

25 

9.70152 

31 

0.29848 

9.95103 

7 

18 

43 

9.65281 

26 

9.70184 

32 

0.29816 

9.95097 

6 

17 

44 

9.65306 

25 

25 

9.70215 

31 

32 

0.29785 

9.95090 

7 

g 

16 

45 

9.65331 

9.70247 

0.29753 

9.95084 

15 

46 

9.65356 

25 

9.70278 

31 

0.29722 

9.95078 

6 

14 

47 

9.65381 

25 

9.70309 

31 

0.29691 

9.95071 

7 

13 

48 

9.65406 

25 

9.70341 

32 

0.29659 

9.95065 

6 

12 

49 

9.65431 

25 

25 

9.70372 

31 

32 

0.29628 

9.95059 

6 

7 

11 

50 

9.65456 

9.70404 

0.29596 

9.95052 

10 

51 

9.65481 

25 

9.70435 

31 

0.29565 

9.95046 

6 

9 

52 

9.65506 

25 

9.70466 

31 

0.29534 

9.95039 

7 

8 

53 

9.65531 

25 

9.70498 

32 

0.29502 

9.95033 

6 

7 

54 

9.65556 

25 

24 

9.70529 

31 

31 

0.29471 

9.95027 

6 

7 

6 

55 

9.65580 

9.70^0 

0.29440 

9.95020 

5 

56 

9.65605 

25 

9.70592 

32 

0.29408 

9.95014 

G 

4 

57 

9.65630 

25 

9.70623 

31 

0.29377 

9.95007 

7 

3 

58 

9.65655 

25 

9.70654 

31 

0.29346 

9.95001 

6 

2 

59 

9.65680 

25 

25 

9.70685 

31 

32 

0.29315 

9.94995 

6 

7 

1 

60 

9.65705 

9.70717 

0.29283 

9.94988 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

■d. 

/ 

P 

. P. 

32 

31 

6 

3.2 

3.1 

7 

3.7 

3.6 

8 

4.3 

4.1 

9 

4.8 

4.7 

10 

5.3 

5.2 

20 

10.7 

10.3 

30 

16.0 

15.5 

40 

21.3 

20.7 

50 

26.7 

25.8 

26 

6 

2.6 

7 

3.0 

8 

3.5 

9 

3.9 

10 

4.3 

20 

8.7 

30 

13.0 

40 

17.3 

50 

21.7 

25 

6 

2.5 

7 

2.9 

8 

3.3 

9 

3.8 

10 

4.2 

20 

8.3 

30 

12.5 

40 

16.7 

50 

20.8 

24 

6 

2.4 

7 

2.8 

8 

3.2 

9 

3.6 

10 

4.0 

20 

8.0 

30 

12.0 

40 

16.0 

50 

20.0 

7 

6 

6 

0.7 

0.6 

7 

0.8 

0.7 

8 

0.9 

0.8 

9 

1.1 

0.9 

10 

1.2 

1.0 

20 

2.3 

2.0 

30 

3.5 

3.0 

40 

4.7 

4.0 

50 

5.8 

5.0 

P. 

P. 

63‘ 


/ 

L.  Sill. 

”F 

9.65705 

1 

9.65729 

2 

9.65754 

3 

9.65779 

4 

9.65804 

5 

9.65828 

6 

9.65853 

7 

9.65878 

8 

9.65902 

9 

9.65927 

10 

9.65952 

11 

9.65976 

12 

9.66001 

13 

9.66025 

14 

9.66050 

15 

9.66075 

16 

9.66099 

17 

9.66124 

18 

9.66148 

19 

9.66173 

20 

9.66197 

2i 

9.66221 

22 

9.66246 

23 

9.66270 

24 

9.66295 

25  , 

9.66319 

26 

9.66343 

27 

9.66368 

28 

9.66392 

29 

9.66416 

30 

9.66441 

31 

9.66465 

32 

9.66489 

33 

9.66513 

34 

9.66537 

35 

9.66562 

36 

9.66586 

37 

9.66610 

38 

9.66634 

39 

9.66658 

40 

9.66682 

41 

9.66706 

42 

9.66731 

43 

9.66755 

44 

9.66779 

45 

9.66803 

46 

9.66827 

47 

9.66851 

48 

9.66875 

49 

9.66899 

50 

9.66922 

51 

9.66946 

52 

9.66970 

53 

9.66994 

54 

9.67018 

55 

9.67042 

56 

9.67066 

57 

9.67090 

58 

9.67113 

59 

9.67137 

60 

9.67161 

L.  Cos. 

LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

27° 


519 


L.  Cotg. 

L.  Cos. 

d. 

0.29283 

9.94988 

6 

60 

0.29252 

9.94982 

59 

0.29221 

9.94975 

7 

58 

0.29190 

9.94969 

6 

57 

0.29159 

9.94962 

7 

g 

56 

0.29127 

9.94956 

55 

0.29096 

9.94949 

7 

54 

0.29065 

9.94943 

6 

53 

0.29034 

9.94936 

7 

52 

0.29003 

9.94930 

6 

7 

51 

0.28972 

9.94923 

50 

0.28941 

9.94917 

6 

49 

0.28910 

9.94911 

6 

48 

0.28879 

9.94904 

7 

47 

0.28847 

9.94898 

6 

7 

46 

0.28816 

9.94891 

45 

0.28785 

9.94885 

6 

44 

0.28754 

9.94878 

7 

43 

0.28723 

9.94871 

7 

42 

0.28692 

9.94865 

6 

y 

41 

0.28661 

9.94858 

6 

40 

0.28630 

9.94852 

39 

0.28599 

9.94845 

7 

38 

0.28569 

9.94839 

6 

37 

0.28538 

9.94832 

7 

g 

36 

0.28507 

9.94826 

35 

0.28476 

9.94819 

7 

34 

0.28445 

9.94813 

6 

33 

0.28414 

9.94806 

7 

32 

0.28383 

9.94799 

7 

6 

31 

0.28352 

9.94793 

30 

0.28321 

9.94786 

7 

29 

0.28291 

9.94780 

6 

28 

0.28260 

9.94773 

7 

6 

7 

27 

0.28229 

9.94767 

26 

0.28198 

9.94760 

25 

0.28167 

9.94753 

7 

24 

0.28137 

9.94747 

6 

23 

0.28106 

9.94740 

7 

6 

7 

22 

0.28075 

9.94734 

21 

0.28045 

9.94727 

20 

0.28014 

9.94720 

7 

19 

0.27983 

9.94714 

6 

18 

0.27952 

9.94707 

7 

17 

0.27922 

9.94700 

7 

6 

16 

0.27891 

9.94694 

15 

0.27860 

9.94687 

7 

14 

0.27830 

9.94680 

7 

13 

0.27799 

9.94674 

6 

12 

0.27769 

9.94667 

7 

y 

11 

0.27738 

9.94660 

10 

0.27707 

9.94654 

6 

9 

0.27677 

9.94647 

7 

8 

0.27646 

9.94640 

7 

7 

0.27616 

9.94634 

6 

7 

6 

0.27585 

9.94627 

5 

0.27555 

9.94620 

7 

4 

0.27524 

9.94614 

6 

3 

0.27494 

9.94607 

7 

2 

0.27463 

9.94600 

7 

7 

1 

o.274iiir 

9.9I593 

1 

0 

L.Tang. 

L.  Sin. 

d.^ 

L.Tang. 


9.70717 

9.70748 

9.70779 

9.70810 

9.70841 

9.70873 

9.70904 

9.70935 

9.70966 

9.70997 

9.71028 

9.71059 

9.71090 

9.71121 

9.71153 

9.71184 

9.71215 

9.71246 

9.71277 

9.71308 

9.71339 

9.71370 

9.71401 

9.71431 

9.71462 

9.71493 

9.71524 

9.71555 

9.71586 

9.71617 

9.71648 

9.71679 

9.71709 

9.71740 

9.71771 

9.71802 

9.71833 

9.71863 

9.71894 

9.71925 

9.71955 

9.71986 

9.72017 

9.72048 

9.72078 

9.72109 

9.72140 

9.72170 

9.72201 

9.72231 

9.72262 

9.72293 

9.72323 

9.72354 

9.72384 

9.72415 

9.72445 

9.72476 

9.72506 

9.72537 

9.72567 

L.  Cotg. 

d.  0^ 


P.  P. 


31 

31 

31 

31 

32 
31 
31 
31 
31 
31 
31 
31 

31 

32 
31 
31 
31 
31 
31 
31 
31 
31 

30 

31 
31 
31 
31 
31 
31 
31 
31 

30 

31 
31 
31 
31 

30 

31 
31 

30 

31 
31 
31 

30 

31 
31 

30 

31 

30 

31 
31 

30 

31 

30 

31 

30 

31 

30 

31 
30 

d.  c. 


32 

3.2 

3.7 

4.3 

4.8 

5.3 

10.7 
16.0 
21.3 

26.7 


31 

3.1 

3.6 

4.1 

4.7 

5.2 
10.3 
15.5 

20.7 

25.8 


30 

3.0 

3.5 

4.0 

4.5 

5.0 
10.0 

15.0 

20.0 
25.0 


25 

2.5 

2.9 

3.3 

3.8 

4.2 

8.3 
12.5 

16.7 

20.8 


24 

2.4 

2.8 

3.2 

3.6 

4.0 

8.0 
12.0 
16.0 
20.0 


23 

2.3 

2.7 
3.1 
3.5 

3.8 
7.7 

11.5 

15.3 

19.2 


6 

0.6 

0.7 

0.8 

0.9 

1.0 

2.0 

3.0 

4.0 

5.0 


P.  P. 


520 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

28° 


' 1 L.  Sin. 

0 

9.67161 

1 

9.67185 

2 

9.67208 

3 

9.67232 

4 

9.67256 

5 

9.67280 

6 

9.67303 

7 

9.67327 

8 

9.67350 

9 

9.67374 

iO 

9.67398 

11 

9.67421 

12 

9.67445 

13 

9.67468 

14 

9.67492 

15 

9.67515 

16 

9.67539 

17 

9.67562 

18 

9.67586 

19 

9.67609 

20 

9.67633 

21 

9.67656 

22 

9.67680 

23 

9.67703 

24 

9.67726 

25 

9.67750 

26 

9.67773 

27 

9.67796 

28 

9.67820 

29 

9.67843 

30 

9.67866 

31 

9.67890 

32 

9.67913 

33 

9.67936 

34 

9.67959 

35 

9.67982 

36 

9.68006 

37 

9.68029 

38 

9.68052 

39 

9.68075 

40 

9.68098 

41 

9.68121 

42 

9.68144 

43 

9.68167 

44 

9.68190 

45 

9.68213 

46 

9.68237 

47 

9.68260 

48 

9.68283 

49 

9.68305 

50 

9.68328 

51 

9.68351 

52 

9.68374 

53 

9.68397 

54 

9.68420 

55 

9.68443 

56 

9.68466 

57 

9.68489 

58 

9.68512 

59 

9.68534 

60 

9.68557 

L.  Cos. 

L.Tang. 


d.  c. 


L.  Cotg. 


L.  Cos.  d. 


P.P. 


9.72567 

9.72598 

9.72628 

9.72659 

9.72689 


9.72720 

9.72750 

9.72780 

9.72811 

9.72841 


9.72872 

9.72902 

9.72932 

9.72963 

9.72993 


9.73023 

9.73054 

9.73084 

9.73114 

9.73144 


9.73175 

9.73205 

9.73235 

9.73265 

9.73295 


9.73326 

9.73356 

9.73386 

9.73416 

9.73446 


9.73476 

9.73507 

9.73537 

9.73567 

9.73597 


9.73627 

9.73657 

9.73687 

9.73717 

9.73747 


9.73777 

9.73807 

9.73837 

9.73867 

9.73897 


9.73927 

9.73957 

9.73987 

9.74017 

9.74047 


9.74077 

9.74107 

9.74137 

9.74166 

9.74196 


9.74226 

9.74256 

9.74286 

9.74316 

9.74345 


9.74375 


31 

30 

31 

30 

31 
30 

30 

31 

30 

31 
30 

30 

31 
30 

30 

31 
30 
30 

30 

31 
30 
30 
30 

30 

31 
30 
30 
30 
30 

30 

31 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 

29 

30 
30 
30 
30 
30 

29 

30 


0.27433 

0.27402 

0.27372 

0.27341 

0.27311 


9.94593 

9.94587 

9.94580 

9.94573 

9.94567 


0.27280 

0.27250 

0.27220 

0.27189 

0.27159 


9.94560 

9.94553 

9.94546 

9.94540 

9.94533 


0.27128 

0.27098 

0.27068 

0.27037 

0.27007 


9.94526 

9.94519 

9.94513 

9.94506 

9.94499 


0.26977 

0.26946 

0.26916 

0.26886 

0.26856 


9.94492 

9.94485 

9.94479 

9.94472 

9.94465 


0.26825 

0.26795 

0.26765 

0.26735 

0.26705 


9.94458 

9.94451 

9.94445 

9.94438 

9.94431 


0.26674 

0.26644 

0.26614 

0.26584 

0.26554 


9.94424 

9.94417 

9.94410 

9.94404 

9.94397 


0.26524 

0.26493 

0.26463 

0.26433 

0.26403 


9.94390 

9.94383 

9.94376 

9.94369 

9.94362 


0.26373 

0.26343 

0.26313 

0.26283 

0.26253 


9.94355 

9.94349 

9.94342 

9.94335 

9.94328 


0.26223 

0.26193 

0.26163 

0.26133 

0.26103 


9.94321 

9.94314 

9.94307 

9.94300 

9.94293 


0.26073 

0.26043 

0.26013 

0.25983 

0.25953 


9.94286 

9.94279 

9.94273 

9.94266 

9.94259 


0.25923 

0.25893 

0.25863 

0.25834 

0.25804 


9.94252 

9.94245 

9.94238 

9.94231 

9.94224 


0.25774 

0.25744 

0.25714 

0.25684 

0.25655 


9.94217 

9.94210 

9.94203 

9.94196 

9.94189 


L.  Cotg.  d.  c. 


0.25625 

L.Tang. 


31 

3.1 

3.6 

4.1 

4.7 

5.2 
10.3 
15.5 

20.7 

25.8 


30 

3.0 

3.5 

4.0 

4.5 

5.0 

10.0 

15.0 

20.0 

25.0 


29 

2.9 

3.4 

3.9 

4.4 
4.8 
9.7 

14.5 

19.3 

24.2 


24 

2.4 

2.8 

3.2 

3.6 

4.0 

8.0 
12.0 
16.0 
20.0 


23 

2.3 

2.7 
3.1 
3.5 

3.8 
7.7 

11.5 

15.3 

19.2 


22 

2.2 

2.6 

2.9 

3.3 
3.7 

7.3 
11.0 
14.7 
18.3 


7 

6 i 0.7 

7 ' 0.8 

8 i 0.9 


P.  P. 


61° 


521 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS, 


29° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

^ P.  P. 

0 

1 

2 

3 

4 

9.68557 

9.68580 

9.68603 

9.68625 

9.68648 

23 

23 

22 

23 

23 

23 

22 

23 

23 

22 

23 

22 

23 

23 

22 

23 

22 

23 

22 

23 

22 

23 

22 

23 

22 

22 

23 

22 

23 

22 

22 

23 

22 

22 

22 

23 

22 

22 

22 

22 

23 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

9.74375 

9.74405 

9.74435 

9.74465 

9.74494 

30 

30 

30 

29 

30 

30 

29 

30 

30 

30 

29 

30 

30 

29 

30 

30 

29 

30 

29 

30 

29 

30 

30 

29 

30 

29 

30 

29 

30 

29 

30 

29 

30 

29 

29 

30 

29 

30 

29 

29 

30 

29 

30 

29 

29 

30 

29 

29 

29 

30 

29 

29 

29 

30 

29 

29 

29 

30 

29 

29 

0.25625 

0.25595 

0.25565 

0.25535 

0.25506 

9.94182 

9.94175 

9.94168 

9.94161 

9.94154 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

8 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

8 

7 

7 

7 

7 

7 

7 

7 

8 

7 

7 

7 

7 

7 

8 

7 

7 

7 

7 

8 

7 

7 

7 

8 

7 

7 

7 

7 

8 

7 

7 

8 

7 

7 

7 

8 

7 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

30 

6 3.0 

7 3.5 

8 4.0 

9 4.5 

10  5.0 

20  10.0 

30  15.0 

40  20.0 

50  25.a 

29 

6 2.9 

7 3.4 

8 3.9 

9 4.4 

10  4.8 

20  9.7 

30  14.5 

40  19.3 

50  24.2 

23 

6 2.3 

7 2.7 

8 3.1 

9 3.5 

10  3.8 

20  7.7 

30  11.5 

40  15.3 

50  19.2 

22 

6 2.2 

7 2.6 

8 2.9 

9 3.3 

10  3.7 

20  7.3 

30  11.0 

40  14.7 

50  18.3 

8 7 

6 0.8  0.7 

7 0.9  0.8 

8 1.1  0.9 

9 1.2  1.1 

10  1.3  1.2 

20  2.7  2.3 

30  4.0  3.5 

40  5.3  4.7 

50  6.7  5.8 

5 

6 

7 

8 

9 

9.68671 

9.68694 

9.68716 

9.68739 

9.68762 

9.74524 

9.74554 

9.74583 

9.74613 

9.74643 

0.25476 

0.25446 

0.25417 

0.25387 

0.25357 

9.94147 

9.94140 

9.94133 

9.94126 

9.94119 

10 

11 

12 

13 

14 

9.68784 

9.68807 

9.68829 

9.68852 

9.68875 

9.74673 

9.74702 

9.74732 

9.74762 

9.74791 

0.25327 

0.25298 

0.25268 

0.25238 

0.25209 

9.94112 

9.94105 

9.94098 

9.94090 

9.94083 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.68897 

9.68920 

9.68942 

9.68965 

9.68987 

9.74821 

9.74851 

9.74880 

9.74910 

9.74939 

0.25179 

0.25149 

0.25120 

0.25090 

0.25061 

9.94076 

9.94069 

9.94062 

9.94055 

9.94048 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.69010 

9.69032 

9.69055 

9.69077 

9.69100 

9.74969 

9.74998 

9.75028 

9.75058 

9.75087 

0.25031 

0.25002 

0.24972 

0.24942 

0.24913 

9.94041 

9.94034 

9.94027 

9.94020 

9.94012 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.69122 

9.69144 

9.69167 

9.69189 

9.69212 

9.75117 

9.75146 

9.75176 

9.75205 

9.75235 

0.24883 

0.24854 

0.24824 

0.24795 

0.24765 

9.94005 

9.93998 

9.93991 

9.93984 

9.93977 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.69234 

9.69256 

9.69279 

9.69301 

9.69323 

9.75264 

9.75294 

9.75323 

9.75353 

9.75382 

0.24736 

0.24706 

0.24677 

0.24647 

0.24618 

9.93970 

9.93963 

9.93955 

9.93948 

9.93941 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.69345 

9.69368 

9.69390 

9.69412 

9.69434 

9.75411 

9.75441 

9.75470 

9.75500 

9.75529 

0.24589 

0.24559 

0.24530 

0.24500 

0.24471 

9.93934 

9.93927 

9.93920 

9.93912 

9.93905 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.69456 

9.69479 

9.69501 

9.69523 

9.69545 

9.75558 

9.75588 

9.75617 

9.75647 

9.75676 

0.24442 

0.24412 

0.24383 

0.24353 

0.24324 

9.93898 

9.93891 

9.93884 

9.93876 

9.93869 

20 

19 

18 

17 

16 

45 

46 
'47 

48 

49 

9.69567 

9.69589 

9.69611 

9.69633 

9.69655 

9.75705 

9.75735 

9.75764 

9.75793 

9.75822 

0.24295 

0.24265 

0.24236 

0.24207 

0.24178 

9.93862 

9.93855 

9.93847 

9 93840 
9.93833 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.69677 

9.69699 

9.69721 

9.69743 

9.69765 

9.75852 

9.75881 

9.75910 

9.75939 

9.75969 

0.24148 

0.24119 

0.24090 

0.24061 

0.24031 

9.93826 

9.93819 

9.93811 

9.93804 

9.93797 

10 

9 

8 

7 

6 

55 

66 

57 

58 

59 

9.69787 

9.69809 

9.69831 

9.69853 

9.69875 

9.75998 

9.76027 

9.76056 

9.76086 

9.76115 

0.24002 

0.23973 

0.23944 

0.23914 

0.23885 

9.93789 

9.93782 

9.93775 

9.93768 

9.93760 

5 

4 

3 

2 

1 

60 

9.69897 

9.76144 

0.23856 

9.93753 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

' 

P.  P. 

60' 


522  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

30° 


t 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos.  1 

d. 

0 

9.69897 

9.76144 

0.23856 

9.93753 

60 

1 

9.69919 

22 

9.76173 

29 

0.23827 

9.93746 

7 

59 

2 

9.69941 

22 

9.76202 

29 

0.23798 

9.93738 

8 

58 

3 

9.69963 

22 

9.76231 

29 

0.23769 

9.93731 

7 

57 

4 

9.69984 

21 

22 

9.76261 

30 

29 

0.23739 

9.93724 

7 

<7 

56 

5 

9.70006 

9.76290 

0.23710 

9.93717 

55 

6 

9.70028 

22 

9.76319 

29 

0.23681 

9.93709 

8 

54 

7 

9.70050 

22 

9.76348 

29 

0.23652 

9.93702 

7 

53 

8 

9.70072 

22 

9.76377 

29 

0.23623 

9.93695 

7 

52 

9 

9.70093 

21 

22 

9.76406 

29 

29 

0.23594 

9.93687 

8 

>7 

51 

10 

9.70115 

9.76435 

0.23565 

9.93680 

50 

11 

9.70137 

22 

9.76464 

29 

0.23536 

9.93673 

7 

49 

12 

9.70159 

22 

9.76493 

29 

0.23507 

9.93665 

8 

48 

13 

9.70180 

21 

9.76522 

29 

0.23478 

9.93658 

7 

47 

14 

9.70202 

22 

22 

9.76551 

29 

29 

0.23449 

9.93650 

8 

<7 

46 

15 

9.70224 

9.76580 

0.23420 

9.93643 

45 

16 

9.70245 

21 

9.76609 

29 

0.23391 

9.93636 

7 

44 

17 

9.70267 

22 

9.76639 

30 

0.23361 

9.93628 

8 

43 

18 

9.70288 

21 

9.76668 

29 

0.23332 

9.93621 

7 

42 

19 

9.70310 

22 

22 

9.76697 

29 

28 

0.23303 

9.93614 

7 

8 

41 

20 

9.70332 

9.76725 

0.23275 

9.93606 

40 

21 

9.70353 

21 

9.76754 

29 

0.23246 

9.93599 

7 

39 

22 

9.70375 

22 

9.76783 

29 

0.23217 

9.93591 

8 

38 

23 

9.70396 

2d\. 

9.76812 

29 

0.23188 

9.93584 

7 

37 

24 

9.70418 

22 

21 

9.76841 

29 

29 

0.23159 

9.93577 

7 

8 

36 

25 

9.70439 

9.76870 

0.23130 

9.93569 

35 

26 

9.70461 

22 

9.76899 

29 

0.23101 

9.93562 

7 

34 

27 

9.70482 

21 

9.76928 

29 

0.23072 

9.93554 

8 

33 

28 

9.70504 

22 

9.76957 

29 

0.23043 

9.93547 

7 

32 

29 

9.70525 

21 

22 

9.76986 

29 

29 

0.23014 

9.93539 

8 

31 

30 

9.70547 

9.77015 

0.22985 

9.93532 

30 

31 

9.70568 

9.77044 

29 

0.22956 

9.93525 

7 

29 

32 

9.70590 

22 

9.77073 

29 

0.22927 

9.93517 

8 

28 

33 

9.70611 

21 

9.77101 

28 

0.22899 

9.93510 

7 

27 

34 

9.70633 

22 

21 

9.77130 

29 

29 

0.-22870 

9.93502 

8 

'j 

26 

35 

9.70654 

9.77159 

0.22841 

9.93495 

25 

36 

9.70675 

21 

9.77188 

29 

0.22812 

9.93487 

8 

24 

37 

9.70697 

22 

9.77217 

29 

0.22783 

9.93480 

7 

23 

38 

9.70718 

21 

9.77246 

29 

0.22754 

9.93472 

8 

22 

39 

§.70739 

21 

22 

9.77274 

28 

29 

0.22726 

9.93465 

7 

8 

21 

40 

9.70761 

9.77303 

0.22697 

9.93457 

20 

41 

9.70782 

21 

9.77332 

29 

0.22668 

9.93450 

7 

19 

42 

9.70803 

21 

9.77361 

29 

0.22639 

9.93442 

8 

18 

43 

9.70824 

21 

9.77390 

29 

0.22610 

9.93435 

7 

17 

44 

9.70846 

22 

21 

9.77418 

28 

29 

0.22582 

9.93427 

8 

<7 

16 

45 

9.70867 

9.77447 

0.22553 

9.93420 

15 

46 

9.70888 

21 

9.77476 

29 

0.22524 

9.93412 

8 

14 

47 

9.70909 

21 

9.77505 

29 

0.22495 

9.93405 

7 

13 

48 

9.70931 

22 

9.77533 

28 

0.22467 

9.93397 

8 

12 

49 

9.70952 

21 

21 

9.77562 

29 

29 

0.22438 

9.93390 

7 

8 

11 

50 

9.70973 

9.77591 

0.22409 

9.93382 

10 

51 

9.70994 

21 

9.77619 

28 

0.22381 

9.93375 

7 

9 

52 

9.71015 

21 

9.77648 

29 

0.22352 

9.93367 

8 

8 

53 

9.71036 

21 

9.77677 

29 

0.22323 

9.93360 

7 

7 

54 

9.71058 

22 

21 

9.77706 

29 

28 

0.22294 

9.93352 

8 

8 

6 

55 

9.71079 

9.77734 

0.22266 

9.93344 

5 

56 

9.71100 

21 

9.77763 

29 

0.22237 

9.93337 

7 

4 

57 

9.71121 

21 

9.77791 

28 

0.22209 

9.93329 

8 

3 

58 

9.71142 

21 

9.77820 

29 

0.22180 

9.93322 

7 

2 

59 

9.71163 

21 

21 

9.77849 

29 

28 

0.22151 

9.93314 

8 

1 

60 

9.71184 

9777877 

0.22123 

9.93307 

0 

L.  Cos. 

1 d. 

L.  Cotg. 

! d.  c. 

L.Tang. 

L.'Sin. 

rd.“ 

/ 

P.  P. 

30 

29 

6 

3.0 

2.9 

7 

3.5 

3.4 

'8 

4.0 

3.9 

9 

4.5 

4.4 

10 

5.0 

4.8 

20 

10.0 

9.7 

30 

15.0 

14.5 

40 

20.0 

19.3 

50 

25.0 

24.2 

• 

28 

6 

2.8 

7 

3.3 

8 

3.7 

9 

4.2 

10 

4.7 

20 

9.3 

30 

14.0 

40 

18.7 

50 

23.3 

22 

6 

2.2 

7 

2.6 

8 

2.9 

9 

3.3 

10 

3.7 

20 

7.3 

30 

11.0 

40 

14.7 

50 

18.3 

21 

6 

2.1 

7 

2.5 

8 

2.8 

9 

3.2 

10 

3.5 

20 

7.0 

30 

10.5 

40 

14.0 

50 

17.5 

8 

7 

6 

0.8 

0.7 

7 

0.9 

0.8 

8 

1.1 

0.9 

9 

1.2 

1.1 

10 

1.3 

1.2 

20 

2.7 

2.3 

30 

4.0 

3.5 

40. 

5.3 

4.7 

50 

6.7 

5.8 

P.  P. 

53° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS.  523 

31° 


/ 

L.  Sin. 

d. 

L.Taiig. 

d.  c.  L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

1 

2 

3 

4 

9.71184 

9.71205 

9.71226 

9.71247 

9.71268 

21 

21 

21 

21 

21 

21 

21 

21 

21 

20 

21 

21 

21 

21 

21 

21 

20 

21 

21 

21 

20 

21 

21 

21 

20 

21 

21 

20 

21 

21 

20 

21 

20 

21 

20 

21 

20 

21 

21 

20 

20 

21 

20 

21 

20 

21 

20 

20 

21 

20 

20 

21 

20 

20 

21 

20 

20 

21 

20 

20 

9.77877 

9.77906 

9.77935 

9.77963 

9.77992 

29 

29 

28 

29 

28 

29 

28 

29 

29 

28 

29 

28 

29 

28 

29 

28 

29 

28 

28 

29 

28 

29 

28 

29 

28 

28 

29 

28 

29 

28 

28 

29 

28 

28 

29 

28 

28 

29 

28 

28 

28 

29 

28 

28 

28 

29 

28 

28 

28 

28 

29 

28 

28 

28 

28 

28 

29 

28 

28 

28 

0.22123 

0.22094 

0.22065 

0.22037 

0.22008 

9.93307 

9.93299 

9.93291 

9.93284 

9.93276 

8 

8 

7 

8 

7 

8 

8 

7 

8 

8 

7 

8 

8 

■ 7 

8 

8 

7 

8 

8 

7 

8 

8 

7 

8 

8 

7 

8 

8 

8 

7 

8 

8 

8 

7 

8 

8 

8 

8 

7 

8 

8 

8 

7 

8 

8 

8 

8 

8 

7 

8 

8 

8 

8 

8 

8 

7 

8 

8 

8 

8 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

29 

6 2.9 

7 3.4 

8 3.9 

9 4.4 

10  4.8 

20  9.7 

30  14.5 

40  19.3 

50  24.2 

28 

6 2.8 

7 3.3 

8 3.7 

9 4.2 

10  4.7 

20  9.3 

30  14.0 

40  18.7 

50  23.3 

21 

6 2.1 

7 2.5 

8 2.8 

9 3.2 

10  3.5 

20  7.0 

30  10.5 

40  14.0 

50  17.5 

20 

6 2.0 

7 2.3 

8 2.7 

9 3.0 

10  3.3 

20  6.7 

30  10.0 

40  13.3 

50  16.7 

8 7 

6 0.8  0.7 

7 0.9  0.8 

8 1.1  0.9 

9 1.2  1.1 

10  1.3  1.2 

20  2.7  2.3 

30  4.0  3.5 

40  5.3  4.7 

50  6.7  5.8 

5 

6 

7 

8 

9 

9.71289 

9.71310 

9.71331 

9.71352 

9.71373 

9.78020 

9.78049 

9.78077 

9.78106 

9.78135 

0.21980 

0.21951 

0.21923 

0.21894 

0.21865 

9.93269 

9.93261 

9.93253 

9.93246 

9.93238 

10 

11 

12 

13 

14 

9.71393 

9.71414 

9.71435 

9.71456 

9.71477 

9.78163 

9.78192 

9.78220 

9.78249 

9.78277 

0.21837 

0.21808 

0.21780 

0.21751 

0.21723 

9.93230 

9.93223 

9.93215 

9.93207 

9.93200 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

15 

16 

17 

18 
19 

9.71498 

9.71519 

9.71539 

9.71560 

9.71581 

9.78306 

9.78334 

9.78363 

9.78391 

9.78419 

0.21694 

0.21666 

0.21637 

0.21609 

0.21581 

9.93192 

9.93184 

9.93177 

9.93169 

9.93161 

20 

21 

22 

23 

24 

9.71602 

9.71622 

9.71643 

9.71664 

9.71685 

9.78448 

9.78476 

9.78505 

9.78533 

9.78562 

0.21552 

0.21524 

0.21495 

0.21467 

0.21438 

9.93154 

9.93146 

9.93138 

9.93131 

9.93123 

40 

39 

38 

37 

36 

2.5 

26 

27 

28 
29 

9.71705 

9.71726 

9.71747 

9.71767 

9.71788 

9.78590 

9.78618 

9.78647 

9.78675 

9.78704 

0.21410 

0.21382 

0.21353 

0.21325 

0.21296 

9.93115 

9.93108 

9.93100 

9.93092 

9.93084 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.71809 

9.71829 

9.71850 

9.71870 

9.71891 

9.78732 

9.78760 

9.78789 

9.78817 

9.78845 

0.21268 

0.21240 

0.21211 

0.21183 

0.21155 

9.93077 

9.93069 

9.93061 

9.93053 

9.93046 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.71911 

9.71932 

9.71952 

9.71973 

9.71994 

9.78874 

9.78902 

9.78930 

9.78959 

9.78987 

0.21126 

0.21098 

0.21070 

0.21041 

0.21013 

9.93038 

9.93030 

9.93022 

9.93014 

9.93007 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.72014 

9.72034 

9.72055 

9.72075 

9.72096 

9.79015 

9.79043 

9.79072 

9.79100 

9.79128 

0.20985 

0.20957 

0.20928 

0.20900 

0.20872 

9.92999 

9.92991 

9.92983 

9.92976 

9.92968 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

45 

46 

47 

48 

49 

9.72116 

9.72137 

9.72157 

9.72177 

9.72198 

9.79156 

9.79185 

9.79213 

9.79241 

9.79269 

0.20844 

0.20815 

0.20787 

0.20759 

0.20731 

9.92960 

9.92952 

9.92944 

9.92936 

9.92929 

5Q 

51 

52 

53 

54 

9.72218 

9.72238 

9.72259 

9.72279 

9.72299 

9.79297 

9.79326 

9.79354 

9.79382 

9.79410 

0.20703 

0.20674 

0.20646 

0.20618 

0.20590 

9.92921 

9.92913 

9.92905 

9.92897 

9.92889 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.72320 

9.72340 

9.72360 

9.72381 

9.72401 

9.79438 

9.79466 

9.79495 

9.79523 

9.79551 

0.20562 

0.20534 

0.20505 

0.20477 

0.20449 

9.92881 

9.92874 

9.92866 

9.92858 

9.92850 

5 

4 

3 

2 

1 

60 

9.72421 

9.79579 

0.20421 

9.92842 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tcang. 

L.  Sin. 

dr 

P.  P. 

58° 


524 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS, 

32° 


/ 

L.  Sin. 

0 

9.72421 

1 

9.72441 

2 

9.72461 

3 

9.72482 

4 

9.72502 

5 

9.72522 

6 

9.72542 

7 

9.72562 

8 

9.72582 

9 

9.72602 

iO 

9.72622 

11 

9.72643 

12 

9.72663 

13 

9.72683 

14 

9.72703 

15 

9.72723 

16 

9.72743 

17 

9.72763 

18 

9.72783 

19 

9.72803 

20 

9.72823 

21 

9.72843 

22 

9.72863 

23 

9.72883 

24 

9.72902 

25 

9.72922 

26 

9.72942 

27 

9.72962 

28 

9.72982 

29 

9.73002 

30 

9.73022 

31 

9.73041 

32 

9.73061 

33 

9.73081 

34 

9.73101 

35 

9.73121 

36 

9.73140 

37 

9.73160 

38 

9.73180 

39 

9.73200 

40 

9.73219 

41 

9.73239 

42 

9.73259 

43 

9.73278 

44 

9.73298 

45 

9.73318 

46 

9.73337 

47 

9.73357 

48 

9.73377 

49 

9.73396 

50 

9.73416 

51 

9.73435 

52 

9.73455 

53 

9.73474 

54 

9.73494 

55 

9.73513 

56 

9.73533 

57 

9.73552 

58 

9.73572 

59 

9.73591 

60 

9.73611 

L.Cos. 

d. 


20 

20 

21 

20 

20 

20 

20 

20 

20 

20 

21 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 

20 

19 

20 
20 
20 
20 
20 
20 

19 
20* 

20 
20 
20 

19 

20 
20 
20 

19 

20 
20 

19 

20 
20 

19 

20 
20 

19 

20 

19 

20 

19 

20 

19 

20 

19 

20 

19 

20 


L.Tang. 


9.79579 

9.79607 

9.79635 

9.79663 

9.79691 


9.79719 

9.79747 

9.79776 

9.79804 

9.79832 


9.79860 

9.79888 

9.79916 

9.79944 

9.79972 


9.80000 

9.80028 

9.80056 

9.80084 

9.80112 


9.80140 

9.80168 

9.80195 

9.80223 

9.80251 


9.80279 

9.80307 

9.80335 

9.80363 

9.80391 


9.80419 

9.80447 

9.80474 

9.80502 

9.80530 


9.80558 

9.80586 

9.80614 

9.80642 

9.80669 


9.80697 

9.80725 

9.80753 

9.80781 

9.80808 


9.80836 

9.80864 

9.80892 

9.80919 

9.80947 


9.80975 

9.81003 

9.81030 

9.81058 

9.81086 

9.81113 

9.81141 

9.81169 

9.81196 

9.81224 


9.81252 


L.  Cotg, 


d.  c. 


28 

28 

28 

28 

28 

28 

29 

28 

28 

28 

28 

28 

28 

28 

28 

28 

28 

28 

28 

28 

28 

27 

28 
28 
28 
28 
28 
28 
28 
28 
28 

27 

28 
28 
28 
28 
28 
28 

27 

28 
28 
28 
28 

27 

28 
28 
28 

27 

28 
28 
28 

27 

28 
28 

27 

28 
28 

27 

28 
28 

d.cT 


L.  Cotg. 


0.20421 

0.20393 

0.20365 

0.20337 

0.20309 


0.20281 

0.20253 

0.20224 

0.20196 

0.20168 


0.20140 

0.20112 

0.20084 

0.20056 

0.20028 


0.20000 

0.19972 

0.19944 

0.19916 

0.19888 


0.19860 

0.19832 

0.19805 

0.19777 

0.19749 


0.19721 

0.19693 

0.19665 

0.19637 

0.19609 


0.19581 

0.19553 

0.19526 

0.19498 

0.19470 


0.19442 

0.19414 

0.19386 

0.19358 

0.19331 


0.19303 

0.19275 

0.19247 

0.19219 

0.19192 


0.19164 

0.19136 

0.19108 

0.19081 

0.19053 


0.19025 

0.18997 

0.18970 

0.18942 

0.18914 


0.18887 

0.18859 

0.18831 

0.18804 

0.18776 


0.18748 


L.Tang. 


L.  Cos.  d 


9.92842 

9.92834 

9.92826 

9.92818 

9.92810 


9.92803 

9.92795 

9.92787 

9.92779 

9.92771 


9.92763 

9.92755 

9.92747 

9.92739 

9.92731 


9.92723 

9.92715 

9.92707 

9.92699 

9.92691 


9.92683 

9.92675 

9.92667 

9.92659 

9.92651 


9.92643 

9.92635 

9.92627 

9.92619 

9.92611 


9.92603 

9.92595 

9.92587 

9.92579 

9.92571 


9.92563 

9.92555 

9.92546 

9.92538 

9.92530 


9.92522 

9.92514 

9.92506 

9.92498 

9.92490 


9.92482 

9.92473 

9.92465 

9.92457 

9.92449 


9.92441 

9.92433 

9.92425 

9.92416 

9.92408 


9.92400 

9.92392 

9.92384 

9.92376 

9.92367 


9.92359 


L.  Sin. 


d. 


P.  P. 


29 

2.9 

3.4 

3.9 

4.4 
4.8 
9.7 

14.5 

19.3 

24.2 


28 

2.8 

3.3 

3.7 

4.2 

4.7 

9.3 
14.0 
18.7 
23.3 


27 

2.7 

3.2 

3.6 

4.1 

4.5 

9.0 

13.5 

18.0 

22.5 


21 

2.1 

2.5 
2.8 
3.2 

3.5 
7.0 

10.5 
14.0 

17.5 


20 

2.0 

2.3 

2.7 
3.0 

3.3 

6.7 
10.0 
13.3 
16.7 


6 

1.9 

7 

2.2 

8 

2.5 

9 

2.9 

10 

3.2 

20 

6.3 

30 

9.5 

40 

12.7 

50 

15.8 

9 

8 

6 

0.9 

0.8 

7 

1.1 

0.9 

8 

1.2 

1.1 

9 

1.4 

1.2 

10 

1.5 

1.3 

20 

3.0 

2.7 

30 

4.5 

4.0 

40 

6.0 

5.3 

50 

7.5 

6.7 

P.  P. 


5T 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

33° 


525 


/ 

L.  Sin. 

0 

9.73611 

1 

9.73630 

2 

9.73650 

3 

9.73669 

4 

9.73689 

5 

9.73708 

6 

9.73727 

7 

9.73747 

8 

9.73766 

9 

9.73785 

10 

9.73805 

11 

9.73824 

12 

9.73843 

13 

9.73863 

14 

9.73882 

15 

9.73901 

16 

9.73921 

17 

9.73940 

18 

9.73959 

19 

9.73978 

20 

9.73997 

21 

9.74017 

22 

9.74036 

23 

9.74055 

24 

9.74074 

25 

9.74093 

26 

9.74113 

27 

9.74132 

28 

9.74151 

29 

9.74170 

30 

9.74189 

31 

9.74208 

32 

9.74227 

33 

9.74246 

34 

9.74265 

35 

9.74284 

36 

9.74303 

37 

9.74322 

38 

9.74341 

39 

9.74360 

40 

9.74379 

41 

9.74398 

42 

9.74417 

43 

9.74436 

44 

9.74455 

45 

9.74474 

46 

9.74493 

47 

9.74512 

48 

9.74531 

49 

9.74549 

50 

9.74568 

51 

9.74587 

52 

9.74606 

53 

9.74625 

54 

9.74644 

55 

9.74662 

56 

9.74681 

57 

9.74700 

58 

9.74719 

59 

9.74737 

60 

9.74756 

L.  Cos. 

L.  Cotg. 

L.  Cos. 

0.18748 

9.92359 

0.18721 

9.92351 

0.18693 

9.92343 

0.18665 

9.92335 

0.18638 

9.92326 

0.18610 

9.92318 

0.18582 

9.92310 

0.18555 

9.92302 

0.18527 

9.92293 

0.18500 

9.92285 

0.18472 

9.92277 

0.18444 

9.92269 

0.18417 

9.92260 

0.18389 

9.92252 

0.18362 

9.92244 

0.18334 

9.92235 

0.18307 

9.92227 

0.18279 

9.92219 

0.18252 

9.92211 

0.18224 

9.92202 

0.18197 

9.92194 

0.18169 

9.92186 

0.18142 

9.92177 

0.18114 

9.92169 

0.18087 

9.92161 

0.18059 

9.92152 

0.18032 

9.92144 

0.18004 

9.92136 

0.17977 

9.92127 

0.17949 

9.92119 

0.17922 

9.92111 

0.17894 

9.92102 

0.17867 

9.92094 

0.17839 

9.92086 

0.17812 

9.92077 

0.17785 

9.92069 

0.17757 

9.92060 

0.17730 

9.92052 

0.17702 

9.92044 

0.17675 

9.92035 

0.17648 

9.92027 

0.17620 

9.92018 

0.17593 

9.92010 

0.17565 

9.92002 

0.17538 

9.91993 

0.17511 

9.91985 

0.17483 

9.91976 

0.17456 

9.91968 

0.17429 

9.91959 

0.17401 

9.91951 

0.17374 

9.91942 

0.17347 

9.91934 

0.17319 

9.91925 

0.17292 

9.91917 

0.17265 

9.91908 

0.17238 

9.91900 

0.17210 

9.91891 

0.17183 

9.91883 

0.17156 

9.91874 

0.17129 

9.91866 

0.17101 

9.91857 

L.Tang. 

L.  Sin. 

L.Tang. 


d.  c. 


P.  P. 


19 

20 

19 

20 
19 

19 

20 
19 

19 

20 
19 

19 

20 
19 

19 

20 
19 
19 
19 

19 

20 
19 
19 
19 

19 

20 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
18 
19 
19 
19 
19 
19 
18 
19 
19 
19 
18 
19 


9.81528 

9.81556 

9.81583 

9.81611 

9.81638 


9.81666 

9.81693 

9.81721 

9.81748 

9.81776 


9.81803 

9.81831 

9.81858 

9.81886 

9.81913 


9.81941 

9.81968 

9.81996 

9.82023 

9.82051 


9.82078 

9.82106 

9.82133 

9.82161 

9.82188 


9.82215 

9.82243 

9.82270 

9.82298 

9.82325 


9.82352 

9.82380 

9.82407 

9.82435 

9.82462 


9.82489 

9.82517 

9.82544 

9.82571 

9.82599 


9.82626 

9.82653 

9.82681 

9.82708 

9.82735 


9.82762 

9.82790 

9.82817 

9.82844 

9.82871 


9.82899 


28 

2.8 

3.3 

3.7 

4.2 

4.7 

9.3 
14.0 
18.7 
23.3 


27 

2.7 

3.2 

3.6 

4.1 

4.5 

9.0 

13.5 
18.0 

22.5 


20 

2.0 

2.3 

2.7 
3.0 

3.3 

6.7 
10.0 
13.3 
16.7 


19 

1.9 

2.2 

2.5 

2.9 

3.2 

6.3 

9.5 

12.7 

15.8 


18 

1.8 

2.1 

2.4 

2.7 

3.0 

6.0 

9.0 

12.0 

15.0 


8 

0.8 

0.9 

1.1 

1.2 

1.3 

2.7 
4.0 

5.3 

6.7 


d. 


L.  Cotg. 


d.  c. 


P.P. 


56° 


526  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

34° 


f 

L.  Sin. 

0 

9.74756 

1 

9.74775 

2 

9.74794 

3 

9.74812 

4 

9.74831 

5 

9.74850 

6 

9.74868 

7 

9.74887 

8 

9.74906 

9 

9.74924 

10 

9.74943 

11 

9.74961 

12 

9.74980 

13 

9.74999 

14 

9.75017 

15 

9.75036 

16 

9.75054 

17 

9.75073 

18 

9.75091 

19 

9.75110 

20 

9.75128 

21 

9.75147 

22 

9.75165 

23 

9.75184 

24 

9.75202 

25 

9.75221 

26 

9.75239 

27 

9.75258 

28 

9.75276 

29 

9.75294 

30 

9.75313 

31 

9.75331 

32 

9.75350 

33 

9.75368 

34 

9.75386 

35 

9.75405 

36 

9.75423 

37 

9.75441 

38 

9.75459 

39 

9.75478 

40 

9.75496 

41 

9.75514 

42 

9.75533 

43 

9.75551 

44 

9.75569 

45 

9.75587 

46 

9.75605 

47 

9.75624 

48 

9.75642 

49 

9.75660 

50 

9.75678 

51 

9.75696 

52 

9.75714 

53 

9.75733 

54 

9.75751 

55 

9.75769 

56 

9.75787 

57 

9.75805 

58 

9.75823 

59 

9.75841 

60 

9.75859 

L.  Cos. 

L.  Cotg. 

L.  Cos. 

d. 

0.17101 

9.91857 

60 

0.17074 

9.91849 

8 

59 

0.17047 

9.91840 

9 

58 

0.17020 

9.91832 

8 

57 

0.16992 

9.91823 

9 

Q 

56 

0.16965 

9.91815 

O 

55 

0.16938 

9.91806 

9 

54 

0.16911 

9.91798 

8 

53 

0.16883 

9.91789 

9 

52 

0.16856 

9.91781 

8 

Q 

51 

0.16829 

9.91772 

a 

50 

0.16802 

9.91763 

9 

49 

0.16775 

9.91755 

8 

48 

0.16748 

9.91746 

9 

47 

0.16720 

9.91738 

8 

9 

46 

0.16693 

9.91729 

45 

0.16666 

9.91720 

9 

44 

0.16639 

9.91712 

8 

43 

0.16612 

9.91703 

9 

42 

0.16585 

9.91695 

8 

41 

Q 

0.16558 

9.91686 

O 

40 

0.16530 

9.91677 

9 

39 

0.16503 

9.91669 

8 

38 

0.16476 

9.91660 

9 

37 

0.16449 

9.91651 

9 

g 

36 

0.16422 

9.91643 

35 

0.16395 

9.91634 

9 

34 

0.16368 

9.91625 

9 

33 

0.16341 

9.91617 

8 

32 

0.16314 

9.91608 

9 

9 

31 

0.16287 

9.91599 

30 

0.16260 

9.91591 

8 

29 

0.16232 

9.91582 

9 

28 

0.16205 

9.91573 

9 

27 

0.16178 

9.91565 

8 

9 

26 

0.16151 

9.91556 

25 

0.16124 

9.91547 

9 

24 

0.16097 

9.91538 

9 

23 

0.16070 

9.91530 

8 

22 

0.16043 

9.91521 

9 

9 

21 

0.16016 

9.91512 

20 

0.15989 

9.91504 

8 

19 

0.15962 

9.91495 

9 

18 

0.15935 

9.91486 

9 

17 

0.15908 

9.91477 

9 

8 

16 

0.15881 

9.91469 

15 

0.15854 

9.91460 

9 

14 

0.15827 

9.91451 

9 

13 

0.15800 

9.91442 

9 

12 

0.15773 

9.91433 

9 

8 

11 

0.15746 

9.91425 

10 

0.15720 

9.91416 

9 

9 

0.15693 

9.91407 

9 

8 

0.15666 

9.91398 

9 

. 7 

0.15639 

9.91389 

9 

8 

6 

0.15612 

9.91381 

5 

0.15585 

9.91372 

9 

4 

0.15558 

9.91363 

9 

3 

0.15531 

9.91354 

9 

2 

0.15504 

9.91345 

9 

9 

1 

0.15477 

9.91336 

0 

L.Tang. 

L.  Sin. 

d. 

/ 

d. 


L.Tang. 


9.82899 

9.82926 

9.82953 

9.82980 

9.83008 


9.83035 

9.83062 

9.83089 

9.83117 

9.83144 


d.  c. 


9.83171 

9.83198 

9.83225 

9.83252 

9.83280 


9.83307 

9.83334 

9.83361 

9.83388 

9.83415 


9.83713 

9.83740 

9.83768 

9.83795 

9.83822 


9.83849 

9.83876 

9.83903 

9.83930 

9.83957 


9.83984 

9.84011 

9.84038 

9.84065 

9.84092 


9.84119 

9.84146 

9.84173 

9.84200 

9.84227 


9.84254 

9.84280 

9.84307 

9.84334 

9.84361 


9.84388 

9.84415 

9.84442 

9.84469 

9.84496 


9.84523 


L.  Cotg. 


27 

27 

27 

28 
27 
27 

27 

28 
27 
27 
27 
27 

27 

28 
27 
27 
27 

■ 27 
27 

27 

28 
27 
27 
27 
27 
27 
27 
27 
27 
27 

27 

28 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
26 
27 
27 
27 
27 
27 
27 
27 
27 
27 

d.  c. 


P.  P. 


28 

2.8 

3.3 

3.7 

4.2 

4.7 

9.3 
14.0 
18.7 
23.3 


27 

2.7 

3.2 

3.6 

4.1 

4.5 

9.0 

13.5 
18.0 

22.5 


26 

6 

2.6 

7 

3.0 

8 

3.5 

9 

3.9 

10 

4.3 

20 

8.7 

30 

13.0 

40 

17.3 

50 

21.7 

19 

1.9 

2.2 

2.5 

2.9 

3.2 

6.3 

9.5 

12.7 

15.8 


18 

1.8 

2.1 

2.4 

2.7 

3.0 

6.0 

9.0 

12.0 

15.0 


9 

8 

6 

0.9 

0.8 

7 

1.1 

0.9 

8 

1.2 

1.1 

9 

1.4 

1.2 

10 

1.5 

1.3 

20 

3.0 

2.7 

30 

4.5 

4.0 

40 

6.0 

5.3 

50 

7.5 

6.7 

P.  P. 


55° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS.  527 


35° 


f 

L.  Sin. 

d. 

L.Tang.j  d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

1 

2 

3 

4 

9.75859 

9.75877 

9.75895 

9.75913 

9.75931 

18 

18 
. 18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

17 

18 

18 

18 

18 

18 

17 

18 

18 

18 

17 

18 

18 

18 

17 

18 

18 

17 

18 

18 

17 

18 

18 

17 

18 

18 

17 

18 

17 

18 

17 

18 

17 

18 

17 

18 

17 

18 

17 

18 

17 

18 

17 

17 

18 

9.84523 

9.84550 

9.84576 

9.84603 

9.84630 

27 

26 

27 

27 

27 

27 

27 

'27 

26 

27 

27 

27 

27 

27 

26 

27 

27 

27 

27 

26 

27 

27 

27 

26 

27 

27 

27 

26 

27 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

26 

27 

27 

26 

27 

26 

27 

27 

26 

0.15477 

0.15450 

0.15424 

0.15397 

0.15370 

9.91336 

9.91328 

9.91319 

9.91310 

9.91301 

8 

9 

9 

9 

9 

9 

‘9 

8 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

8 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

10 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

10 

9 

9 

9 

9 

9 

9 

10 

9 

9 

9 

9 

60 

59 

58 

57 

56 

27  26 

6 2.7  2.6 

7 3.2  3.0 

8 3.6  3.5 

9 4.1  3.9 

10  4.5  4.3 

20  9.0  8.7 

30  13.5  13.0 

40  18.0  17.3 

50  22.5  21.7 

18 

6 1.8 

7 2.1 

8 2.4 

9 2.7 

10  3.0 

20  6.0 

30  9.0 

40  12.0 

50  15.0 

17 

6 1.7 

7 2.0 

8 2.3 

9 2.6 

10  2.8 

20  5.7 

30  8.5 

40  11.3 

50  14.2 

10 

6 1.0 

7 1.2 

8 1.3 

9 1.5 

10  1.7 

20  3.3 

30  5.0 

40  6.7 

50  8.3 

6 1 0^9  0% 

7 1.1  0.9 

8 1 1.2  1.1 

9 1 1.4  1.2 

10  1.5  1.3 

20  3.0  2.7 

30  4.5  4.0 

40  6.0  5.3 

50  i 7.5-  6.7 

5 

6 

7 

8 

9 

9.75949 

9.75967 

9.75985 

9.76003 

9.76021 

9.84657 

9.84684 

9.84711 

9.84738 

9.84764 

0.15343 

0.15316 

0.15289 

0.15262 

0.15236 

9.91292 

9.91283 

9.91274 

9.91266 

9.91257 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.76039 

9.76057 

9.76075 

9.76093 

9.76111 

9.84791 

9.84818 

9.84845 

9.84872 

9.84899 

0.15209 

0.15182 

0.15155 

0.15128 

0.15101 

9.91248 

9.91239 

9.91230 

9.91221 

9.91212 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.76129 

9.76146 

9.76164 

9.76182 

9.76200 

9.84925 

9.84952 

9.84979 

9.85006 

9.85033 

0.15075 

0.15048 

0.15021 

0.14994 

0.14967 

9.91203 

9.91194 

9.91185 

9.91176 

9.91167 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

20 

21 

22 

23 

24 

9.76218 

9.76236 

9.76253 

9.76271 

9.76289 

9.85059 

9.85086 

9.85113 

9.85140 

9.85166 

0.14941 

0.14914 

0.14887 

0.14860 

0.14834 

9.91158 

9.91149 

9.91141 

9.91132 

9.91123 

25 

26 

27 

28 
29 

9.76307 

9.76324 

9.76342 

9.76360 

9.76378 

9.85193 

9.85220 

9.85247 

9.85273 

9.85300 

0.14807 

0.14780 

0.14753 

0.14727 

0.14700 

9.91114 

9.91105 

9.91096 

9.91087 

9.91078 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.76395 

9.76413 

9.76431 

9.76448 

9.76466 

9.85327 

9.85354 

9.85380 

9.85407 

9.85434 

0.14673 

0.14646 

0.14620 

0.14593 

0.14566 

9.91069 

9.91060 

9.91051 

9.91042 

9.91033 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

35 

36 

37 

38 

39 

9.76484 

9.76501 

9.76519 

9.76537 

9.76554 

9.85460 

9.85487 

9.85514 

9.85540 

9.85567 

0.14540 

0.14513 

0.14486 

0.14460 

0.14433 

9.91023 

9.91014 

9.91005 

9.90996 

9.90987 

40 

41 

42 

43 

44 

9.76572 

9.76590 

9.76607 

9.76625 

9.76642 

9.85594 

9.85620 

9.85647 

9.85674 

9.85700 

0.14406 

0.14380 

0.14353 

0.14326 

0.14300 

9.90978 

9.90969 

9.90960 

9.90951 

9.90942 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.76660 

9.76677 

9.76695 

9.76712 

9.76730 

9.85727 

9.85754 

9.85780 

9.85807 

9.85834 

0.14273 

0.14246 

0.14220 

0.14193 

0.14166 

9.90933 

9.90924 

9.90915 

9.90906 

9.90896 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

50 

51 

52 

53 

54 

9.76747 

9.76765 

9.76782 

9.76800 

9.76817 

9.85860 

9.85887 

9.85913 

9.85940 

9.85967 

0.14140 

0.14113 

0.14087 

0.14060 

0.14033 

9.90887 

9.90878 

9.90869 

9.90860 

9.90851 

55 

56 

57 

58 

59 

9.76835 

9.76852 

9.76870 

9.76887 

9.76904 

9.85993 

9.86020 

9.86046 

9.86073 

9.86100 

0.14007 

0.13980 

0.13954 

0.13927 

0.13900 

9.90842 

9.90832 

9.90823 

9.90814 

9.90805 

5 

4 

3 

2 

1 

60 

9.76922 

9.86126 

0.13874 

9.90796 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

“dr 

/ 

P.  P. 

54^ 


528  LOGARimuS  OF  TRIGONOMETRIC  FUNCTIONS, 

36° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

0 

9.76922 

17 

9.86126 

'■  27 

0.13874 

9.90796 

1 

9.76939 

9.86153 

0.13847 

9.90787 

2 

9.76957 

18 

9.86179 

26 

0.13821 

9.90777 

3 

9.76974 

17 

9.86206 

27 

0.13794 

9.90768 

4 

9.76991 

17 

18 

17 

9.86232 

26 

27 

26 

0.13768 

9.90759 

5 

6 

9.77009 

9.77026 

9.86259 

9.86285 

0.13741 

0.13715 

9.90750 

9.90741 

7 

9.77043 

17 

9.86312 

27 

0.13688 

9.90731 

8 

9.77061 

18 

9.86338 

26 

0.13662 

9.90722 

9 

9.77078 

17 

17 

17 

9.86365 

27 

27 

26 

0.13635 

9.90713 

0 

11 

9.77095 

9.77112 

9.86392 

9.86418 

0.13608 

0.13582 

9.90704 

9.90694 

12 

9.77130 

18 

9.86445 

27 

0.13555 

9.90685 

13 

9.77147 

17 

9.86471 

26 

0.13529 

9.90676 

14 

9.77164 

17 

17 

18 

9.86498 

27 

26 

27 

0.13502 

9.90667 

15 

16 

9.77181 

9.77199 

9.86524 

9.86551 

0.13476 

0.13449 

9.90657 

9.90648 

17 

9.77216 

17 

9.86577 

26 

0.13423 

9.90639 

18 

9.77233 

17 

9.86603 

26 

0.13397 

9.90630 

19 

9.77250 

17 

18 

17 

9.86630 

27 

26 

27 

0.13370 

9.90620 

20 

21 

9.77268 

9.77285 

9.86656 

9.86683 

0.13344 

0.13317 

9.90611 

9.90602 

22 

9.77302 

17 

9.86709 

26 

0.13291 

9.90592 

23 

9.77319 

17 

9.86736 

27 

0.13264 

9.90583 

24 

9.77336 

17 

17 

17 

9.86762 

26 

27 

26 

0.13238 

9.90574 

25 

26 

9.77353 

9.77370 

9.86789 

9.86815 

0.13211 

0.13185 

9.90565 

9.90555 

27 

9.77387 

17 

9.86842 

27 

0.13158 

9.90546 

28 

9.77405 

18 

9.86868 

26 

0.13132 

9.90537 

29 

9.77422 

17 

17 
. 17 

9.86894 

26 

27 

26 

0.13106 

9.90527 

30 

31 

9.77439 

9.77456 

9.86921 

9.86947 

0.13079 

0.13053 

9.90518 

9.90509 

32 

9.77473 

17 

9.86974 

27 

0.13026 

9.90499 

33 

9.77490 

17 

9.87000 

26 

0.13000 

9.90490 

34 

9 77507 

17 

17 

17 

9.87027 

27 

26 

26 

0.12973 

9.90480 

35' 

36 

9.77524 

9.77541 

9.87053 

9.87079 

0.12947 

0.12921 

9.90471 

9.90462 

37 

9.77558 

17 

9.87106 

27 

/0. 12894 

9.90452 

38 

9.77575 

17 

9.87132 

26 

0.12868 

9.90443 

39 

9.77592 

17 

17 

17 

9.87158 

26 

27 

26 

0.12842 

9.90434 

40 

41 

9.77609 

9.77626 

9.87185 

9.87211 

0.12815 

0.12789 

9.90424 

9.90415 

42 

9.77643 

17 

9.87238 

27 

0.12762 

9.90405 

43 

9.77660 

17 

9.87264 

26 

0.12736 

9.90396 

44 

9.77677 

17 

17 

17 

9.87290 

26 

27 

26 

0.12710 

9.90386 

45 

46 

9.77694 

9.77711 

9.87317 

9.87343 

0.12683 

0.12657 

9.90377 

9.90368 

47 

9.77728 

17 

9.87369 

26 

0.12631 

9.90358 

48 

9.77744 

16 

9.87396 

27 

0.12604 

^.90349 

49 

9.77761 

17 

17 

17 

9.87422 

26 

26 

27 

0.12578 

9.90339 

50 

51 

9.77778 

9.77795 

9.87448 

9.87475 

0.12552 

0.12525 

9.90330 

9.90320 

52 

9.77812 

17 

9.87501 

26 

0.12499 

9.90311 

53 

9.77829 

17 

9.87527 

26 

0.12473 

9.90301 

54 

9.77846 

17 

16 

17 

9.87554 

27 

26 

26 

0.12446 

9.90292 

55 

56 

9.77862 

9.77879 

9.87580 

9.87606 

0.12420 

0.12394 

9.90282 

9.90273 

57 

9.77896 

17 

9.87633 

27 

0.12367 

9.90263 

58 

9.77913 

17 

9.87659 

26 

0.12341 

9.90254 

59 

9.77930 

17 

16 

9.87685 

26 

26 

0.12315 

9.90244 

60 

9.77946 

9.87711 

0.12289 

9.90235 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin  1 

P.  P. 


27 

2.7 

3.2 

3.6 

4.1 

4.5 

9.0 

13.5 
18.0 

22.5 


26 

2.6 

3.0 

3.5 

3.9 

4.3 

8.7 

13.0 

17.3 

21.7 


18 

1.8 

2.1 

2.4 

2.7 

3.0 

6.0 

9.0 

12.0 

15.0 


17 

1.7 
2.0 
2.3 
2.6 

2.8 
5.7 
8.5 

11.3 

14.2 


16 

1.6 

1.9 

2.1 

2.4 

2.7 

5.3 

8.0 

10.7 

13.3 


9 

0.9 

1.1 

1.2 

1.4 

1.5 

3.0 

4.5 

6.0 

7.5 


P.  P. 


53‘ 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

37° 


529 


L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.P. 

0 

1 

2 

3 
' 4 

9.77946 

9.77963 

9.77980 

9.77997 

9.78013 

17 

17 

17 

16 

17 

17 

16 

17 

17 

16 

17 

17 

16 

17 

17 

16 

17 

16 

17 

17 

16 

17 

16 

17 

16 

17 

16 

17 

16 

17 

16 

17 

16 

16 

17 

16 

17 

16 

16 

17 

16 

17 

16 

16 

17 

16 

16 

16 

17 

16 

16 

17 

16 

16 

16 

16 

17 

16 

16 

16 

9.87711 

9.87738 

9.87764 

9.87790 

9.87817 

27 

26 

26 

27 

26 

26 

26 

27 

26 

26 

26 

27 

26 

26 

26 

26' 

27 

26 

26 

26 

26 

27 

26 

26 

26 

26 

27 

26 

26 

26 

26 

26 

27 

26 

26 

26 

26 

26 

26 

26 

27 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

27 

26 

26 

26 

26 

26 

26 

26 

26 

0.12289 

0.12262 

0.12236 

0.12210 

0.12183 

9.90235 

9.90225 

9.90216 

9.90206 

9.90197 

10 

9 

10 

9 

10 

9 

10 

9 

10 

10 

9 

10 

9 

10 

10 

9 

10 

9 

10 

10 

9 

10 

10 

9 

10 

10 

9 

10 

10 

9 

10 

10 

9 

10 

10 

10 

9 

10 

10 

10 

9 

10 

10 

10 

9 

10 

10 

10 

10 

9 

10 

10 

10 

10 

10 

9 

10 

10 

10 

10 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

27 

6 2.7 

7 3.2 

8 3.6 

9 4.1 

10  4.5 

20  9.0 

30  13.5 

40  18.0 

50  22.5 

26 

6 2.6 

7 3.0 

8 3.5 

9 3.9 

10  4.3 

20  8.7 

30  13.0 

40  17.3 

60  21.7 

17 

6 1.7  . 

7 2.0 

8 2.3 

9 2.6 

10  2.8 

20  5.7 

30  8.5 

40  11.3 

50  14.2 

16 

6 1.6 

7 1.9 

8 2.1 

9 2.4 

10  2.7 

20  5.3 

30  8.0 

40  10.7 

50  13.3 

10  9 

6 1 1.0  0.9 

7 1.2  1.1 

8 1.3  1.2 

9 1.5  1.4 

10  1.7  1.5 

20  3.3  3.0 

30  5.0  4.5 

40  6.7  6.0 

50  8.3  7.5 

5 

6 

7 

8 

9 

9.78030 

9.78047 

9.78063 

9.78080 

9.78097 

9.87843 

9.87869 

9.87895 

9.87922 

9.87948 

0.12157 

0.12131 

0.12105 

0.12078 

0.12052 

9.90187 

9.90178 

9.90168 

9.90159 

9.90149 

10 

11 

12 

13 

14 

9.78113 

9.78130 

9.78147 

9.78163 

9.78180 

9.87974 

9.88000 

9.88027 

9.88053 

9.88079 

0.12026 

0.12000 

0.11973 

0.11947 

0.11921 

9.90139 

9.90130 

9.90120 

9.90111 

9.90101 

15 

16 

17 

18 
19 

9.78197 

9.78213 

9.78230 

9.78246 

9.78263 

9.88105 

9.88131 

9.88158 

■9.88184 

9.88210 

0.11895 

0.11869 

0.11842 

0.11816 

0.11790 

9.90091 

9.90082 

9.90072 

9.90063 

9.90053 

20 

21 

22 

23 

24 

9.78280 

9.78296 

9.78313 

9.78329 

9.78346 

9.88236 

9.88262 

9.88289 

9.88315 

9.88341 

0.11764 

0.11738 

0.11711 

0.11685 

0.11659 

9.90043 

9.90034 

9.90024 

9.90014 

9.90005 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

26 

27 

28 
29 

9.78362 

9.78379 

9.78395 

9.78412 

9.78428 

9.88367 

9.88393 

9.88420 

9.88446 

9.88472 

0.11633 

0.11607 

0.11580 

0.11554 

0.11528 

9.89995 

9.89985 

9.89976 

9.89966 

9.89956 

30 

31 

32 

33 

34 

9.78445 

9.78461 

9.78478 

9.78494 

9.78510 

9.88498 

9.88524 

9.88550 

9.88577 

9.88603 

0.11502 

0.11476 

0.11450 

0.11423 

0.11397 

9.89947 

9.89937 

9.89927 

9.89918 

9.89908 

35 

36 

37 

38 

39 

9.78527 

9.78543 

9.78560 

9.78576 

9.78592 

9.88629 

9.88655 

9.88681 

9.88707 

9.88733 

0.11371 

0.11345 

0.11319 

0.11293 

0.11267 

9.89898 

9.89888 

9.89879 

9.89869 

9.89859 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

40 

41 

42 

43 

44 

9.78609 

9.78625 

9.78642 

9.78658 

9.78674 

9.88759 

9.88786 

9.88812 

9.88838 

9.88864 

0.11241 

0.11214 

0.11188 

0.11162 

0.11136 

9.89849 

9.89840 

9.89830 

9.89820 

9.89810 

45 

46 

47 

48 

49 

9.78691 

9.78707 

9.78723 

9.78739 

9.78756 

9.88890 

9.88916 

9.88942 

9.88968 

9.88994 

0.11110 

0.11084 

0.11058 

0.11032 

0.11006 

9.89801 

9.89791 

9.89781 

9.89771 

9.89761 

50 

51 

52 

53 

54 

9.78772 

9.78788 

9.78805 

9.78821 

9.78837 

9.89020 

9.89046 

9.89073 

9.89099 

9.89125 

0.10980 

0.10954 

0.10927 

0.10901 

0.10875 

9.89752 

9.89742 

9.89732 

9.89722 

9.89712 

55 

56 

57 

58 

59 

9.78853 

9.78869 

9.78886 

9.78902 

9.78918 

9.89151 

9.89177 

9.89203 

9.89229 

9.89255 

0.10849 

0.10823 

0.10797, 

0.10771 

0.10745 

9.89702 

9.89693 

9.89683 

9.89673 

9.89663 

60 

9.78934 

9.89281 

0.10719 

9.89653 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

~~dr 

' 

P.  P. 

530  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS, 

38° 


/ 

L.  Sin. 

0 

9.78934 

1 

9.78950 

2 

9.78967 

3 

9.78983 

4 

9.78999 

5 

9.79015 

6 

9.79031 

7 

9.79047 

8 

9.79063 

9 

9.79079 

10 

9.79095 

11 

9.79111 

12 

9.79128 

13 

9.79144 

14 

9.79160 

15 

9.79176 

16 

9.79192 

17 

9.79208 

18 

9.79224 

19 

9.79240 

20 

9.79256 

21 

9.79272 

22 

9.79288 

23 

9.79304 

24 

9.79319 

25 

9.79335 

26 

9.79351 

27 

9.79367 

28 

9.79383 

29 

9.79399 

30 

9.79415 

31 

9.79431 

32 

9.79447 

33 

9.79463 

34 

9.79478 

35 

9.79494 

36 

9.79510 

37 

9.79526 

38 

9.79542 

39 

9.79558 

40 

9.79573 

41 

9.79589 

42 

9.79605 

43 

9.79621 

44 

9.79636 

45 

9.79652 

46 

9.79668 

47 

9.79684 

48 

9.79699 

49 

9.79715 

50 

9.79731 

51 

9.79746 

52 

9.79762 

53 

9.79778 

54 

9.79793 

55 

9.79809 

56 

9.79825 

57 

9.79840 

58 

9.79856 

59 

9.79872 

60 

9.79887 

L.  Cos. 

L.  Cotg. 

L.  Cos. 

0.10719 

9.89653 

0.10693 

9.89643 

0.10667 

9.89633 

0.10641 

9.89624 

0.10615 

9.89614 

0.10589 

9.89604 

0.10563 

9.89594 

0.10537 

9.89584 

0.10511 

9.89574 

0.10485 

9.89564 

0.10459 

9.89554 

0.10433 

9.89544 

0.10407 

9.89534 

0.10381 

9.89524 

0.10355 

9.89514 

0.10329 

9.89504 

0.10303 

9.89495 

0.10277 

9.89485 

0.10251 

9.89475 

0.10225 

9.89465 

0.10199 

9.89455 

0.10173 

9.89445 

0.10147 

9.89435 

0.10121 

9.89425 

0.10095 

9.89415 

0.10069 

9.89405 

0.10043 

9.89395 

0.10017 

9.89385 

0.09991 

9.89375 

0.09965 

9.89364 

0.09939 

9.89354 

0.09914 

9.89344 

0.09888 

9.89334 

0.09862 

9.89324 

0.09836 

9.89314 

0.09810 

9.89304 

0.09784 

9.89294 

0.09758 

9.89284 

0.09732 

9.89274 

0.09706 

9.89264 

0.09680 

9.89254 

0.09654 

9.89244 

0.09629 

9.89233 

0.09603 

9.89223 

0.09577 

9.89213 

0.09551 

9.89203 

0.09525 

9.89193 

0.09499 

9.89183 

0.09473 

9.89173 

0.09447 

9.89162 

0.09422 

9.89152 

0.09396 

9.89142 

0.09370 

9.89132 

0.09344 

9.89122 

0.09318 

9.89112 

0.09292 

9.89101 

0.09266 

9.89091 

0.09241 

9.89081 

0.09215 

9.89071 

0.09189 

9.89060 

0.09163 

9.890.50 

L.Tang. 

L.  Sin. 

L.Tang. 


d.  c. 


P.  P. 


9.89281 

9.89307 

9.89333 

9.89359 

9.89385 


9.89411 

9.89437 

9.89463 

9.89489 

9.89515 


9.89541 

9.89567 

9.89593 

9.89619 

9.89645 


9.89671 

9.89697 

9.89723 

9.89749 

9.89775 

9.89801 

9.89827 

9.89853 

9.89879 

9.89905 


9.89931 

9.89957 

9.89983 

9.90009 

9.90035 

9.90061 

9.90086 

9.90112 

9.90138 

9.90164 


9.90190 

9.90216 

9.90242 

9.90268 

9.90294 


9.90320 

9.90346 

9.90371 

9.90397 

9.90423 


9.90449 

9.90475 

9.90501 

9.90527 

9.90553 


9.90578 

9.90604 

9.90630 

9.90656 

9.90682 


9.90708 

9.90734 

9.90759 

9.90785 

9.90811 


9.90837 


L.  Cotg, 


26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

25 

26 
26 
26 
26 
26 
26 
26 
26 
26 
26 

25 

26 
26 
26 
26 
26 
26 
26 

25 

26 
26 
26 
26 
26 
26 

25 

26 
26 
26 

~d.  c. 


26 

2.6 

3.0 

3.5 

3.9 

4.3 

8.7 

13.0 

17.3 

21.7 


25 

2.5 

2.9 

3.3 

3.8 

4.2 

8.3 
12.5 

16.7 

20.8 


17 

1.7 
2.0 
2.3 
2.6 

2.8 
5.7 
8.5 

11.3 

14.2 


16 

1.6 

1.9 

2.1 

2.4 

2.7 

5.3 

8.0 

10.7 

13.3 


15 

1.5 
1.8 
2.0 
2.3 

2.5 
5.0 

7.5 
10.0 
12.5 


II 

1.1 

1.3 

1.5 

1.7 

1.8 

3.7 

5.5 

7.3 
9.2 


9 

0.9 

1.1 

1.2 

1.4 

1.5 

3.0 

4.5 

6.0 

7.5 


P.  P. 


51° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS.  531 


39° 


L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

1 

2 

3 

4 

9.79887 

9.79903 

9.79918 

9.79934 

9.79950 

16 

15 

16 

16 

15 

16 

15 

16 

15 

16 

15 

16 

15 

16 

15 

16 

15 

15 

16 

15 

16 

15 

16 

15 

15 

16 

15 

15 

16 

15 

15 

16 

15 

15 

16 

15 

15 

15 

16 

15 

15 

15 

16 

15 

15 

15 

15 

15 

16 

15 

15 

15 

15 

15 

15 

15 

16 

15 

15 

15 

9.90837 

9.90863 

9.90889 

9.90914 

9.90940 

26 

26 

25 

26 

26 

26 

26 

25 

26 

26 

26 

26 

25 

26 

26 

26 

26 

25 

26 

26 

26 

25 

26 

26 

26 

25 

26 

26 

26 

25 

26 

26 

26 

25 

26 

26 

26 

25 

26 

26 

25 

26 

26 

26 

25 

26 

26 

25 

26 

26 

25 

26 

26 

25 

26 

26 

25 

26 

26 

25 

0.09163 

0.09137 

0.09111 

0.09086 

0.09060 

9.89050 

9.89040 

9.89030 

9.89020 

9.89009 

10 

10 

10 

11 

10 

10 

11 

10 

10 

10 

11 

10 

10 

11 

10 

10 

11 

10 

10 

11 

10 

10 

11 

10 

10 

11 

10 

11 

10 

10 

11 

10 

11 

10 

11 

10 

10 

11 

10 

11 

10 

11 

10 

11 

10 

11 

10 

11 

10 

11 

10 

11 

11 

10 

11 

10 

11 

10 

11 

11 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

50 

49 

48 

47 

46 

26 

6 2.6 

7 3.0 

8 3.5 

9 3.9 

10  4.3 

20  8.7 

30  13.0 

40  17.3 

50  21.7 

25 

6 2.5 

7 2.9 

8 3.3 

9 3.8 

10  4.2 

20  8.3 

30  12.5 

40  16.7 

50  20.8 

16 

6 1.6 

7 1.9 

8 2.1 

9 2.4 

10  2.7 

20  5.3 

30  8.0 

40  10.7 

50  13.3 

15 

6 1.5 

7 1.8 

8 2.0 

9 2.3 

10  2.5 

20  5.0 

30  7.5 

40  10.0 

50  12.5 

II  10 

6 1.1  1.0 

7 1.3  1.2 

8 1.5  1.3 

9 1.7  1.5 

10  1.8  1.7 

20  3.7  3.3 

30  5.5  5.0 

40  7.3  6.7 

50  9.2  8.3 

5 

6 

7 

8 

9 

9.79965 

9.79981 

9.79996 

9.80012 

9.80027 

9.90966 

9.90992 

9.91018 

9.91043 

9.91069 

0.09034 

0.09008 

0.08982 

0.08957 

0.08931 

9.88999 

9.88989 

9.88978 

9.88968 

9.88958 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

9.80043 

9.80058 

9.80074 

9.80089 

9.80105 

9.91095 

9.91121 

9.91147 

9.91172 

9.91198 

0.08905 

0.08879 

0.08853 

0.08828 

0.08802 

9.88948 

9.88937 

9.88927 

9.88917 

9.88906 

9.80120 

9.80136 

9.80151 

9.80166 

9.80182 

9.91224 

9.91250 

9.91276 

9.91301 

9.91327 

0.08776 

0.08750 

0.08724 

0.08699 

0.08673 

9.88896 

9.88886 

9.88875 

9.88865 

9.88855 

45 

44 

43 

42 

41 

9.80197 

9.80213 

9.80228 

9.80244 

9.80259 

9.91353 

9.91379 

9.91404 

9.91430 

9.91456 

0.08647 

0.08621 

0.08596 

0.08570 

0.08544 

9.88844 

9.88834 

9.88824 

9.88813 

9.88803 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.80274 

9.80290 

9.80305 

9.80320 

9.80336 

9.91482 

9.91507 

9.91533 

9.91559 

9.91585 

0.08518 

0.08493 

0.08467 

0.08441 

0.08415 

9.88793 

9.88782 

9.88772 

9.88761 

9.88751 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

30 

31 

32 

33 

34 

9.80351 

9.80366 

9.80382 

9.80397 

9.80412 

9.91610 

9.91636 

9.91662 

9.91688 

9.91713 

0.08390 

0.08364 

0.08338 

0.08312 

0.08287 

9.88741 

9.88730 

9.88720 

9.88709 

9.88699 

35 

36 

37 

38 

39 

9.80428 

9.80443 

9.80458 

9.80473 

9.80489 

9.91739 

9.91765 

9.91791 

9.91816 

9.91842 

0.08261 

0.08235 

0.08209 

0.08184 

0.08158 

9.88688 

9.88678 

9.88668 

9.88657 

9.88647 

40 

41 

42 

43 

44 

9.80504 

9.80519 

9.80534 

9.80550 

9.80565 

9.91868 

9.91893 

9.91919 

9.91945 

9.91971 

0.08132 

0.08107 

0.08081 

0.08055 

0.08029 

9.88636 

9.88626 

9.88615 

9.88605 

9.88594 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.80580 

9.80595 

9.80610 

9.80625 

9.80641 

9.91996 

9.92022 

9.92048 

9.92073 

9.92099 

0.08004 

0.07978 

0.07952 

0.07927 

0.07901 

9.88584 

9.88573 

9.88563 

9.88552 

9.88542 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

50 

51 

52 

53 

54 

9.80656 

9.80671 

9.80686 

9.80701 

9.80716 

9.92125 

9.92150 

9.92176 

9.92202 

9.92227 

0.07875 

0.07850 

0.07824 

0.07798 

0.07773 

9.88531 

9.88521 

9.88510 

9.88499 

9.88489 

55 

56 

57 

58 

59 

9.80731 

9.80746 

9.80762 

9.80777 

9.80792 

9.92253 

9.92279 

9.92304 

9.92330 

9.92356 

0.07747 

0.07721 

0.07696 

0.07670 

0.07644 

9.88478 

9.88468 

9.88457 

9.88447 

9.88436 

60 

9.80807 

9.92381 

0.07619 

9.88425 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

' 

P.  P. 

50^ 


532  LOGAUimMS  OF  miGONOMETRIC  FUNCTIONS. 


40° 


' 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

1 

2 

3 

4 

9.80807 

9.80822 

9.80837 

9.80852 

9.80867 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

14 

15 

15 

15 

15 

15 

15 

15 

14 

15 

15 

15 

15 

14 

15 

15 

15 

15 

14 

15 

15 

14 

15 

15 

15 

14 

15 

15 

14 

15 

15 

14 

15 

15 

14 

15 

14 

15 
15* 

14 

15 

14 

15 

14 

9.92381 

9.92407 

9.92433 

9.92458 

9.92484 

26 

26 

25 

26 

26 

25 

26 

26 

25 

26 

25 

26 

26 

25 

26 

26 

25 

26 

25 

26 

26 

25 

26 

25 

26 

26 

25 

26 

25 

26 

25 

26 

26 

25 

26 

25 

26 

25 

26 

26 

25 

26 

25 

26 

25 

26 

25 

26 

26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

0.07619 

0.07593 

0.07567 

0.07542 

0.07516 

9.88425 

9.88415 

9.88404 

9.88394 

9.88383 

10 

11 

10 

11 

11 

10 

11 

11 

10 

11 

11 

10 

11 

11 

10 

11 

11 

10 

11 

11 

11 

10 

11 

11 

11 

10 

11 

11 

11 

10 

11 

11 

11 

11 

10 

11 

11 

11 

11 

11 

11 

10 

11 

11 

11 

11 

11 

11 

11 

11 

10 

11 

11 

11 

11 

11 

11 

11 

11 

11 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

26 

6 2.6 

7 3.0 

8 3.5 

9 3.9 

10  4.3 

20  8.7 

30  13.0 

40  17.3 

50  21.7 

25 

6 2.5 

7 2.9 

8 3.3 

9 3.8 

10  4.2 

20  8.3 

30  12.5 

40  16.7 

60  20.8 

15 

6 1.5 

7 1.8 

8 2.0 

9 2.3 

10  2.5 

20  5.0 

30  • 7.5 

40  10.0 

50  12.5 

14 

6 1.4 

7 1.6 

8 1.9 

9 2.1 

10  2.3 

20  4.7 

30  7.0 

40  9.3 

50  11.7 

II  10 

6 1.1  1.0 

7 1.3  1.2 

8 1.5  1.3 

9 1.7  1.5 

10  1.8  1.7 

20  3.7  3.3 

30  5.5  5.0 

40  7.3  6.7 

50  9.2  8.3 

5 

6 

7 

8 

9 

9.80882 

9.80897 

9.80912 

9.80927 

9.80942 

9.92510 

9.92535 

9.92561 

9.92587 

9.92612 

0.07490 

0.07465 

0.07439 

0.07413 

0.07388 

9.88372 

9.88362 

9.88351 

9.88340 

9.88330 

10 

11 

12 

13 

14 

9.80957 

9.80972 

9.80987 

9.81002 

9.81017 

9.92638 

9.92663 

9.92689 

9.92715 

9.92740 

0.07362 

0.07337 

0.07311 

0.07285 

0.07260 

9.88319 

9.88308 

9.88298 

9.88287 

9.88276 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.81032 

9.81047 

9.81061 

9.81076 

9.81091 

9.92766 

9.92792 

9.92817 

9.92843 

9.92868 

0.07234 

0.07208 

0.07183 

0.07157 

0.07132 

9.88266 

9.88255 

9.88244 

9.88234 

9.88223 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.81106 

9.81121 

9.81136 

9.81151 

9.81166 

9.92894 

9.92920 

9.92945 

9.92971 

9.92996 

0.07106 

0.07080 

0.07055 

0.07029 

0.07004 

9.88212 

9.88201 

9.88191 

9.88180 

9.88169 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.81180 

9.81195 

9.81210 

9.81225 

9.81240 

9.93022 

9.93048 

9.93073 

9.93099 

9.93124 

0.06978 

0.06952 

0.06927 

0.06901 

0.06876 

9.88158 

9.88148 

9.88137 

9.88126 

9.88115 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.81254 

9.81269 

9.81284 

9.81299 

9.81314 

9.93150 

9.93175 

9.93201 

9.93227 

9.93252 

0.06850 

0.06825 

0.06799 

0.06773 

0.06748 

9.88105 

9.88094 

9.88083 

9.88072 

9.88061 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.81328 

9.81343 

9.81358 

9.81372 

9.81387 

9.93278 

9.93303 

9.93329 

9.93354 

9.93380 

0.06722 

0.06697 

0.06671 

0.06646 

0.06620 

9.88051 

9.88040 

9.88029 

9.88018 

9.88007 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

40 

41 

42 

43 

44 

9.81402 

9.81417 

9.81431 

9.81446 

9.81461 

9.93406 

9.93431 

9.93457 

9.93482 

9.93508 

0.06594 

0.06569 

0.06543 

0.06518 

0.06492 

9.87996 

9.87985 

9.87975 

9.87964 

9.87953 

45 

46 

47 

48 

49 

9.81475 

9.81490 

9.81505 

9.81519 

9.81534 

9.93533 

9.93559 

9.93584 

9.93610 

9.93636 

0.06467 

0.06441 

0.06416 

0.06390 

0.06364 

9.87942 

9.87931 

9.87920 

9.87909 

9.87898 

50 

51 

52 

53 

54 

9.81549 

9.81563 

9.81578 

9.81592 

9.81607 

9.93661 

9.93687 

9.93712 

9.93738 

9.93763 

0.06339 

0.06313 

0.06288 

0.06262 

0.06237 

9.87887 

9.87877 

9.87866 

9.87855 

9.87844 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.81622 

9.81636 

9.81651 

9.81665 

9.81680 

9.93789 

9.93814 

9.93840 

9.93865 

9.93891 

0.06211 

0.06186 

0.06160 

0.06135 

0.06109 

9.87833 

9.87822 

9.87811 

9.87800 

9.87789 

5 

4 

3 

2 

1 

60 

9.81694 

9.93916 

0.06084 

9.87778 

0 

L.  Cos. 

d. 

L.  Cotg. 

”d.~c. 

L.Tang. 

L.  Sin. 

^d7 

/ 

P.  P. 

49* 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS.  533  . 


41° 


L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

9.81694 

9.93916 

0.06084 

9.87778 

60 

1 

9.81709 

15 

9.93942 

26 

0.06058 

9.87767 

11 

59 

2 

9.81723 

14 

9.93967 

0.06033 

9.87756 

11 

58 

3 

9.81738 

15 

9.93993 

26 

0.06007 

9.87745 

11 

57 

CQ 

o a. 

4 

9.81752 

14 

9.94018 

25 

26 

0.05982 

9.87734 

11 

11 

56 

6 

7 

Z.o 

3.0 

5 

9.81767 

9.94044 

0.05956 

9.87723 

55 

8 

3.5 

6 

9.81781 

14 

9.94069 

Zly 

0.05931 

9.87712 

11 

54 

9 

3.9 

7 

9.81796 

15 

9.94095 

26 

0.05905 

9.87701 

11 

53 

10 

4.3 

8 

9.81810 

14 

9.94120 

25 

0.05880 

9.87690 

11 

52 

20 

8.7 

9 

9.81825 

15 

14 

9.94146 

26 

25 

0.05854 

9.87679 

11 

11 

51 

30 

13.0 

10 

9.81839 

9.94171 

0.05829 

9.87668 

50 

40 

17.3 

11 

9.81854 

15 

9.94197 

26 

0.05803 

9.87657 

11 

49 

50 

21.7 

12 

9.81868 

14 

9.94222 

0.05778 

9.87646 

11 

48 

13 

9.81882 

M 

9.94248 

26 

0.05752 

9.87635 

11 

47 

14 

9.81897 

15 

14 

9.94273 

25 

26 

0.05727 

9.87624 

11 

11 

46 

25 

15 

9.81911 

9.94299 

0.05701 

9.87613 

45 

6 

1 2.5 

16 

9.81926 

15 

9.94324 

25 

0.05676 

9.87601 

12 

44 

7 

2.9 

17 

9.81940 

14 

9.94350 

26 

0.05650 

9.87590 

11 

43 

8 

3.3 

18 

9.81955 

15 

9.94375 

0.05625 

9.87579 

11 

42 

9 

3.8 

19 

9.81969 

14 

14 

9.94401 

26 

25 

0.65599 

9.87568 

11 

11 

41 

10 

4.2 

20 

9.81983 

9.94426 

0.05574 

9.87557 

40 

20 

8.3 

21 

9.81998 

15 

9.94452 

26 

0.05548 

9.87546 

11 

39 

30 

12.5 

22 

9.82012 

14 

9.94477 

0.05523 

9.87535 

11 

38 

40 

16.7 

23 

9.82026 

14 

9.94503 

26 

0.05497 

9.87524 

11 

37 

50 

20.8 

24 

9.82041 

15 

14 

9.94528 

^5 

26 

0.05472 

9.87513 

11 

12 

36 

25 

9.82055 

9.94554 

0.05446 

9.87501 

35 

26 

9.82069 

14 

9.94579 

0.05421 

9.87490 

11 

34 

15 

27 

9.82084 

45 

9.94604 

jiS 

0.05396 

9.87479 

11 

33 

6 

1.5 

28 

9.82098 

14 

9.94630 

26 

0.05370 

9.87468 

11 

32 

7 

1.8 

29 

9.82112 

14 

14 

9.94655 

25 

26 

0.05345 

9.87457 

11 

11 

31 

8 

2.0 

30 

9.82126 

9.94681 

0.05319 

9.87446 

30 

in 

2.3 

31 

9.82141 

15 

9.94706 

25 

0.05294 

9.87434 

12 

29 

lU 

on 

z«o 

32 

9.82155 

14 

9.94732 

26 

0.05268 

9.87423 

11 

28 

Qn 

O.U 

33 

9.82169 

14 

5.94757 

25 

0.05243 

9.87412 

11 

27 

oU 

/in 

/.D 
in  A 

34 

9.82184 

15 

14 

9.94783 

26 

25 

0.05217 

9.87401 

11 

11 

26 

.'sn 

lU.U 

I9 

35 

9.82198 

9.94808 

0.05192 

9.87390 

25 

36 

9.82212 

14 

9.94834 

26 

0.05166 

9.87378 

12 

24 

37 

9.82226 

14 

9.94859 

25 

0.05141 

9.87367 

11 

23 

38 

9.82240 

14 

9.94884 

25 

0.05116 

9.87356 

11 

22 

I4 

39 

9.82255 

15 

14 

9.94910 

26 

25 

0.05090 

9.87345 

11 

11 

21 

6 

>7 

1.4 

1 fi 

40 

9.82269 

9.94935 

0.05065 

9.87334 

20 

8 

1.0 

1.9 

41 

9.82283 

14 

9.94961 

26 

0.05039 

9.87322 

12 

19 

Q 

2!i 

42 

9.82297 

14 

9.94986 

25 

0.05014 

9.87311 

11 

18 

10 

2^3 

43 

9.82311 

14 

9.95012 

26 

0.04988 

9.87300 

11 

17 

20 

4 7 

44 

9.82326 

15 

14 

9.95037 

25 

25 

0.04963 

9.87288 

12 

11 

16 

30 

7.0 

45 

9.82340 

9.95062 

0.04938 

9.87277 

15 

40 

9.3 

46 

9.82354 

14 

9.95088 

26 

0.04912 

9.87266 

11 

14 

50 

11.7 

47 

9.82368 

14 

9.95113 

25 

0.04887 

9.87255 

11 

13 

48 

9.82382 

14 

9.95139 

26 

0.04861 

9.87243 

12 

12 

49 

9.82396 

14 

14 

9.95164 

25 

26 

0.04836 

9.87232 

11 

11 

11 

II 

50 

9.82410 

9.95190 

0.04810 

9.87221 

10 

6 

1.2 

1.1 

51 

9.82424 

14 

9.95215 

25 

0.04785 

9.87209 

12 

9 

7 

1.4 

1.3 

52 

9.82439 

15 

9.95240 

25 

0.04760 

9.87198 

11 

8 

8 

1.6 

1.5 

53 

9.82453 

14 

9.95266 

26 

0.04734 

9.87187 

11 

7 

9 

1.8 

1.7 

54 

9.82467 

14 

14 

9.95291 

25 

26 

0.04709 

9.87175 

12 

11 

6 

10 

2.0 

1.8 

55 

9.82481 

9.95317 

0.04683 

9.87164 

5 

20 

4.0 

3.7 

56 

9.82495 

14 

9.95342 

25 

0.04658 

9.87153 

11 

4 

30 

6.0 

5.5 

57 

9.82509 

14 

9.95368 

26 

0.04632 

9.87141 

12 

3 

40 

8.0 

7.3 

58 

9.82523 

14 

9.95393 

25 

0.04607 

9.87130 

11 

2 

50 

10.0 

9.2 

59 

9.82537 

14 

14 

9.95418 

25 

26 

0.04582 

9.87119 

11 

12 

1 

60 

9.82551 

9.95444 

0.04556 

9.87107 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.P. 

49’ 


534 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 

420 


/ 

L.  Sin. 

0 

9.82551 

1 

9.82565 

2 

9.82579 

3 

9.82593 

4 

9.82607 

5 

9.82621 

6 

9.82635 

7 

9.82649 

8 

9.82663 

9 

9.82677 

10 

9.82691 

11 

9.82705 

12 

9.82719 

13 

9.82733 

14 

9.82747 

15 

9.82761  : 

16 

9.82775  ^ 

17 

9.82788 

18 

9.82802 

19 

9.82816 

20 

9.82830 

21 

9.82M4 

22 

9.82858 

23 

9.82872 

24 

9.82885 

25 

9.82899 

26 

9.82913 

27 

9.82927 

28 

9.82941 

29 

9.82955 

30 

9.82968 

31 

9.82982 

32 

9.82996 

33 

9.83010 

34 

9.83023 

35 

9.83037 

36 

9.83051 

37 

9.83065 

38 

9.83078 

39 

9.83092 

40 

9.83106 

41 

9.83120 

42 

9.83133 

43 

9.83147 

44 

9.83161 

45 

9.83174 

46 

9.83188 

47 

9.83202 

48 

9.83215 

49 

9.83229 

50 

9.83242 

51 

9.83256 

52 

9.83270 

53 

9.83283 

54 

9.83297 

55 

9.83310 

56 

9.83324  1 

57 

9.83338  i 

58 

9.83351  i 

59 

9.83365  1 

60" 

9.83378 

l:cos. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

9.95444 

0.04556 

9.87107 

60 

9.9^69 

25 

0.04531 

9.87096 

11 

59 

9.95495 

26 

0.04505 

9.87085 

11 

58 

9.95520 

25 

0.04480 

9.87073 

12 

57 

9.95545 

25 

26 

0.04455 

9.87062 

11 

12 

56 

9.95571 

0.04429 

9.87050 

55 

9.95596 

25 

0.04404 

9.87039 

11 

54 

9.95622 

26 

0.04378 

9.87028 

11 

53 

9.95647 

25 

0.04353 

9.87016 

12 

52 

9.95672 

25 

26 

0.04328 

9.87005 

11 

12 

51 

9.95698 

0.04302 

9.86993 

50 

9.95723 

25 

0.04277 

9.86982 

11 

49 

9.95748 

25 

0.04252 

9.86970 

12 

48 

9.95774 

26 

0.04226 

9.86959 

11 

47 

9.95799 

25 

26 

0.04201 

9.86947 

12 

11 

46 

9.95825 

0.04175 

9.86936 

45 

9.95850 

25 

0.04150 

9.86924 

12 

44 

9.95875 

25 

0.04125 

9.86913 

11 

43 

9.95901 

26 

0.04099 

9.86902 

11 

42 

9.95926 

25 

26 

0.04074 

9.86890 

12 

11 

41 

9.95952 

0.04048 

9.86879 

40 

9.95977 

25 

0.04023 

9.86867 

12 

39 

9.96002 

25 

0.03998 

9.86855 

12 

38 

9.96028 

26 

0.03972 

9.86844 

11 

37 

9.96053 

25 

25 

0.03947 

9.86832 

12 

11 

36 

9.96078 

0.03922 

9.86821 

35 

9.96104 

26 

0.03896 

9.86809 

12 

34 

9.96129 

25 

0.03871 

9.86798 

11 

33 

9.96155 

26 

0.03845 

9.86786 

12 

32 

9.96180 

25 

25 

0.03820 

9.86775 

11 

12 

31 

9.96205 

0.03795 

9.86763 

30 

9.96231 

26 

0.03769 

9.86752 

11 

29 

9.96256 

25 

0.03744 

9.86740 

12 

28 

9.96281 

25 

0.03719 

9.86728 

12 

27 

9.96307 

26 

25 

0.03693 

9.86717 

11 

1 0 

26 

9.96332 

0.03668 

9.86705 

25 

9.96357 

25 

0.03043 

9.86694 

11 

24 

9.96383 

.26 

0.03617 

9.86682 

12 

23 

9.90408 

25 

0.03592 

9.86670 

12 

22 

9.96433 

25 

26 

0.03567 

9.86659 

11 

io 

21 

9.90459 

0.03041 

9.86647 

iz 

20 

9.96404 

25 

0.03516 

9.86635 

12 

19 

9.96510 

26 

0.03490 

9.86624 

11 

18 

9.96535 

25 

0.03465 

9.86612 

12 

17 

9.96560 

25 

26 

0.03440 

9.86600 

12 

11 

16 

9.96586 

0.03414 

9.86589 

15 

9.96611 

25 

0.03389 

9.86577 

12 

14 

9.96636 

25 

0.03304 

9.86565 

12 

13 

9.96662 

26 

0.03338 

9.86554 

11 

12 

9.96687 

25 

25 

0.03313 

9.86642 

12 

12 

11 

9.96712 

0.03288 

9.86530 

10 

9.96738 

26 

0.03262 

9.86518 

12 

9 

9.96763 

25 

0.03237 

9.86507 

11 

8 

9.96788 

25 

0.03212 

9.86495 

12 

7 

9.96814 

26 

25 

0.03186 

9.86483 

12 

11 

6 

9.96839 

0.03161 

9.86472 

5 

9.96804 

2d 

0.03136 

9.86460 

12 

4 

9.90890 

26 

0.03110 

9.86448 

12 

3 

9.96915 

25 

0.03085 

9.86436 

12 

2 

9.96940 

25 

26 

0.03060 

9.86425 

11 

12 

1 

9.96966 

0.03004 

9.86413 

_0 

P 

. P. 

26 

6 

2.6 

7 

3.0 

8 

3.5 

9 

3.9 

10 

4.3 

20 

8.7 

30 

13.0 

40 

17.3 

50 

21.7 

25 

6 

2.5 

7 

2.9 

8 

3.3 

9 

3.8 

10 

4.2 

20 

8.3 

30 

12.5 

40 

16.7 

50 

20.8 

(4 

6 

1.4 

7 

1.6 

8 

1.9 

9 

2.1 

10 

2.3 

20 

4.7 

30 

7.0 

40 

9.3 

50 

11.7 

6 

1.3 

7 

1.5 

8 

1.7 

9 

2.0 

10 

2.2 

20 

, 4.3 

30 

6.5 

40 

i 8.7 

50 

i 10.8 

12 

II 

6 

1.2 

1.1 

7 

1.4 

1.3 

8 

1.6 

1.5 

9 

1.8 

1.7 

10 

2.0 

1.8 

20 

4.0 

3.7 

30 

6.0 

5.5 

40 

8.0 

7.3 

50 

10.0 

9.2 

L.  Cotg. 


d.  c.  L.Tang. 


L.  Sin.  ! d. 


P.  P. 


47° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS.  585 


43° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

1 

2 

3 

4 

9.83378 

9.83392 

9.83405 

9.83419 

9.83432 

14 

13 

14 

13 

14 

13 

14  . 

13 

14 

13 

14 

13 

14 

13 

14 

13 

14 

13 

13 

14 

13 

13 

14 

13 

14 

13 

13 

14 

13 

13 

14 

13 

13 

13 

. 14 

13 

13 

13 

14 

13 

13 

13 

14 

13 

13 

13 

13 

14 

13 

13 

13 

13 

13 

13 

14 

13 

13 

13 

13 

13 

9.96966 

9.96991 

9.97016 

9.97042 

9.97067 

25 

25 

26 

25 

25 

26 

25 

25 

25 

26 

25 

25 

26 

25 

25 

26 

25 

25 

26 

25 

25 

26 

25 

25 

25 

26 

25 

25 

26 

25 

25 

26 

25 

25 

25 

26 

25 

25 

26 

25 

25 

26 

25 

25 

25 

26 

25 

25 

26 

25 

25 

25 

26 

25 

25 

26 

25 

25 

25 

26 

0.03034 

0.03009 

0.02984 

0.02958 

0.02933 

9.86413 

9.86401 

9.86389 

9.86377 

9.86366 

12 
12 
• 12 
11 
12 

12 

12 

12 

12 

11 

12 

12 

12 

12 

12 

12 

12 

11 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

12 

13 

12 

12 

12 

12 

12 

12 

13 

12 

12 

12 

12 

12 

13 

60 

59 

58 

57 

56 

26 

6 2.6 

7 3.0 

8 3.5 

9 3.9 

10  4.3 

20  8.7 

30  13.0 

40  17.3 

50  21.7 

25 

6 2.5 

7 2.9 

8 3.3 

9 3.8 

10  4.2 

20  8.3 

30  12.5 

40  16.7 

50  20.8 

14 

6 1.4 

7 1.6 

8 1.9 

9 2.1 

10  2.3 

20  4.7 

30  7.0 

40  9.3 

50  11.7 

13 

6 1.3 

7 1.5 

8 1.7 

9 2.0 

10  2.2 

20  4.3 

30  6.5 

40  8.7 

50  10.8 

12  II 

6 1.2  1.1 

7 1.4  1.3 

8 1.6  1.5 

9 1.8  1.7 

10  2.0  1.8 

20  4.0  3.7 

30  6.0  5.5 

40  8.0  7.3 

50  10.0  9.2 

5 

6 

7 

8 

9 

9.83446 

9.83459 

9.83473 

9.83486 

9.83500 

9.97092 

9.97118 

9.97143 

9.97168 

9.97193 

0.02908 

0.02882 

0.02857 

0.02832 

0.02807 

9.86354 

9.86342 

9.86330 

9.86318 

9.86306 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.83513 

9.83527 

9.83540 

9.83554 

9.83567 

9.97219 

9.97244 

9.97269 

9.97295 

9.97320 

0.02781 

0.02756 

0.02731 

0.02705 

0.02680 

9.86295 

9.86283 

9.86271 

9.86259 

9.86247 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

15 

16 

17 

18 
19 

9.83581 

9.83594 

9.83608 

9.83621 

9.83634 

9.97345 

9.97371 

9.97396 

9.97421 

9.97447 

0.02655 

0.02629 

0.02604 

0.02579 

0.02553 

9.86235 

9.86223 

9.86211 

9.86200 

9.86188 

20 

21 

22 

23 

24 

9.83648 

9.83661 

9.83674 

9.83688 

9.83701 

9.97472 

9.97497 

9.97523 

9.97548 

9.97573 

0.02528 

0.02503 

0.02477 

0.02452 

0.02427 

9.86176 

9.86164 

9.86152 

9.86140 

9.86128 

25 

26 

27 

28 
29 

9.83715 

9.83728 

9.83741 

9.83755 

9.83768 

9.97598 

9.97624 

9.97649 

9.97674 

9.97700 

0.02402 

0.02376 

0.02351 

0.02326 

0.02300 

9.86116 

9.86104 

9.86092 

9.86080 

9.86068 

30 

31 

32 

33 

34 

9.83781 

9.83795 

9.83808 

9.83821 

9.83834 

9.97725 

9.97750 

9.97776 

9.97801 

9.97826 

0.02275 

0.02250 

0.02224 

0.02199 

0.02174 

9.86056 

9.86044 

9.86032 

9.86020 

9.86008 

35 

36 

37 

38 

39 

9.83848 

9.83861 

9.83874 

9.83887 

9.83901 

9.97851 

9.97877 

9.97902 

9.97927 

9.97953 

0.02149 

0.02123 

0.02098 

0.02073 

0.02047 

9.85996 

9.85984 

9.85972 

9.85960 

9.85948 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.83914 

9.83927 

9.83940 

9.83954 

9.83967 

9.97978 

9.98003 

9.98029 

9.98054 

9.98079 

0.02022 

0.01997 

0.01971 

0.01946 

0.01921 

9.85936 

9.85924 

9.85912 

9.85900 

9.85888 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

45 

46 

47 

48 

49 

9.83980 

9.83993 

9.84006 

9.84020 

9.84033 

9.98104 

9.98130 

9.98155 

9.98180 

9.98206 

0.01896 

0.01870 

0.01845 

0.01820 

0.01794 

9.85876 

9.85864 

9.85851 

9.85839 

9.85827 

50 

51 

52 

53 

54 

9.84046 

9.84059 

9.84072 

9.84085 

9.84098 

9.98231 

9.98256 

9.98281 

9.98307 

9.98332 

0.01769 

0.01744 

0.01719 

0.01693 

0.01668 

9.85815 

9.85803 

9.85791 

9.85779 

9.85766 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.84112 

9.84125 

9.84138 

9.84151 

9.84164 

9.98357 

9.98383 

9.98408 

9.98433 

9.98458 

0.01643 

0.01617 

0.01592 

0.01567 

0.01542 

^9.85754 

9.85742 

9.85730 

9.85718 

9.85706 

5 

4 

3 

2 

1 

0 

60 

9.84177 

9.98484 

0.01516 

9.85693 

L.  Cos. 

d. 

L.  Cotg. 

d.  G. 

L.Tang. 

L.  Sin. 

“dT 

' 

P.  P. 

46° 


536  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 


440 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.  P. 

0 

1 

2 

3 

4 

9.84177 

9.84190 

9.84203 

9.84216 

9.84229 

13 

13 

13 

13 

13 

13 

14 

13 

13 

13 

13 

13 

13 

13 

13 

12 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

12 

13 

13 

13 

13 

13 

13 

12 

13 

13 

13 

13 

12 

13 

13 

13 

12 

13 

13 

13 

12 

13 

13 

13 

12 

13 

13 

12 

13 

13 

12 

13 

13 

9.98484 

9.98509 

9.98534 

9.98560 

9.98585 

25 

25 

26 

25 

25 

25 

26 

25 

25 

26 

25 

25 

25 

26 

25 

25 

25 

26 

25 

25 

26 

25 

25 

25 

26 

25 

25 

25 

26 

25 

25 

26 

25 

25 

25 

26 

25 

25 

25 

26 

25 

25 

25 

26 

25 

25 

26 

25 

25 

25 

26 

25 

25 

25 

26 

25 

25 

25 

26 

25 

0.01516 

0.01491 

0.01466 

0.01440 

0.01415 

9.85693 

9.85681 

9.85669 

9.85657 

9.85645 

12 

12 

12 

12 

13 

12 

12 

12 

13 

12 

12 

12 

13 

12 

12 

13 

12 

12 

13 

12 

12 
. 13 
12 
12 
13 

12 

13 

12 

12 

13 

12 

13 

12 

13 

12 

12 

13 

12 

13 

12 

13 

12 

13 

12 

13 

12 

13 

12 

13 

13 

12 

13 

12 

13 

12 

13 

13 

12 

13 

12 

60 

59 

58 

57 

56 

26 

6 2.6 

7 3.0 

8 3.5 

9 3.9 

10  4.3 

20  8.7 

30  13.0 

40  17.3 

50  21.7 

25 

6 2.5 

7 2.9 

8 3.3 

9 3.8 

10  4.2 

20  8.3 

30  12.5 

40  16.7 

50  20.8 

14 

6 1.4 

7 1.6 

8 1.9 

9 2.1 

10  2.3 

20  4.7 

30  7.0 

40  9.3 

50  11.7 

13 

6 1.3 

7 1.5 

8 1.7 

9 2.0 

10  2.2 

20  4.3 

30  6.5 

40  8.7 

50  10.8 

12 

6 1.2 

7 1.4 

8 1.6 

9 1.8 

10  2.0 

20  4.0 

30  6.0 

40  8.0 

50  10.0 

5 

6 

7 

8 

9 

9.84242 

9.84255 

9.84269 

9.84282 

9.84295 

9.98610 

9.98635 

9.98661 

9.98686 

9.98711 

0.01390 

0.01365 

0.01339 

0.01314 

0.01289 

9.85632 

9.85620 

9.85608 

9.85596 

9.85583 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.84308 

9.84321 

9.84334 

9.84347 

9.84360 

9.98737 

9.98762 

9.98787 

9.98812 

9.98838 

0.01263 

0.01238 

0.01213 

0.01188 

0.01162 

9.85571 

9.85559 

9.85547 

9.85534 

9.85522 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

15 

16 

17 

18 
19 

9.84373 

9.84385 

9.84398 

9.84411 

9.84424 

9.98863 

9.98888 

9.98913 

9.98939 

9.98964 

0.01137 

0.01112 

0.01087 

0.01061 

0.01036 

9.85510 

9.85497 

9.85485 

9.85473 

9.85460 

20 

21 

22 

23 

24 

9.84437 

9.84450 

9.84463 

9.84476 

9.84489 

9.98989 

9.99015 

9.99040 

9.99065 

9.99090 

0.01011 

0.00985 

0.00960 

0.00935 

0.00910 

9.85448 

9.85436 

9.85423 

9.85411 

9.85399 

25 

26 

27 

28 
29 

9.84502 

9.84515 

9.84528 

9.84540 

9.84553 

9.99116 

9.99141 

9.99166 

9.99191 

9.99217 

0.00884 

0.00859 

0.00834 

0.00809 

0.00783 

9.85386 

9.85374 

9.85361 

9.85349 

9.85337 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.84566 

9.84579 

9.84592 

9.84605 

9.84618 

9.99242 

9.99267 

9.99293 

9.99318 

9.99343 

0.00758 

0.00733 

0.00707 

0.00682 

0.00657 

9.85324 

9.85312 

9.85299 

9.85287 

9.85274 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.84630 

9.84643 

9.84656 

9.84669 

9.84682 

9.99368 

9.99394 

9.99419 

9.99444 

9.99469 

0.00632 

0.00606 

0.00581 

0.00556 

0.00531 

9.85262 

9.85250 

9.85237 

9.85225 

9.85212 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

40 

41 

42 

43 

44 

9.84694 

9.84707 

9.84720 

9.84733 

9.84745 

9.99495 

9.99520 

9.99545 

9.99570 

9.99596 

0.00505 

0.00480 

0.00455 

0.00430 

0.00404 

9.85200 

9.85187 

9.85175 

9.85162 

9.85150 

45 

46 

47 

48 

49 

9.84758 

9.84771 

9.84784 

9.84796 

9.84809 

9.99621 

9.99646 

9.99672 

9.99697 

9.99722 

0.00379 

0.00354 

0.00328 

0.00303 

0.00278 

9.85137 

9.85125 

9.85112 

9.85100 

9.85087 

50 

51 

52 

53 

54 

9.84822 

9.84835 

9.84847 

9.84860 

9.84873 

9.99747 

9.99773 

9.99798 

9.99823 

9.99848 

0.00253 

0.00227 

0.00202 

0.00177 

0.00152 

9.85074 

9.85062 

9.85049 

9.85037 

9.85024 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

55 

56 

57 

58 

59 

9.84885 

9.84898 

9.84911 

9.84923 

9.84936 

9.99874 

9.99899 

9.99924 

9.99949 

9.99975 

0.00126 

0.00101 

0.00076 

0.00051 

0.00025 

9.85012 

9.84999 

9.84986 

9.84974 

9.84961 

60 

9.84949 

0.00000 

0.00000 

9.84949 

L.  Cos. 

d. 

L.  Cotg. 

d.  c.  L.Tang. 

L.  Sin. 

d. 

/ 

P.  P. 

45‘ 


TRAVERSE  TABLES. 


537 


TRAVERSE  TABLES. 

To  use  the  tables,  find  the  number  of  degrees  in  the  left-hand  column  if 
the  angle  be  less  than  45°,  and  in  the  right-hand  column  if  greater  than  45°. 
The  numbers  on  the  same  line  running  across  the  page  are  the  latitudes  and 
departures  for  that  angle  and  for  the  respective  distances,  1,  2, 3,  4,  5, 6,  7, 8,  9, 
which  appear  at  the  top  and  bottom  of  the  pages.  Thus,  if  the  bearing  of  a 
line  be  10°  and  the  distance  4,  the  latitude  will  be  3.939  and  the  departure 
0.695;  with  the  same  bearing,  and  the  distance  8,  the  latitude  will  be  7.878  and 
the  departure  1.389.  The  latitude  and  departure  for  80  is  10  times  the  latitude 
and  departure  for  8,  and  is  found  by  moving  the  decimal  point  one  place  to 
the  right;  that  for  500  is  100  times  the  latitude  and  departure  for  5,  and  is  found 
by  moving  the  decimal  point  two  places  to  the  right  and  so  on.  By  moving 
the  decimal  point  one,  two,  or  more  places  to  the  right,  the  latitude  and 
departure  may  be  found  for  any  multiple  of  any  number  given  in  the  table. 
In  finding  the  latitude  and  departure  for  any  number  such  as  453,  the  number 
is  resolved  into  three  numbers,  viz. : 400,  50,  3,  and  the  latitude  and  departure 
for  each  taken  from  the  table  and  then  added  together. 

We  thus  obtain  the  following: 

Rule. — Write  down  the  latitude  and  departure,  neglecting  the  decimal  points, 
for  the  first  figure  of  the  given  distance;  write  under  them  the  latitude  and  depar- 
ture for  the  second  figure,  setting  them  one  place  farther  to  the  right;  under  these, 
place  the  latitude  and  departure  for  the  third  figure,  setting  them  one  place  still 
farther  to  the  right,  and  so  continue  until  all  the  figures  of  the  given  distance  have 
been  used;  add  these  latitudes  and  departures,  and  point  off  on  the  right  of  their 
sums  a number  of  decimal  places  equal  to  the  number  of  decimal  places  to  which 
the  tables  being  used  are  carried;  the  resulting  numbers  will  be  the  latitude  and 
departure  of  the  given  distance  in  feet,  links,  chains,  or  whatever  unit  of  measure- 
ment is  adopted. 

Example.— A bearing  is  16°  and  the  distance  725  ft.;  what  is  the  latitude 


and  departure? 

Distances. 

Latitudes. 

Departures. 

700 

6729 

1929 

20 

1923 

0551 

5 

4806 

1378 

725 

6 9 6.9  3 6 

1 9 9.7  8 8 

Taking  the  nearest  whole  numbers  and  rejecting  the  decimals,  we  find 
the  latitude  and  departure  to  be  697  and  200. 

When  a 0 occurs  in  the  given  number,  the  next  figure  must  be  set  two 
places  to  the  right  as  in  the  following  example: 

The  bearing  is  22°  and  the  distance  907  ft. ; required,  the  latitude  and 


departure. 

Distances. 

Latitudes. 

Departures. 

900 

8345 

337  1 

7 

6490 

2622 

907 

8 4 0.9  9 0 

3 3 9.7  2 2 

Here  the  place  of  0 both  in  the  distance  column  and  in  the  latitude  and 
departure  columns  is  occupied  by  a dash  — . Rejecting  the  decimals,  the 
latitude  is  841  ft.  and  the  departure  340  ft.  When  the  bearing  is  more  than 
45°,  the  names  of  the  columns  must  be  read  from  the  bottom  of  the  page. 
The  latitude  of  any.  bearing,  as  60°,  is  the  departure  of  its  complement,  30°; 
and  the  departure  of  any  bearing,  as  30°,  is  the  latitude  of  its  complement, 
60°.  Where  the  bearings  are  given  in  smaller  fractions  of  degrees  than  is 
found  in  the  table,  the  latitudes  and  departures  can  be  found  by  inter- 
polation. 


538 


LATITUDES  AND  DEPARTURES. 


tkO 

c 

1 

2 

3 

4 

5 

txo 

c 

€Q 

CO 

0> 

CQ 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

fiO 

0° 

1.000 

0.000 

2.000 

0.000 

3.000 

1 

i 0.000 

4.000 

0.000 

5.000 

90® 

Oi 

1.000 

0.004 

2.000 

0.009 

3.000 

1 0.013 

4.000 

0.017 

5.000 

89^ 

Oh 

1.000 

0.009 

2.000 

0.017 

3.000 

0.026 

4.000 

0.035 

5.000 

89i 

0^ 

1.000 

0.013 

2.000 

0.026 

3.000 

0.039 

4.000 

0.052 

5.000 

89i 

|0 

1.000 

0.017 

2.000 

0.035 

3.000 

0.052 

3.999 

0.070 

4.999 

89® 

li 

1.000 

0.022 

2.000 

0.044 

2.999 

0.065 

3.999 

0.087 

4.999 

m 

u 

1.000 

0.026 

1.999 

0.052 

2.999 

0.079 

3.999 

0.105 

4.998 

88h 

u 

1.000 

0.031 

1.999 

0.061 

2.999 

0.092 

3.998 

0.122 

4.998 

88i 

20 

0.999 

0.035 

1.999 

0.070 

2.998 

0.105 

3.998 

0.140 

4.997 

88® 

2i 

0.999 

0.039 

1.998 

0.079 

2.998 

0.118 

3.997 

0.157 

4.996 

87f 

2i 

0.999 

0.044 

1.998 

0.087 

2.997 

0.131 

3.996 

0.174 

4.995 

87i 

2^ 

0.999 

0.048 

1.998 

0.096 

2.997 

0.144 

3.995 

0.192 

4.994 

87i 

3° 

0.999 

0.052 

1.997 

0.105 

2.996 

0.157 

3.995 

0.209 

4.993 

87® 

3i 

0.998 

0.057 

1.997 

0.113 

2.995 

0.170 

3.994 

0.227 

4.992 

86f 

3i 

0.998 

0.061 

1.996 

0.122 

2.994 

0.183 

3.993 

0.244 

4.991 

86h 

3^ 

0.998 

0.065 

1.996 

0.131 

2.994 

0.196 

3.991 

0.262 

4.989 

867 

40 

0.998 

0.070 

1.995 

0.140 

2.993 

0.209 

3.990 

0.279 

4.988 

86® 

41- 

0.997 

0.074 

1.995 

0.148 

2.992 

0.222 

3.989 

0.296 

4.986 

85^ 

4i 

0.997 

0.078 

1.994 

0.157 

2.991 

0.235 

3.988 

0.314 

4.985 

85i 

4J 

0.997 

0.083 

1.993 

0.166 

2.990 

0.248 

3.986 

0.331 

4.983 

85i 

5° 

0.996 

0.087 

1.992 

0.174 

2.989 

0.261 

3.985 

0.349 

4.981 

85® 

5i 

0.996 

0.092 

1.992 

0.183 

2.987 

0.275 

3.983 

0.366 

4.979 

84^ 

0.995 

0.096 

1.991 

0.192 

2.986 

0.288 

3.982 

0.383 

4.977 

84h 

5f 

0.995 

0.100 

1.990 

0.200 

2.985 

0.301 

3.980 

0.401 

4.975 

84i 

6° 

0.995 

0.105 

1.989 

0.209 

2.984 

0.314 

3.978 

0.418 

4.973 

84® 

6i 

0.994 

0.109 

1.988 

0.218 

2.982 

0.327 

3.976 

0.435 

4.970 

83i 

6i 

0.994 

0.113 

1.987 

0.226 

2.981 

0.340 

3.974 

0.453 

4.968 

8Sh 

6^ 

0.993 

0.118 

1.986 

0.235 

2.979 

0.353 

3.972 

0.470 

4.965 

83i 

7® 

0.993 

0.122 

1.985 

0.244 

2.978 

0.366 

3.970 

0.487 

4.963 

83® 

0.992 

0.126 

1.984 

0.252 

2.976 

0.379 

3.968 

0.505 

4.960 

82^ 

0.991 

0.131 

1.983 

0.261 

2.974 

0.392 

3.966 

0.522 

4.957 

82h 

7# 

0.991 

0.135 

1.982 

0.270 

2.973 

0.405 

3.963 

0.539 

4.954 

82i 

8° 

0.990 

0.139 

1.981 

0.278 

2.971 

0.418 

3.961 

0.557 

4.951 

82® 

8i 

0.990 

0.143 

1.979 

0.287 

2.969 

0.430 

3.959 

0.574 

4.948 

8ii 

81 

0.989 

0.148 

1.978 

0.296 

2.967 

0.443 

3.956 

0.591 

4.945 

8H 

8i 

0.988 

0.152 

1.977 

0.304 

2.965 

0.456 

3.953 

0.608 

4.942 

81i 

90 

0.988 

0.156 

1.975 

0.313 

2.963 

0.469 

3.951 

0.626 

4.938 

81® 

9i 

0.987 

0.161 

1.974 

0.321 

2.961 

0.482 

3.948 

0.643 

4.935 

80i 

9i 

0.986 

0.165 

1.973 

0.330 

2.959 

0.495 

3.945 

0.660 

4.931 

80h 

9^ 

0.986 

0.169 

1.971 

0.339 

2.957 

0.508 

3.942 

0.677 

4.928 

80i 

10® 

0.985 

0.174 

1.970 

0.347 

2.954 

0.521 

3.939 

0.695 

4.924 

80® 

lOi 

0.984 

0.178 

1.968 

0.356 

2.952 

0.534 

3.936 

0.712 

4.920 

79^ 

lOi 

0.983 

0.182 

1.967 

0.364 

2.950 

0.547 

3.933 

0.729 

4.916 

79h 

10^ 

0.982 

0.187 

1.965 

0.373 

2.947 

0.560 

3.9.30 

0.746 

4.912 

79i 

II® 

0.982 

0.191 

1.963 

0.382 

2.945 

0.572 

3.927 

0.763 

4.908 

79® 

Hi 

0.981 

0.195 

1.962 

0.390 

2.942 

0.585 

3.923 

0.780 

4.904 

78i 

lU 

0.980 

0.199 

1.960 

0.399 

2.940 

0.598 

3.920 

0.797 

4.900 

78i 

lU 

0.979 

0.204 

1.958 

0.407 

2.937 

0.611 

3.916 

0.815 

4.895 

78i 

12® 

0.978 

0-208 

1.956 

0-416 

2.934 

0.624 

3.913 

0.832 

4.891 

78® 

12i 

0.977 

0.212 

1.954 

0.424 

2.932 

0.637 

3.909 

0.849 

4.886 

771 

12i 

0.976 

0.216 

1.953 

0.433 

2.929 

0.649 

3.905 

0.866 

4.881 

77h 

m 

0.975 

0.221 

1.951 

0.441 

2.926 

0.662 

3.901  , 

0.883 

4.877 

77i 

13® 

0.974 

0.225 

1.949 

0.450 

2.923 

0.675 

3.897  1 

1 

0.900 

4.872 

77® 

b0 

Dep. 

Lati 

Dep. 

Lat. 

Dep. 

Lat. 

Dep.  1 

Lat. 

Dep. 

bc 

c 

<0 

a> 

flO 

1 

2 

3 

4 

5 

CD 

V 

CD 

LATITUDES  AND  DEPARTURES. 


539 


Bearing. 

5 

6 

7 

8 

9 

Bearing. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

0° 

0.000 

6.000 

0.000 

7.000 

0.000 

8.000 

0.000 

9.000 

0.000 

90° 

Oi 

0.022 

6.000 

0.026 

7.000 

0.031 

8.000 

0.035 

9.000 

0.039 

89f 

Oi 

0.044 

6.000 

0.052 

7.000 

0.061 

8.000 

0.070 

9.000 

0.079 

89i 

Of 

0.065 

5.999 

0.079 

6.999 

0.092 

7.999 

0.105 

8.999 

0.118 

89i 

|0 

0.087 

5.999 

0.105 

6.999 

0.122 

7.999 

0.140 

8.999 

0.157 

89° 

If 

0.109 

5.999 

0.131 

6.998 

0.153 

7.998 

0.175 

8.998 

0.196 

88f 

0.131 

5.998 

0.157 

6.998 

0.183 

7.997 

0.209 

8.997 

0.236 

88i 

If 

0.153 

5.997 

0.183 

6.997 

0.214 

7.996 

0.244 

8.996 

0.275 

88i 

20 

0.174 

5.996 

0.209 

6.996 

0.244 

7.995 

0.279 

8.995 

0.314 

88° 

2i 

0.196 

5.995 

0.236 

6.995 

0.275 

7.994 

0.314 

8.993 

0.353 

87f 

2f 

0.218 

5.994 

0.262 

6.993 

0.305 

7.992 

0.349 

8.991 

0.393 

87i 

2f 

0.240 

5.993 

0.288 

6.992 

0.336 

7.991 

0.384 

8.990 

0.432 

87i 

3° 

0.262 

5.992 

0.314 

6.990 

0.366 

7.989 

0.419 

8.988 

0.471 

87° 

3i 

0.283 

5.990 

0.340 

6.989 

0.397 

7.987 

0.454 

8.986 

0.510 

86f 

3i 

0.305 

5.989 

0.366 

6.987 

0.427 

7.985 

0.488 

8.983 

0.549 

86i 

3f 

0.327 

5.987 

0.392 

6.985 

0.458 

7.983 

0.523 

8.981 

0.589 

86i 

40 

0.349 

5.985 

0.419 

6.983 

0.488 

7.981 

0.558 

8.978 

0.628 

86° 

4f 

0.371 

5.984 

0.445 

6.981 

0.519 

7.978 

0.593 

8.975 

0.667 

85f 

4i 

0.392 

5.982 

0.471 

6.978 

0.549 

7.975 

0.628 

8.972 

0.706 

85i 

4f 

0.414 

5.979 

0.497 

6.976 

0.580 

7.973 

0.662 

8.969 

0.745 

85i 

5° 

0.436 

5.977 

0.523 

6.973 

0.610 

7.970 

0.697 

8.966 

0.784 

85° 

5f 

0.458 

5.975 

0.549 

6.971 

0.641 

7.966 

0.732 

8.962 

0.824 

84f 

5f 

0.479 

5.972 

0.575 

6.968 

0.671 

7.963 

0.767 

8.959 

0.863 

84i 

5f 

0.501 

5.970 

0.601 

6.965 

0.701 

7.960 

0.802 

8.955 

0.902 

84i 

6° 

0.523 

5.967 

0.627 

6.962 

0.732 

7.956 

0.836 

8.951 

0.941 

84° 

Of 

0.544 

5.964 

0.653 

6.958 

0.762 

7.952 

0.871 

8.947 

0.980 

83f 

6i 

0.566 

5.961 

0.679 

6.955 

0.792 

7.949 

0.906 

8.942 

1.019 

83i 

6f 

0.588 

5.958 

0.705 

6.951 

0.823 

7.945 

0.940 

8.938 

1.058 

83i 

70 

0.609 

5.955 

0.731 

6.948 

0.853 

7.940 

0.975 

8.933 

1.097 

83° 

7f 

0.631 

5.952 

0.757 

6.944 

0.883 

7.936 

1.010 

8.928 

1.136 

82f 

7i 

0.653 

5.949 

0.783 

6.940 

0.914 

7.932 

1.044 

8.923 

1.175 

82i 

7f 

0.674 

5.945 

0.809 

6.936 

0.9H 

7.927 

1.079 

8.918 

1.214 

82i 

8° 

0.696 

5.942 

0.835 

6.932 

0.974 

7.922 

1.113 

8.912 

1.253 

82° 

8f 

0.717 

5.938 

0.861 

6.928 

1.004 

7.917 

1.148 

8.907 

1.291 

81f 

8i 

0.739 

5.934 

0.887 

6.923 

1.035 

7.912 

1.182 

8.901 

1.330 

81i 

8f 

0.761 

5.930 

0.913 

6.919 

1.065 

7.907 

1.217 

8.895 

1.369 

81i 

9° 

0.782 

5.926 

0.939 

6.914 

1.095 

7.902 

1.251 

8.889 

1.408 

81° 

9f 

0.804 

5.922 

0.964 

6.909 

1.125 

7.896 

1.286 

8.883 

1.447 

80f 

9f 

0.825 

5.918 

0.990 

6.904 

1.155 

7.890 

1.320 

8.877 

1.485 

80i 

9f 

0.847 

5.913 

1.016 

6.899 

1.185 

7.884 

1.355 

8.870 

1.524 

80i 

10° 

0.868 

5.909 

1.042 

6.894 

1.216 

7.878 

1.389 

8.863 

1.563 

80° 

lOf 

0.890 

5.904 

1.068 

6.888 

1.246 

7.872 

1.424 

8.856 

1.601 

79f 

lOf 

0.911 

5.900 

1.093 

6.883 

1.276 

7.866 

1.458 

8.849 

1.640 

79i 

lOf 

0.933 

5.895 

1.119 

6.877 

1.306 

7.860 

1.492 

8.842 

1.679 

79i 

IP 

0.954 

5.890 

1.145 

6.871 

1.336 

7.853 

1.526 

8.835 

1.717 

79° 

Hi 

0.975 

5.885 

1.171 

6.866 

1.366 

7.846 

1.561 

8.827 

1.756 

78f 

Hi 

0.997 

5.880. 

1.196 

6.859 

1.396 

7.839 

1.595 

8.819 

1.794 

78i 

Hf 

1.018 

5.874 

1.222 

6.853 

1.425 

7.832 

1.629 

8.811 

1.833 

78i 

(20 

1.040 

5.869 

1.247 

6.847 

1.455 

7.825 

1.663 

8.803 

1.871 

78° 

12i 

1.061 

5.863 

1.273 

6.841 

1.485 

7.818 

1.697 

8.795 

1.910 

77f 

12i 

1.082 

5.858 

1.299 

6.834 

1.515 

7.810 

1.732 

8.787 

1.948 

77i 

12f 

1.103 

5.852 

1.324 

6.827 

1.545 

7.803 

1.766 

8.778 

1.986 

77i 

13° 

1.125 

5.846 

1.350 

6.821 

1.575 

7.795 

1.800 

8.769 

2.025 

77° 

bi> 

c 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

tai> 

a 

to 

0> 

CD 

5 

6 

7 

8 

9 

«D 

a> 

CQ 

540 


LATITUDES  AND  DEPARTURES. 


i 

2 

3 

4 

5 

£ 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

£ 

13° 

0.974 

0.225 

1.949 

0.450 

2.923 

0.675 

3.897 

0.900 

4.872 

77° 

13i 

0.973 

0.229 

1.947 

0.458 

2.920 

0.688 

3.894 

0.917 

4.867 

761 

13i 

0.972 

0.233 

1.945 

0.467 

2.917 

0.700 

3.889 

0.934 

4.862 

76i 

13^ 

0.971 

0.238 

1.943 

0.475 

2.914 

0.713 

3.885 

0.951 

4.857 

761 

140 

0.970 

0.242 

1.941 

0.484 

2.911 

0.726 

3.881 

0.968 

4.851 

76® 

14i 

0.969 

0.246 

1.938 

0.492 

2.908 

0.738 

3.877 

0.985 

4.846 

75f 

14i 

0.968 

0.250 

1.936 

0.501 

2.904 

0.751 

3.873 

1.002 

4.841 

751 

751 

14^ 

0.967 

0.255 

1.934 

0.509 

2.901 

0.764 

3.868 

1.018 

4.835 

15® 

0.966 

0.259 

1.932 

0.518 

2.898 

0.776 

3.864 

1.035 

4.830 

75® 

15i 

0.965 

0.263 

1.930 

0.526 

2.894 

0.789 

3.859 

1.052 

4.824 

741 

15i 

0.964 

0.267 

1.927 

0.534 

2.891 

0.802 

3.855 

1.069 

4.818 

741 

15^ 

0.962 

0.271 

1.925 

0.543 

2.887 

0.814 

3.850 

1.086 

4.812 

741 

16® 

0.961 

0.276 

1.923 

0.551 

2.884 

0.827 

3.845 

1.103 

4.806 

74® 

16i 

0.960 

0.280 

1.920 

0.560 

2.880 

0.839 

3.840 

1.119 

4.800 

731 

16i 

0.959 

0.284 

1.918 

0.568 

2.876 

0.852 

3.835 

1.136 

4.794 

731 

16f 

0.958 

0.288 

1.915 

0.576 

2.873 

0.865 

3.830 

1.153 

4.788 

731 

17® 

0.956 

0.292 

1.913 

0.585 

2.869 

0.877 

3.825 

1.169 

4.782 

73® 

17i 

0.955 

0.297 

1.910 

0.593 

2.865 

0.890 

3.820 

1.186 

4.775 

721 

17i 

0.954 

0.301 

1.907 

0.601 

2.861 

0.902 

3.815 

1.203 

4.769 

721 

17^ 

0.952 

0.305 

1.905 

0.610 

2.857 

0.915 

3.810 

1.220 

4.762 

721 

18® 

0.951 

0.309 

1.902 

0.618 

2.853 

0.927 

3.804 

1.236 

4.755 

72® 

m 

0.950 

0.313 

1.899 

0.626 

2.849 

0.939 

3.799 

1.253 

4.748 

711 

18^- 

0.948 

0.317 

1.897 

0.635 

2.845 

0.952 

3.793 

1.269 

4.742 

711 

m 

0.947 

0.321 

1.894 

0.643 

2.841 

0.964 

3.788 

1.286 

4.735 

711 

(9® 

0.946 

0.326 

1.891 

0.651 

2.837 

0.977 

3.782 

1.302 

4.728 

71° 

19i 

0.944 

0.330 

1.888 

0.659 

2.832 

0.989 

3.776 

1.319 

4.720 

701 

19i 

0.943 

0.334 

1.885 

0.668 

2.828 

1.001 

3.771 

1.335 

4.713 

701 

m 

0.941 

0.338 

1.882 

0.676 

2.824 

1.014 

3.765 

1.352 

4.706 

701 

20® 

0.940 

0.342 

1.879 

0.684 

2.819 

1.026 

3.759 

1.368 

4.698 

70® 

20i 

0.938 

0.346 

1.876 

0.692 

2.815 

1.038 

3.753 

1.384 

4.691 

691 

20i 

0.937 

0.350 

1.873 

0.700 

2.810 

1.051 

3.747 

1.401 

4.683 

691 

201 

0.935 

0.354 

1.870 

0.709 

2.805 

1.063 

3.741 

1.417 

4.676 

691 

21® 

0.934 

0.358 

1.867 

0.717 

2.801 

1.075 

3.734 

1.433 

4.668 

69® 

21i 

0.932 

0.362 

1.864 

0.725 

2.796 

1.087 

3.728 

1.450 

4.660 

681 

21i 

0.930 

0.367 

1.861 

0.733 

2.791 

1.100 

3.722 

1.466 

4.652 

681 

21^ 

0.929 

0.371 

1.858 

0.741 

2.786 

1.112 

3.715 

1.482 

4.644 

681 

22® 

0.927 

0.375 

1.854 

0.749 

2.782 

1.124 

3.709 

1.498 

4.636 

68® 

22i 

0.926 

0.379 

1.851 

0.757 

2.777 

1.136 

3.702 

1.515 

4.628 

671 

22i 

0.924 

0.383 

1.848 

0.765 

2.772 

1.148 

3.696 

1.531 

4.619 

671 

221 

0.922 

0.387 

1.844 

0.773 

2.767 

1.160 

3.689 

1.547 

4.611 

671 

23® 

0.921 

0.391 

1.841 

0.781 

2.762 

1.172 

3.682 

1.563 

4.603 

67® 

23i 

0.919 

0.395 

1.838 

0.789 

2.756 

1.184 

3.675 

1.579 

4.594 

661 

23i 

0.917 

0.399 

1.834 

0.797 

2.751 

1.196 

3.668 

1.595 

4.585 

661 

23^ 

0.915 

0.403 

1.831 

0.805 

2.746 

1.208 

3.661 

1.611 

4.577 

661 

24® 

0.914 

0.407 

1.827 

0.813 

2.741 

1.220 

3.654 

1.627 

4.568 

66® 

24i 

0.912 

0.411 

1.824 

0.821 

2.735 

1.232 

3.647 

1.643 

4.559 

651 

24i 

0.910 

0.415 

1.820 

0.829 

2.730 

1.244 

3.640 

1.659 

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1.256 

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1.268 

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1.805 

0.861 

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1.303 

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5.846 

1.350 

6.821 

1.575 

7.795 

1.800 

8.769 

2.025 

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1.146 

5.840 

1.375 

6.814 

1.604 

7.787 

1.834 

8.760 

2.063 

76^ 

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1.167 

5.834 

1.401 

6.807 

1.634 

7.779 

1.868 

8.751 

2.101 

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1.188 

5.828 

1.426 

6.799 

1.664 

7.771 

1.902 

8.742 

2.139 

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140 

1.210 

5.822 

1.452 

6.792 

1.693 

7.762 

1.935 

8.733 

2.177 

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1.231 

5.815 

1.477 

6.785 

1.723 

7.754 

1.969 

8.723 

2.215 

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m 

1.252 

5.809 

1.502 

6.777 

1.753 

7.745 

2.003 

8.713 

2.253 

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1.273 

5.802 

1.528 

6.769 

1.782 

7.736 

2.037 

8.703 

2.291 

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15° 

1.294 

5.796 

1.553 

6.761 

1.812 

7.727 

2.071 

8.693 

2.329 

75° 

15i 

1.315 

5.789 

1.578 

6.754 

1.841 

7.718 

2.104 

8.683 

2.367 

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1.336 

5.782 

1.603 

6.745 

1.871 

7.709 

2.138 

8.673 

2.405 

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1.357 

5.775 

1.629 

6.737 

1.900 

7.700 

2.172 

8.662 

2.443 

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16° 

1.378 

5.768 

1.654 

6.729 

1.929 

7.690 

2.205 

8.651 

2.481 

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16i 

1.399 

5.760 

1.679 

6.720 

1.959 

7.680 

2.239 

8.640 

2.518 

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1.420 

5.753 

1.704 

6.712 

1.988 

7.671 

2.272 

8.629 

2.556 

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1.441 

5.745 

1.729 

6.703 

2.017 

7.661 

2.306 

8.618 

2.594 

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17° 

1.462 

5.738 

1.754 

6.694 

2.047 

7.650 

2.339 

8.607 

2.631 

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1.483 

5.730 

1.779 

6.685 

2.076 

7.640 

2.372 

8.595 

2.669 

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1.504 

5.722 

1.804 

6.676 

2.105 

7.630 

2.406 

8.583 

2.706 

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1.524 

5.714 

1.829 

6.667 

2.134 

7.619 

2.439 

8.572 

2.744 

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1.545 

5.706 

1.854 

6.657 

2.163 

7.608 

2.472 

8.560 

2.781 

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1.566 

5.698 

1.879 

6.648 

2.192 

7.598 

2.505 

8.547 

2.818 

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1.587 

5.690 

1.904 

6.638 

2.221 

7.587 

2.538 

8.535 

2.856 

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1.607 

5.682 

1.929 

6.629 

2.250 

7.575 

2.572 

8.522 

2.893 

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1.628 

5.673 

1.953 

6.619 

2.279 

7.564 

2.605 

8.510 

2.930 

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1.648 

5.665 

1.978 

6.609 

2.308 

7.553 

2.638 

8.497 

2.967 

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1.669 

5.656 

2.003 

6.598 

2.337 

7.541 

2.670 

8.484 

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1.690 

5.647 

2.028 

6.588 

2.365 

7.529 

2.703 

8.471 

3.041 

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1.710 

5.638 

2.052 

6.578 

2.394 

7.518 

2.736 

8.457 

3.078 

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5.629 

2.077 

6.567 

2.423 

7.506 

2.769 

8.444 

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5.620 

2.101 

6.557 

2.451 

7.493 

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8.430 

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1.771 

5.611 

2.126 

6.546 

2.480 

7.481 

2.834 

8.416 

3.189 

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5.601 

2.150 

6.535 

2.509 

7.469 

2.867 

8.402 

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5.592 

2.175 

6.524 

2.537 

7.456 

2.900 

8.388 

3.262 

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5.582 

2.199 

6.513 

2.566 

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8.374 

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6.502 

2.594 

7.430 

2.964 

8.359 

3.335 

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5.563 

2.248 

6.490 

2.622 

7.417 

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8.345 

3.371 

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2.272 

6.479 

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3.029 

8.330 

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5.543 

2.296 

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7.391 

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8.315 

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5.533 

2.320 

6.455 

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7.378 

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8.300 

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1.954 

5.523 

2.344 

6.444 

2.735 

7.364 

3.126 

8.285 

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2.368 

6.432 

2.763 

7.350 

3.158 

8.269 

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5.502 

2.392 

6.419 

2.791 

7.336 

3.190 

8.254 

3.589 

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2.014 

5.492 

2.416 

6.407 

2.819 

7.322 

3.222 

8.238 

3.625 

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2.034 

5.481 

2.440 

6.395 

2.847 

7.308 

3.254 

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2.464 

6.382 

2.875 

7.294 

3.286 

8.206 

3.696 

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2.488 

6.370 

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7.280 

3.318 

8.190 

3.732 

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5.449 

2.512 

6.357 

2.931 

7.265 

3.349 

8.173 

3.768 

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5.438 

2.536 

6.344 

2.958 

7.250 

3.381 

8.157 

3.804 

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2.133 

5.427 

2.559 

6.331 

2.986 

7.236 

3.413 

8.140 

3.839 

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2.583 

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8.123 

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3.476 

8.106 

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2.630 

6.292 

3.069 

7.190 

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5.003 

3.312 

5.837 

3.864 

6.671 

4.416 

7.505 

4.967 

56i 

33^ 

2.778 

4.989 

3.333 

5.820 

3.889 

6.652 

4.445 

7.483 

5.000 

56i 

34° 

2.796 

4.974 

3.355 

5.803 

3.914 

6.632 

4.474 

7.461 

5.033 

56° 

34i 

2.814 

4.960 

3.377 

5.786 

3.940 

6.613 

4.502 

7.439 

5.065 

55} 

34i 

2.832 

4.945 

3.398 

5.769 

3.965 

6.593 

4.531 

7.417 

5.098 

55i 

2.850 

4.930 

3.420 

5.752 

3.990 

6.573 

4.560 

7.395 

5.130 

55i 

35° 

2.868 

4.915 

3.441 

5.734 

4.015 

6.553 

4.589 

7.372 

5.162 

55° 

35i 

2.886 

4.900 

3.463 

5.716 

4.040 

6.533 

4.617 

7.350 

5.194 

54^ 

35i 

2.904 

4.885 

3.484 

5.699 

4.065 

6.513 

4.646 

7.327 

5.226 

54i 

35J 

2.921 

4.869 

3.505 

5.681 

4.090 

6.493 

4.674 

7.304 

5.258 

54i 

36° 

2.939 

4.854 

3.527 

5.663 

4.115 

6.472 

4.702 

7.281 

5.290 

54° 

36i 

2.957 

4.839 

3.548 

5.645 

4.139 

6.452 

4.730 

7.258 

5.322 

53} 

36i 

2.974 

4.823 

3.569 

5.627 

4.164 

6.431 

4.759 

7.235 

5.353 

53i 

36^ 

2.992 

4.808 

3.590 

5.609 

4.188 

6.410 

4.787 

7.211 

5.385 

53i 

37° 

3.009 

4.792 

3.611 

5.590 

4.213 

6.389 

4.815 

7.188 

5.416 

53° 

37i 

3.026 

4.776 

3.632 

5.572 

4.237 

6.368 

4.842 

7.164 

5.448 

52} 

37i 

3.044 

4.760 

3.653 

5.554 

4.261 

6.347 

4.870 

7.140 

5.479 

52i 

371 

3.061 

4.744 

3.673 

5.535 

4.286 

6.326 

4.898 

7.116 

5.510 

52} 

38° 

3.078 

4.728 

3.694 

5.516 

4.310 

6.304 

4.925 

7.092 

5.541 

52° 

38i 

3.095 

4.712 

3.715 

5.497 

4.334 

6.283 

4.953 

7.068 

5.572 

51} 

38i 

3.113 

4.696 

3.735 

5.478 

4.358 

6.261 

4.980 

7.043 

5.603 

5U 

38f 

3.130 

4.679 

3.756 

5.459 

4.381 

6.239 

5.007 

7.019 

5.633 

51} 

39° 

3.147 

4.663 

3.776 

5.440 

4.405 

6.217 

5.035 

6.994 

5.664 

51° 

txb 

c 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

c 

<0 

V 

CO 

5 

6 

7 

8 

9 

<0 

03 

CQ 

544 


LATITUDES  AND  DEPARTURES. 


C 

1 

2 

3 

4 

5 

to 

ca 

0> 

OQ 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

0} 

OQ 

39° 

0.777 

0.629 

1.554 

1.259 

2.331 

1.888 

3.109 

2.517 

3.886 

51° 

39i 

0.774 

0.633 

1.549 

1.265 

2.323 

1.898 

3.098 

2.531 

3.872 

50f 

39i 

0.772 

0.636 

1.543 

1.272 

2.315 

1.908 

3.086 

2.544 

3.858 

50i 

39^ 

0.769 

0.639 

1.538 

1.279 

2.307 

1.918 

3.075 

2.558 

3.844 

50i 

40° 

0.766 

0.643 

1.532 

1.286 

2.298 

1.928 

3.064 

2.571 

3.830 

50° 

40i 

0.763 

0.646 

1.526 

1.292 

2.290 

1.938 

3.053 

2.584 

3.816 

49^ 

40i 

0.760 

0.649 

1.521 

1.299 

2.281 

1.948 

3.042 

2.598 

3.802 

40^ 

0.758 

0.653 

1.515 

1.306 

2.273 

1.958 

3.030 

2.611 

3.788 

491 

41° 

0.755 

0.656 

1.509 

1.312 

2.264 

1.968 

3.019 

2.624 

3.774 

49° 

41i- 

0.752 

0.659 

1.504 

1.319 

2.256 

1.978 

3.007 

2.637 

3.759 

481 

4H 

0.749 

0.663 

1.498 

1..325 

2.247 

1.988 

2.996 

2.650 

3.745 

481 

41^ 

0.746 

0.666 

1.492 

1.332 

2.238 

1.998 

2.984 

2.664 

3.730 

481 

42° 

0.743 

0.669 

1.486 

1.338 

2.229 

2.007 

2.973 

2.677 

3.716 

48° 

42i 

0.740 

0.672 

1.480 

1.345 

2.221 

2.017 

2.961 

2.689 

3.701 

471 

m 

0.737 

0.676 

1.475 

1.351 

2.212 

2.027 

2.949 

2.702 

3.686 

471 

m 

0.734 

0.679 

1.469 

1.358 

2.203 

2.036 

2.937 

2.715 

3.672 

471 

43° 

0.731 

0.682 

1.463 

1.364 

2.194 

2.046 

2.925 

2.728 

3.657 

47° 

43i 

0.728 

0.685 

1.457 

1.370 

2.185 

2.056 

2.913 

2.741 

3.642 

461 

43i 

0.725 

0.688 

1.451 

1.377 

2.176 

2.065 

2.901 

2.753 

3.627 

461 

43f 

0.722 

0.692 

1.445 

1.383 

2.167 

2.075 

2.889 

2.766 

3.612 

461 

44° 

0.719 

0.695 

1.439 

1.389 

2.158 

2.084 

2.877 

2.779 

3.597 

46° 

44i 

0.716 

0.698 

1.433 

1.396 

2.149 

2.093 

2.865 

2.791 

3 582' 

451 

44i 

0.713 

0.701 

1.427 

1.402 

2.140 

2.103 

2.853 

2.804 

3.566 

451 

44f 

0.710 

0.704 

1.420 

1.408 

2.131 

2.112 

2.841 

2.816 

3.551 

451 

45° 

0.707 

0.707 

1.414 

1.414 

2.121 

2.121 

2.828 

2.828 

3.536 

45° 

Bear- 

ing. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Bear- 

ing. 

fZ 

5 

6 

7 

8 

9 

bi> 

c 

CO 

CO 

0} 

CO 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

SQ 

39° 

3.147 

4.663 

3.776 

5.440 

4.405 

6.217 

5.035 

6.994 

5.664 

51° 

39i 

3.164 

4.646 

3.796 

5.421 

4.429 

6.195 

5.062 

6.970 

5.694 

501 

39i 

3.180 

4.630 

3.816 

5.401 

4.453 

6.173 

5.089 

6.945 

5.725 

501 

39f 

3.197 

4.613 

3.837 

5.382 

4.476 

6.151 

5.116 

6.920 

5.755 

501 

40° 

3.214 

4.596 

3.857 

5.362 

4.500 

6.128 

5.142 

6.894 

5.785 

50° 

40i 

3.231 

4.579 

3.877 

5.343 

4.523 

6.106 

5.169 

6.869 

5.815 

491 

40i 

3.247 

4.562 

3.897 

5.323 

4.546 

6.083 

5.196 

6.844 

5.845 

491 

40^ 

3.264 

4.545 

3.917 

5.303 

4.569 

6.061 

5.222 

6.818 

5.875 

491 

41° 

3.280 

4.528 

3.936 

5.283 

4.592 

6.038 

5.2^18 

6.792 

5.905 

49° 

41i 

3.297 

4.511 

3.956 

5.263 

4.615 

6.015 

5.275 

6.767 

5.934 

481 

41i 

3.313 

4.494 

3.976 

5.243 

4.638 

5.992 

5.301 

6.741 

5.964 

481 

41f 

3.329 

4.476 

3.995 

5.222 

4.661 

5.968 

5.327 

6.715 

5.993 

481 

42° 

3.346 

4.459 

4.015 

5.202 

4.684 

5.945 

5.353 

6.688 

6.022 

48° 

42i 

3.362 

4.441 

4.034 

5.182 

4.707 

5.922 

5.379 

6.662 

6.051 

471 

42i 

3.378 

4.424 

4.054 

5.161 

4.729 

5.898 

5.405 

6.635 

6.080 

471 

42^ 

3.394 

4.406 

4.073 

5.140 

4.752 

5.875 

5.430 

6.609 

6.109 

471 

43° 

3.410 

4.388 

4.092 

5.119 

4.774 

5.851 

5.456 

6.582 

6.138 

47° 

43i 

3.426 

4.370 

4.111 

5.099 

4.796 

5.827 

5.481 

6.555 

6.167 

461 

43i 

3.442 

4.352 

4.130 

5.078 

4.818 

5.803 

5.507 

6.528 

6.195 

461 

43f 

3.458 

4.334 

4.149 

5.057 

4.841 

5.779 

5.532 

6.501 

6.224 

461 

44° 

3.473 

4.316 

4.168 

5.035 

4.863 

5.755 

5.557 

6.474 

6.252 

46° 

44i 

3.489 

4.298 

4.187 

5.014 

4.885 

5.730 

5.582 

6.447 

6.280 

451 

44i 

3.505 

4.280 

4.206 

4.993 

4.906 

5.706 

5.607 

6.419 

6.308 

451 

44f 

3.520 

4.261 

4.224 

4.971 

4.928 

5.681 

5.632 

6.392 

6.336 

451 

45° 

3.536 

4.243 

4.243 

4.950 

4.950 

5.657 

5.657 

6.364 

6.364 

45° 

Bear- 

ing. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Bear- 

ing. 

CIRCVMFERENCES,  AND  AREAS. 


545 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 
CIRCUMFERENCES,  AND  AREAS. 


No. 

Square. 

Cube. 

1 Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

1 

1 

1 

1.0000 

1.0000 

1.000000000 

3.1416 

0.7854 

2 

4 

8 

1.4142 

1.2599 

.500000000 

6.2832 

3.1416 

3 

9 

27 

1.7321 

1.4422 

.333333333 

9.4248 

7.068G 

4 

16 

64 

2.0000 

1.5874 

.250000000 

12.5664 

12.5664 

5 

25 

125 

2.2361 

1.7100 

.200000000 

15.7080 

19.635 

6 

36 

216 

2.4495 

1.8171 

.166666667 

18.850 

28.274 

7 

49 

343 

2.6458 

1.9129 

.142857143 

21.991 

38.485 

8 

64 

512 

2.8284 

2.0000 

.125000000 

25.133 

50.266 

9 

81 

729 

3.0000 

2.0801 

.111111111 

28.274 

63.617 

10 

100 

1,000 

3.1623 

2.1544 

.100000000 

31.416 

78.540 

11 

121 

1,331 

3.3166 

2.2240 

.090909091 

34.558 

95.033 

12 

144 

1,728 

3.4641 

2.2894 

.083333333 

37,699 

113.10 

13 

169 

2,197 

3.6056 

2.3513 

.076923077 

40.841 

132.73 

14 

196 

2,744 

3.7417 

2.4101 

.071428571 

43.982 

153.94 

15 

225 

3,375 

3.8730 

2.4662 

.066666667 

47.124 

176.71 

16 

256 

4,096 

4.0000 

2.5198 

.062500000 

50.265 

201.06 

17 

289 

4,913 

4.1231 

2.5713 

.058823529 

53.407 

226.98 

18 

324 

5,832 

4.2426 

2.6207 

.055555556 

56.549 

254.47 

19 

361 

6,859 

4.3589 

2.6684 

.052631579 

59.690 

283.53 

20 

400 

8,000 

4.4721 

2.7144 

.050000000 

62.832 

314.16 

21 

441 

9,261 

4.5826 

2.7589 

.047619048 

65.973 

346.36 

22 

484 

10,648 

4.6904 

2.8020 

.045454545 

69.115 

380.13 

23 

529 

12,167 

4.7958 

2.8439 

.043478261 

72.257 

415.48 

24 

576 

13,824 

4.8990 

2.8845 

.041666667 

75.398 

452.39 

25 

625 

15,625 

5.0000 

2.9240 

.040000000 

78.540 

490.87 

26 

676 

17,576 

5.0990 

2.9625 

.038461538 

81.681 

530.93 

27 

729 

19,683 

5.1962 

3.0000 

.037037037 

84.823 

572.56 

28 

784 

21,952 

5.2915 

3.0366 

.035714286 

87.965 

615.75 

29 

841 

24,389 

5.3852 

3.0723 

.034482759 

91.106 

660.52 

30 

900 

27,000 

5.4772 

3.1072 

.033333333 

94.248 

706.86 

31 

961 

29,791 

5.5678 

3.1414 

.032258065 

97.389 

754.77 

32 

1,024 

32,768 

5.6569 

3.1748 

.031250000 

100.53 

804.25 

33 

1,089 

35,937 

5.7446 

3.2075 

.030303030 

103.67 

855.30 

34 

1,156 

39,304 

5.8310 

3.2396 

.029411765 

106.81 

907.92 

35 

1,225 

42,875 

5.9161 

3.2717 

.028571429 

109.96 

962.11 

36 

1,296 

46,656 

6.0000 

3.3019 

.027777778 

113.10 

1,017.88 

37 

1,369 

50,653 

6.0828 

3.3322 

.027027027 

116.24 

1,075.21 

38 

1,444 

54,872 

6.1644 

3.3620 

.026315789 

119.38 

1,134.11 

39 

1,521 

69,319 

6.2450 

3.3912 

.025641026 

122.52 

1,194.59 

40 

1,600 

64,000 

6.3246 

3.4200 

.025000000 

125.66 

1,256.64 

41 

1,681 

68,921 

6.4031 

3.4482 

.024390244 

128.81 

1,320.25 

42 

1,764 

74,088 

6.4807 

3.4760 

.023809524 

131.95 

1,385.44 

43 

1,849 

79,507 

6.5574 

3.5034 

.023255814 

135.09 

1,452.20 

44 

1,936 

85,184 

6.6332 

3.5303 

.022727273 

138.23 

1,520.53 

45 

2,025 

91,125 

6.7082 

3.5569 

.022222222 

141.37 

1,590.43 

46 

2,116 

97,336 

6.7823 

3.5830 

.021739130 

144.51 

1,661.90 

47 

2,209 

103,823 

6.8557 

3.6088 

.021276600 

147.65 

1,734.94 

48 

2,304 

110,592 

6.9282 

3.6342 

.020833333 

150.80 

1,809.56 

49 

2,401 

117,649 

7.0000 

3.6593 

.020408163 

153.94 

1,885.74 

50 

2,500 

125,000 

7.0711 

3.6840 

.020000000 

157.08 

1,963.50 

51 

2,601 

132,651 

7.1414 

3.7084 

.019607843 

160.22 

2,042.82 

52 

2,704 

140,608 

7.2111 

3.7325 

.019230769 

163.36 

2,123.72 

53 

2,809 

148,877 

7.2801 

3.7563 

.018867925 

166.50 

2,206.18 

54 

2,916 

157,464 

7.3485 

3.7798 

.018518519 

169.65 

2,290.22 

55 

3,025 

166,375 

7.4162 

3.8030 

.018181818 

172.79 

2,375.83 

54G 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

56 

3,136 

175,616 

7.4833 

3.8259 

.017&57143 

175.93 

2,463.01 

57 

3,249 

185,193 

7.5498 

3.8485 

.017543860 

179.07 

2,551.76 

58 

3,364 

195,112 

7.6158 

3.8709 

.017241379 

182.21 

2,642.08 

59 

3,481 

205,379 

7.6811 

3.8930 

.016949153 

185.35 

2,733.97 

60 

3,600 

216,000 

7.7460 

3.9149 

.016666667 

188.50 

2,827.43 

61 

3,721 

226,981 

7.8102 

3.9365 

.016393443 

191.64 

2,922.47 

62 

3,844 

238,328 

7.8740 

3.9579 

.016129032 

194.78 

3,019.07 

63 

3,969 

250,047 

7.9373 

3.9791 

.015873016 

197.92 

3,117.25 

64 

4,096 

262,144 

8.0000 

4.0000 

.015625000 

201.06 

3,216.99 

65 

4,225 

274,625 

8.0623 

4.0207 

.015384615 

204.20 

3,318.31 

66 

4,356 

287,496 

8.1240 

4.0412 

.015151515 

207.34 

3,421.19 

67 

4,489 

300,763 

8.1854 

4.0615 

.014925373 

210.49 

3,525.65 

68 

4,624 

314,432 

8.2462 

4.0817 

.014705882 

213.63 

3,631.68 

69 

4,761 

328,509 

8.3066 

4.1016 

.014492754 

216.77 

3,739.28 

70 

4,900 

343,000 

8.3666 

4.1213 

.014285714 

219.91 

3,848.45 

71 

5,041 

357,911 

8.4261 

4.1408 

.014084517 

223.05 

3,959.19 

72 

5,184 

373,248 

8.4853 

4.1602 

.013888889 

226.19 

4,071.50 

73 

5,329 

389,017 

8.5440 

4.1793 

.013698630 

229.34 

4,185.39 

74 

5,476 

405,224 

8.6023 

4.1983 

.013513514 

232.48 

4,300.84 

75 

5,625 

421,875 

8.6603 

4.2172 

.013333333 

235.62 

4,417.86 

76 

5,776 

438,976 

8.7178 

4.2358 

.013157895 

238.76 

4,536.46 

77 

5,929 

456,533 

8.7750 

4.2543 

.012987013 

241.90 

4,656.63 

78 

6,084 

474,552 

8.8318 

4.2727 

.012820513 

245.04 

4,778.36 

79 

6,241 

493,039 

8.8882 

4.2908 

.012658228 

248.19 

4,901.67 

80 

6,400 

512,000 

8.9443 

4.3089 

.012500000 

251.33 

5,026.55 

81 

6,561 

531,441 

9.0000 

4.3267 

.012345679 

254.47 

5,153.00 

82 

6,724 

551,368 

9.0554 

4.3445 

.012195122 

257.61 

5.281.02 

83 

6,889 

571,787 

9.1104 

4.3621 

.012048193 

260.75 

5,410.61 

84 

7,056 

592,704 

9.1652 

4.3795 

.011904762 

263.89 

5,541.77 

85 

7,225 

614,125 

9.2195 

4.3968 

.011764706 

267.04 

5,674.50 

86 

7,396 

636,056 

9.2736 

4.4140 

.011627907 

270.18 

5,808.80 

87 

7,569 

658,503 

9.3274 

4.4310 

.011494253 

273.32 

5,944.68 

88 

7,744 

681,472 

9.3808 

4.4480 

.011363636 

276.46 

6,082.12 

89 

7.921 

704,969 

9.4340 

4.4647 

.011235955 

279.60 

6,221.14 

90 

8,100 

729,000 

9.4868 

4.4814 

.011111111 

282.74 

6,361.73 

91 

8,281 

753,571 

9.5394 

4.4979 

.010989011 

28.5.88 

6,503.88 

92 

8,464 

778,688 

9.5917 

4.5144 

.010869565 

289.03 

6,647.61 

93 

8,649 

804,357 

9.6437 

4.5307 

.010752688 

292.17 

6,792.91 

94 

8,836 

830,584 

9.6954 

4.5468 

.010638298 

295.31 

6,939.78 

95 

9,025 

857,375 

9.7468 

4.5629 

.010526316 

298.45 

7,088.22 

96 

9,216 

884,736 

9.7980 

4.5789 

.410416667 

301.59 

7,238.23 

97 

9,409 

912,673 

9.8489 

4.5947 

.010309278 

304.73 

7,389.81 

98 

9,604 

941,192 

9.8995 

4.6104 

.010204082 

307.88 

7,542.96 

99 

9,801 

970,299 

9.9499 

4.6261 

.010101010 

311.02 

7,697.69 

100 

10,000 

1,000,000 

10.0000 

4.6416 

.010000000 

314.16 

7,853.98 

101 

10,201 

1,030,301 

10.0499 

4.6570 

.009900990 

317.30 

8,011.85 

102 

10,404 

1,061,208 

10.0995 

4.6723 

.009803922 

320.44 

8,171.28 

103 

10,609 

1,092,727 

10.1489 

4.6875 

.009708738 

323.58 

8.332.29 

104 

10,816 

1,124,864 

10.1980 

4.7027 

.0096153^5 

326.73 

8,494.87 

105 

11,025 

1,157,625 

10.2470 

4,7177 

.009523810 

329.87 

8,659.01 

106 

11,236 

1,191,016 

10.2956 

4.7326 

.009433962 

333.01 

8,824.73 

107 

11,449 

1,225,043 

10.3441 

4.7475 

.009345794 

336.15 

8,992.02 

108 

11,664 

1,259,712 

10.3923 

4.7622 

.009259259 

339.29 

9,160.88 

109 

11,881 

1,295,029 

10.4403 

4.7769 

.009174312 

342.43 

9,331.32 

110 

12,100 

1,331,000 

10.4881 

4.7914 

.009090909 

345.58 

9,503.32 

111 

12,321 

1,367,631 

10.5357 

4.8059 

.009009009 

348.72 

9,676.89 

112 

12,544 

1,404,928 

10.5830 

4.8203 

.008928571 

351.86 

9,852.03 

113 

12,769 

1,442,897 

10.6301 

4.8346 

.008849558 

355.00 

10,028.75 

114 

12,996 

1,481,544 

10.6771 

4.8488 

.0087719.30 

358.14 

10,207.03 

115 

13,225 

1,520,875 

10.7238 

4.8629 

.008695652 

361.28 

10,386.89 

116 

13,456 

1,560,896 

10.7703 

4.8770 

.008020690 

364.42 

10,568.32 

117 

13,689 

1,601,613 

10.8167 

4.8910 

.008547009 

367.57 

10,751.32 

118 

13,924 

1,643,032 

10.8628 

4.9049 

.008474576 

370.71 

10,935.88 

CIRCUMFERENCES,  AND  AREAS.  547 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

119 

14,161 

1,685,159 

10.9087 

4.9187 

.008403361 

373.85 

11,122.02 

120 

14,400 

1,728,000 

10.9545 

4.9324 

.008333333 

376.99 

11,309.73 

121 

14,641 

1,771,561 

11.0000 

4.9461 

.008264463 

380.13 

11,499.01 

122 

14,834 

1,815,848 

11.0454 

4.9597 

.008196721 

383.27 

11,689.87 

123 

15,129 

1,860,867 

11.0905 

4.9732 

.008130081 

386.42 

11,882.29 

124 

15,376 

1,906,624 

11.1355 

4.9866 

.008064516 

389.56 

12,076.28 

125 

15,625 

1,953,125 

11.1803 

5.0000 

.008000000 

392.70 

12,271.85 

126 

15,876 

2,000,376 

11.2250 

5.0133 

.007936508 

395.84 

12,468.98 

127 

16,129 

2,048,383 

11.2694 

5.0265 

.007874016 

398.98 

12,667.69 

128 

16,384 

2,097,152 

11.3137 

5.0397 

.007812500 

402.12 

12,867.96 

129 

16,641 

2,146,689 

11.3578 

5.0528 

.007751938 

405.27 

13,069.81 

130 

16,900 

2,197,000 

11.4018 

5.0658 

.007692308 

408.41 

13,273.23 

131 

17,161 

2,248,091 

11.4455 

5.0788 

.007633588 

411.55 

13,478.22 

132 

17,424 

2,299,968 

11.4891 

5.0916 

.007575758 

414.69 

13,684.78 

133 

17,689 

2,352,637 

11.5326 

5.1045 

.007518797 

417.83 

13,892.91 

134 

17,956 

2,406,104 

11.5758 

5.1172 

.007462687 

420.97 

14,102.61 

135 

18,225 

2,460,375 

11.6190 

5.1299 

.007407407 

424.12 

14,313.88 

136 

18,496 

2,515,456 

11.6619 

5.1426 

.007352941 

427.26 

14,526.72 

137 

18,769 

2,571,353 

11.7047 

5.1551 

.007299270 

430.40 

14,741.14 

138 

19,044 

2,628,072 

11.7473 

51676 

.007246377 

433.54 

14,957.12 

139 

19,321 

2,685,619 

11.7898 

5.1801 

.007194245 

436.68 

15,174.68 

140 

19,600 

2,744,000 

11.8322 

5.1925 

.007142857 

439.82 

15,393.80 

141 

19,881 

2,803,221 

11.8743 

5.2048 

.007092199 

442.96 

15,614.50 

142 

20,164 

2,863,288 

11.9164 

5.2171 

.007042254 

446.11 

15,836.77 

143 

20,449 

2,924,207 

11.9583 

5.2293 

.006993007 

449.25 

16,060.61 

144 

20,736 

2,985,984 

12.0000 

5.2415 

.006944444 

452.39 

16,286.02 

145 

21,025 

3,048,625 

12.0416 

5.2536 

.006896552 

455.53 

16,513.00 

146 

21,316 

3,112,136 

12.0830 

5.2656 

.006849315 

458.67 

16,741.55 

147 

21,609 

3,176,523 

12.1244 

5.2776 

.006802721 

461.81 

16,971.67 

148 

21,904 

3,241,792 

12.1655 

5.2896 

.006756757 

464.96 

17,203.36 

149 

22,201 

3,307,949 

12.2066 

5.3015 

.006711409 

468.10 

17,436.62 

150 

22,500 

3,375,000 

12.2474 

5.3133 

.006666667 

471.24 

17,671.46 

151 

22,801 

3,442,951 

12.2882 

5.3251 

.006622517 

474.38 

17,907.86 

152 

23,104 

3,511,008 

12.3288 

5.3368 

.006578947 

477.52 

18,145.84 

153 

23,409 

3,581,577 

12.3693 

5.3485 

.006535948 

480.66 

18,385.39 

154 

23,716 

3,652,264 

12.4097 

5.3601 

.006493506 

483.81 

18,626.50 

155 

24,025 

3,723,875 

12.4499 

5.3717 

.006451613 

486.95 

18,869.19 

156 

24,336 

3,796,416 

12.4900 

5.3832 

.006410256 

490.09 

19.113.45 

157 

24,649 

3,869,893 

12.5300 

5.3947 

.006369427 

493.23 

19,359.28 

158 

24,964 

3,944,312 

12.5698 

5.4061 

.006329114 

496.37 

19,606.68 

159 

25,281 

4,019,679 

12.6095 

5.4175 

.006289308 

499.51 

19,855.65 

160 

25,600 

4,096,000 

12.6491 

5.4288 

.006250000 

502.65 

20,106.19 

161 

25,921 

4,173,281 

12.6886 

5.4401 

.006211180 

505.80 

20,358.31 

162 

26,244 

4,251,528 

12.7279 

5.4514 

.006172840 

508.94 

20,611.99 

163 

26,569 

4,330,747 

12.7671 

5.4626 

.006134969 

512.08 

20,867.24 

164 

26,896 

4,410,944 

12.8062 

5.4737 

.006097561 

515.22 

21,124.07 

165 

27,225 

4,492,125 

12.8452 

5.4848 

.006060606 

518.36 

21,382.46 

166 

27,556 

4,574,296 

12.8841 

5.4959 

.006024096 

521.50 

21,642.43 

167 

27,889 

4,657,463 

12.9228 

5.5069 

.005988024 

524.65 

21,903.97 

168 

28,224 

• 4,741,632 

12.9615 

5.5178 

.005952381 

527.79 

22,167.08 

169 

28,561 

4,826,809 

13.0000 

5.5288 

.005917160 

530.93 

22,431.76 

170 

28,900 

4,913,000 

13.9384 

5.5397 

.005882353 

534.07 

22,698.01 

171 

29,241 

5,000,211 

13.0767 

5.5505 

.005847953 

537.21 

22,965.83 

172 

28,584 

5,088,448 

13.1149 

5.5613 

.005813953 

540.35 

23,235.22 

173 

29,929 

5,177,717 

13.1529 

5.5721 

.005780347 

M3.50 

23,506.18 

174 

30,276 

5,268,024 

13.1909 

5.5828 

.005747126 

546.64 

23,778.71 

175 

30,625  ' 

5,359,375 

13.2288 

5.5934 

.005714286 

549.78 

24,052.82 

176 

30,976 

' 5,451,776 

13.2665 

5.6041 

.005681818 

552.92 

24,328.49 

177 

31,329 

5,545,233 

13.3041 

5.6147 

.005649718 

556.06 

24,605.74 

178 

31,684 

5,639,752 

13.3417 

5.6252 

.005617978 

559.20 

24,884.56 

179 

32,041 

5,735,339 

13.3791 

5.6357 

.005586592 

562.35 

25,164.94 

180 

32,400 

5,832,000 

13.4164 

5.6462 

.005555556 

565.49 

25,446.90 

181 

32,761 

5,929,741 

13.4536 

5.6567 

.005524862 

563.63 

25,730.43 

548 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 


No. 

Square, 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

182 

33,124 

6,028,568 

13.4907 

5.6671 

.005494505 

571.77 

26,015.53 

183 

33,489 

6,128,487 

13.5277 

5.6774 

.005464481 

574.91 

26,302.20 

184 

33,856 

6,229,504 

13.5647 

5.6877 

.005434783 

578.05 

26,590.44 

185 

34,225 

6,331,625 

13.6015 

5.6980 

.005405405 

581.19 

26,880.25 

186 

34,596 

6,434,856 

13.6382 

5.7083 

.005376344 

584.34 

27,171.63 

187 

34,969 

6,539,203 

13.6748 

5.7185 

.005347594 

587.48 

27,464.59 

188 

35,344 

6,644,672 

13.7113 

5.7287 

.005319149 

590.62 

27,759.11 

189 

35,721 

6,751,269 

13.7477 

5.7388 

.005291005 

593.76 

28,055.21 

190 

36,100 

6,859,000 

13.7840 

5.7489 

.005263158 

596.90 

28,352.87 

191 

36,481 

6,967,871 

13.8203 

5.7590 

.005235602 

600.04 

28,652.11 

192 

36,864 

7,077,888 

13.8564 

5.7690 

.005208333 

603.19 

28,952.92 

193 

37,249 

7,189,017 

13.8924 

5.7790 

.005181347 

606.33 

29,255.30 

194 

37,636 

7,301,384 

13.9284 

5.7890 

.005154639 

609.47 

29,559.25 

195 

38,025 

7,414,875 

13.9642 

5.7989 

.005128205 

612.61 

29,864.77 

196 

38,416 

7,529,536 

14.0000 

5.8088 

.005102041 

615.75 

30,171.86 

197 

38,809 

7,645,373 

14.0357 

5.8186 

.005076142 

618.89 

30,480.52 

198 

39,204 

7,762,392 

14.0712 

5.8285 

.005050505 

622.04 

30,790.75 

199 

39,601 

7,880,599 

14.1067 

5.8383 

.005025126 

625.18 

31,102.55 

200 

40,000 

8,000,000 

14.1421 

5.8480 

.005000000 

628.32 

31,415.93 

201 

40,401 

8,120,601 

14.1774 

5.8578 

.004975124 

631.46 

31,730.87 

202 

40,804 

8,242,408 

14.2127 

5.8675 

.004950495 

634.60 

32,047.39 

203 

41,209 

8,365,427 

14.2478 

5.8771 

.004926108 

637.74 

32,365.47 

204 

41,616 

8,489,664 

14.2829 

5.8868 

.004901961 

640.88 

32,685.13 

205 

42,025 

8,615,125 

14.3178 

5.8964 

.004878049 

644.03 

33,006.36 

206 

42,436 

8,741,816 

14.3527 

5.9059 

.004854369 

647.17 

33,329.16 

207 

42,849 

8,869,743 

14.3875 

5.9155 

.004830918 

650.31 

33,653.53 

208 

43,264 

8,998,912 

14.4222 

5.9250 

.004807692 

653.45 

33,979.47 

209 

43,681 

9,129,329 

14.456: 

5.9345 

.004784689 

656.59 

34,306.98 

210 

44,100 

9,261,000 

14.4914 

5.9439 

.004761905 

659.73 

34,636.06 

211 

44,521 

9,393,931 

14.5258 

5.9533 

.004739336 

662.88 

34,966.71 

212 

44,944 

9,528,128 

14.5602 

5.9627 

.004716981 

666.02 

35,298.94 

213 

45,369 

^,663,597 

14.5945 

5.9721 

.004694836 

669.16 

35,632.73 

214 

45,796 

9,800,344 

14.6287 

5.9814 

.004672897 

672.30 

35,968.09 

215 

46,225 

9,938,375 

14.6629 

5.9907 

.004651163 

675.44 

36,305.03 

216- 

46,656 

10,077,696 

14.6969 

6.0000 

.004629630 

678.58 

36,643.54 

217 

47,089 

10,218,313 

14.7309 

G.0092 

.004608295 

681.73 

36,983.61 

218 

47,524 

10,360,232 

14.7648 

6.0185 

.004587156 

684.87 

37,325.26 

219 

47,961 

10,503,459 

14.7986 

6.0277 

.004566210 

688.01 

37,668.48 

220 

48,400 

10,648,000 

14.8324 

6.0368 

.004545455 

691.15 

38,013.27 

221 

48,841 

10,793,861 

14.8661 

6.0459 

.004524887 

694.29 

38,359.63 

222 

49,284 

10,941,048 

14.8997 

6.0550 

.004504505 

697.43 

38,707.56 

223 

49,729 

11,089,567 

14.9332 

6.0641 

.004484305 

700.58 

39,057.07 

224 

50,176 

11,239,424 

14.9666 

6.0732 

.004464286 

703.72 

39,408.14 

225 

50,625 

11,390,625 

15.0000 

6.0822 

.004444444 

706.86 

39,760.78 

226 

51,076 

11,543,176 

15.0333 

6.0912 

.004424779 

710.00 

40,115.00 

227 

51,529 

11,697,083 

15.0665 

6.1002 

.004405286 

713.14 

40,470.78 

228 

51,984 

11,852,352 

15.0997 

6.1091 

.004385965 

716.28 

40,828.14 

229 

52,441 

12,008,989 

15.1327 

6.1180 

.004366812 

719.42 

41,187.07 

230 

52,900 

12,167,000 

15.1658 

6.1269 

.004347826 

722.57 

41,547.56 

231 

53,361 

12,326,391 

15.1987 

6.1358 

.004329004 

725.71 

41,909.63 

232 

53,824 

12,487,168 

15.2315 

6.1446 

.004310345 

728.85 

42,273.27 

233 

54,289 

12,649,337 

15.2643 

6.1534 

.004291845 

731.99 

42,638.48 

234 

54,756 

12,812,904 

15.2971 

6.1622 

.004273504 

735.13 

43,005.26 

235 

55,225 

12,977,875 

15.3297 

6.1710 

.004255319 

738.27 

43,373.61 

236 

55,696 

13,144,256 

15.3623 

6.1797 

.004237288 

741.42 

43,743.54 

237 

56,169 

13,312,053 

15.3948 

6.1885 

.004219409 

744.56 

44,115.03 

238 

56,644 

13,481,272 

15.4272 

6.1672 

.004201681 

747.70 

44,488.09 

239 

57,121 

13,651,919 

15.4596 

6.2058 

.004184100 

750.84 

44,862.73 

240 

57,600 

13,824,000 

15.4919 

6.2145 

.004166667 

753.98 

45,238.93 

241 

58,081 

13,997,521 

15.5242 

6.2231 

.004149378 

757.12 

45,616.71 

242 

58,564 

14,172,488 

15.5563 

6.2317 

.004132231 

760.27 

45,996.06 

243 

59,049 

14,348,907 

15.5885 

6.2403 

.004115226 

763.41 

46,376.98 

244 

59,536 

14,526,784 

15.6205 

6.2488 

.004098361 

766.55 

46,759.47 

CIRCUMFERENCES,  AND  AREAS. 


549 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

245 

60,025 

14,706,125 

15.6525 

6.2573 

.004081633 

769.69 

47,143.52 

246 

60,516 

14,886,936 

15.6844 

6.2658 

.004065041 

772.83 

47,529.16 

,247 

61,009 

15,069,223 

15.7162 

6.2743 

.004048583 

775.97 

47,916.36 

248 

61,504 

15,252,992 

15.7480 

6.2828 

.004032258 

779.11 

48,305.13 

249 

62,001 

15,438,249 

15.7797 

6.2912 

.004016064 

782.26 

48,695.47 

250 

62,500 

15,625,000 

15.8114 

6.2996 

.004000000 

785.40 

49,087.39 

251 

63,001 

15,813,251 

15.8430 

6.3080 

.003984064 

788.54 

49,480.87 

252 

63,504 

16,003,008 

15.8745 

6.3164 

.003968254 

791.68 

49,875.92 

253 

64,009 

16,194,277 

15.9060 

6.3247 

.003952569 

794.82 

50,272.55 

254 

64,516 

16,387,064 

15.9374 

6.3330 

.003937008 

797.96 

50,670.75 

255 

65,025 

16,581,375 

15.9687 

6.3413 

.003921569 

801.11 

51,070.52 

256 

65,536 

16,777,216 

16.0000 

6.3496 

.003906250 

804.25 

51,471.85 

257 

66,049 

16,974,593 

16.0312 

6.3579 

.003891051 

807.39 

51,874.76 

258 

66,564 

17,173,512 

16.0624 

6.3661 

.003875969 

810.53 

52,279.24 

259 

67,081 

17,373,979 

16.0935 

6.3743 

.003861004 

813.67 

52,685.29 

260 

67,600 

17,576,000 

16.1245 

6.3825 

.003846154 

816.81 

53,092.92 

261 

68,121 

17,779,581 

16.1555 

6.3907 

.003831418 

819.96 

53,502.11 

262 

68,644 

17,984,728 

16.1864 

6.3988 

.003816794 

823.10 

53,912.87 

263 

69,169 

18,191,447 

16.2173 

6.4070 

.003802281 

826.24 

54,325.21 

264 

69,696 

18,399,744 

16.2481 

6.4151 

.003787879 

829.38 

54,739.11 

265 

70,225 

18,609,625 

16.2788 

6.4232 

.003773585 

832.52 

55,154.59 

266 

70,756 

18,821,096 

16.3095 

6.4312 

.003759398 

835.66 

55,571.63 

267 

71,289 

19,034,163 

16.3401 

6.4393 

.003745318 

838.81 

55,990.25 

268 

71,824 

19,248,832 

16.3707 

6.4473 

.003731343 

841.95 

56,410.44 

269 

72,361 

19,465,109 

16.4012 

6.4553 

.003717472 

845.09 

56,832.20 

270 

72,900 

19,683,000 

16.4317 

6.4633 

.003703704 

848.23 

57,255.53 

271 

73,441 

19,902,511 

16.4621 

6.4713 

.003690037 

851.37 

57,680.43 

272 

73,984 

20,123,643 

16.4924 

6.4792 

.003676471 

854.51 

58,106.90 

273 

74,529 

20,346,417 

16.5227 

6.4872 

.003663004 

857.65 

58,534.94 

274 

75,076 

20,570,824 

16.5529 

6.4951 

.003649635 

860.80 

58,964.55 

275 

75,625 

20,796,875 

16.5831 

6.5030 

.003636364 

863.94 

59,395.74 

276 

76,176 

21,024,576 

16.6132 

6.5108 

.003623188 

867.08 

59,828.49 

277 

76,729 

21,253,933 

16.6433 

6.5187 

.003610108 

870.22 

60,262.82 

278 

77,284 

21,484,952 

16.6783 

6.5265 

.003597122 

873.36 

60,698.71 

279 

77,841 

21,717,639 

16.7033 

6.5343 

.003584229 

876.50 

61,136.18 

280 

78,400 

21,952,000 

16.7332 

6.5421 

.003571429 

879.65 

61,575.22 

281 

78,961 

22,188,041 

16.7631 

6.5499 

.003558719 

882.79 

62,015.82 

282 

79,524 

22,425,768 

16.7929 

6.5577 

.003546099 

885.93 

62,458.00 

283 

80,089 

22,665,187 

16.8226 

6.5654 

.003533569 

889.07 

62,901.75 

284 

80,656 

22,906,304 

16.8523 

6.5731 

.003522127 

892.21 

63,347.07 

285 

81,225 

23,149,125 

16.8819 

6.5808 

.003508772 

895.35 

63,793.97 

286 

81,796 

23,393,656 

16.9115 

6.5885 

.003496503 

898.50 

64,242.43 

287 

82,369 

23,639,903 

16.9411 

6.5962 

.003484321 

901.64 

64,692.46 

288 

82,944 

23,887,872 

16.9706 

6.6039 

.003472222 

904.78 

65,144.07 

289 

83,521 

24,137,569 

17.0000 

6.6115 

.003460208 

907.92 

65,597.24 

290 

84,100 

24,389,000 

17.0294 

6.6191 

.003448276 

911.06 

66,051.99 

291 

84,681 

24,642,171 

17.0587 

6.6267 

.003436426 

914.20 

66,508.30 

292 

85,264 

24,897,088 

17.0880 

6.6343 

.003424658 

917.35 

66,966.19 

293 

85,849 

25,153,757 

17.1172 

6.6419 

.008412969 

920.49 

67,425.65 

294 

86,436 

25,412,184 

17.1464 

6.6494 

.003401361 

923.63 

67,886.68 

295 

87,025 

25,672,375 

17.1756 

6.6569 

.003389831 

926.77 

68,349.28 

296 

87,616 

25,934,836 

17.2047 

6.6644 

.003378378 

929.91 

68,813.45 

297 

88,209 

26,198,073 

17.2337 

6.6719 

.003367003 

933.05 

69,279.19 

298 

88,804 

26,463,592 

17.2627 

6.6794 

.003355705 

936.19 . 

69,746.50 

299 

89,401 

26,730,899 

17.2916 

6.6869 

.003344482 

939.34 

70,215.38 

300 

90,000 

27,000,000 

17.3205 

6.6943 

.003333333 

942.48 

70,685.83 

301 

90,601 

27,270,901 

17.3494 

6.7018 

.003322259 

945.62 

71,157.86 

302 

91,204 

27,543,608 

17.3781 

6.7092 

.003311258 

948.76 

71,631.45 

303 

91,809 

27,818,127 

17.4069 

6.7166 

.003301330 

951.90 

72,106.62 

304 

92,416 

28,094,464 

17.4356 

6.7240 

.003289474 

955.04 

72,583.36 

305 

93,025 

28,372,625 

17.4642 

6.7313 

.003278689 

958.19 

73,061.66 

306 

93,636 

28,652,616 

17.4929 

6.7387 

.003267974 

961.33 

73,541.54 

307 

94,249 

28,934,443 

17.5214 

6.7460 

.003257329 

964.47 

74,022.99 

550 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

308 

309 

310 

311 

312 

313 

314 

315 

316 

317 

318 

319 

320 

321 

322 

323 

324 

325 

326 

327 

328 

329 

330 

331 

332 

333 

334 

335 

336 

337 

338 

339 

340 

341 

342 

343 

344 

345 

346 

347 

348 

349 

350 

351 

352 

353 

354 

355 

356 

357 

358 

359 

360 

361 

362 

363 

364 

365 

366 

367 

368 

369 

370 

94,864 

95,481 

96,100 

96,721 

97,344 

97,969 

98,596 

99,225 

99,856 

100,489 

101,124 

101,761 

102,400 

103,041 

103,684 

104,329 

104,976 

105,625 

106,276 

106,929 

107,584 

108,241 

108.900 
109,561 

110.224 
110,889 
111,556 

112.225 
112,896 
113,569 
114,244 
114,921 

115.600 
116,281 
116,964 
117,649 
118,336 

119.025 
119,716  • 
120,409 
121,104 
121,801 
122,500 
123,201 
123,904 
124,609 
125,316 

126.025 
126,736 
127,449 
128,164 
128,881 

129.600 
130,321 
131,044 
131,769 
132,496 

133.225 
133,956 
134,689 
135,424 
136,161 

136.900 

29,218,112 

29,503,629 

29.791.000 
30,080,231 
30,371,328 
30,664,297 
30,959,144 

31.255.875 
31,554,496 
31,855,013 
32,157,432 
32,461,759 

32.768.000 
33,076,161 
33,386,248 
33,698,267 
34,012,224 

34.328.125 

34.645.976 
34,965,783 
35,287,552 
35,611,289 

35.937.000 
36,264,691 
36,594,368 
36,926,037 
37,259,704 
37,595,375 
37,933,056 
38,272,753 
38,614,472 
38,958,219 

39.304.000 
39,651,821 
40,001,688 
40,353,607 
40,707,584 
41,063,625 
41,421,736 
41,781,923 
42,144,192 
42,508,549 

42.875.000 
43,243,551 
43,614,208 

43.986.977 
44,361,864 

44.738.875 
45,118,016 
45,499,293 
45,882,712 
46,268,279 

46.656.000 
47,045,881 
47,437,928 
47,832,147 
48.228,544 

48.627.125 
49,027,896 
49,430,863 
49,836,032 
50,243,409 

50.653.000 

17.5499 

17.5784 

17.6068 

17.6352 

17.6635 

17.6918 

17.7200 

17.7482 

17.7764 

17.8045 

17.8326 

17.8606 

17.8885 

17.9165 

17.9444 

17.9722 

18.0000 

18.0278 

18.0555 

18.0831 

18.1108 

18.1384 

18.1659 

18.1934 

18.2209 

18.2483 

18.2757 

18.3030 

18.3303 

18.3576 

18.3848 

18.4120 

18.4391 

18.4662 

18.4932 

18.5203 

18.5472 

18.5742 

18.6011 

18.6279 

18.6548 

18.6815 

18.7083 

18.7350 

18.7617 

18.7883 

18.8149 

18.8414 

18.8680 

18.8944 

18.9209 

18.9473 

18.9737 

19.0000 

19.0263 

19.0526 

19.0788 

19.1050 

19.1311 

19.1572 

19.1833 

19.2094 

19.2354 

6.7533 

6.7606 

6.7679 

6.7752 

6.7824 

6.7897 

6:7969 

6.8041 

6.8113 

6.8185 

6.8256 

6.8328 

6.8399 

6.8470 

6.8541 

6.8612 

6.8683 

6.8753 

6.8824 

6.8894 

6.8964 

6.9034 

6.9104 

6.9174 

6.9244 

6.9313 

6.9382 

6.9451 

6.9521 

6.9589 

6.9658 

6.9727 

6.9795 

6.9864 

6.9932 

7.0000 

7.0068 

7.0136 

7.0203 

7.0271 

7.0338 

7.0406 

7.0473 

7.0540 

7.0607 

7.0674 

7.0740 

7.0807 

7.0873 

7.0940 

7.1006 

7.1072 

7.1138 

7.1204 

7.1269 

7.1335 

7.1400 

7.1466 

7.1531 

7.1596 

7.1661 

7.1726 

7.1791 

.003246753 

.003236246 

.003225806 

.003215434 

.003205128 

.003194888 

.003184713 

.003174603 

.003164557 

.003154574 

.003144654 

.003134796 

.003125000 

.003115265 

.003105590 

.003095975 

.003086420 

.003076923 

.003067485 

.003058104 

.003048780 

.003039514 

.003030303 

.003021148 

.003012048 

.003003003 

.002994012 

.002985075 

.002976190 

.002967359 

.002958580 

.002949853 

.002941176 

.002932551 

.002923977 

.002915452 

.002906977 

.002898551 

.002890173 

.002881844 

.002873563 

.002865330 

.002857143 

.002849003 

.002840909 

.002832861 

.002824859 

.002816901 

.002808989 

.002801120 

.002793296 

.002785515 

.002777778 

.002770083 

.002762431 

.002754821 

.002747253 

.002739726 

.002732240 

.002721796 

.002717391 

.002710027 

.002702703 

967.61 

970.75 

973.89 

977.04 

980.18 

983.32 

986.46 

989.60 

992.74 

995.88 

999.03 

1,002.17 

1,005.31 

1,008.45 

1,011.59 

1.014.73 
1,017.88 
1,021.02 
1,024.16 
1,027.30 
1,030.44 

1.033.58 

1.036.73 
1,039.87 
1,043.01 
1,046.15 
1,049.29 
1,052.43 

1.055.58 
1,058.72 
1,061.86 
1,065.00 
1,068.14 
1,071.28 

1.074.42 
1,077.57 
1,080.71 
1,083.85 
1,086.99 
1,090.13 

1.093.27 

1.096.42 
1,099.56 
1,102.70 
1,105.84 
1,108.98 
1,112.12 

1.115.27 
1,118.41 
1,121.55 
1,124.69 
1,127.83 
1,130.97 

1.134.11 
1,137.26 
1,140.40 
1,143.54 
1,146.68 
1,149.82 
1,152.96 

1.156.11 
1,159.25 
1,162.39  j 

74.506.01 
74,990.60 
75,476.76 
75,964.50 

76.453.80 

76.944.67 

77.437.12 

77.931.13 

78.426.72 

78.923.88 

1 79,422.60 

1 79,922.90 
! 80,424.77 
i 80,928.21 

81.433.22 

81.939.80 

82.447.96 

82.957.68 
83,468.98 

83.981.84 

84.496.28 

85.012.28 

85.529.86 

86.049.01 

86.569.73 

87.092.02 

87.615.88 

88.141.31 

88.668.31 

89.196.88 

89.727.03 

90.258.74 

90.792.03 

91.326.88 

91.863.31 

92.401.31 

92.940.88 
93,482.02 
94,024.73 
94,569.01 

95.114.86 

95.662.28 

96.211.28 

96.761.84 

97.313.97 

97.867.68 
98,422.96 

98.979.80 

99.538.22 
100,098.21 
100,659.77 
101,222.90 

101.787.60 
102,353.87 
102,921.72 
103,491.13 
104,062.12 
104,634.67 
105,208.80 
105,7&4.49 
106,361.76 

106.940.60 
107,521.01 

CIRCUMFERENCES,  AND  AREAS. 


551 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

371 

,372 

373 

374 

375 

376 

377 

378 

379 

380 

381 

382 

383 

384 

385 

386 

387 

388 

389 

390 

391 

392 

393 

394 

395 

396 

397 

398 

399 

400 

401 

402 

403 

404 

405 

406 

407 

408 

409 

410 

411 

412 

413 

414 

415 

416 

417 

418 

419 

420 

421 

422 

423 

424 

425 

426 

427 

428 

429 

430 

431 

432 

433 

137.641 
138,384 

139.129 
139,876 

140.625 
141,376 

142.129 
142,884 

143.641 
144,400 
145,161 
145,924 
146,689 
147,456 

148.225 
148,996 
149,769 
150,544 
151,321 

152.100 
152,881 
153,664 
154,449 
155,236 
156,025 
156,816 
157,609 
158,404 
159,201 
160,000 
160,801 
161,604 
162,409 
163,216 
164,-625 
164,836 
165,649 
166,464 
167,281 

168.100 
168,921 
169,744 
170,569 
171,396 

172.225 
173,056 
173,889 
174,724 
175,561 
-176,400 
177,241 
178,084 
178,929 
179,776 

180.625 
181,476 
182,329 
183,184 
184,041 
184,900 
185,761 
186,624 
187,489 

51,064,811 

51,478,848 

51,895,117 

52.313.624 

52.734.375 

53.157.376 
53,582,633 
54,010,152 
54,439,939 

54.872.000 
55,306,341 
55,742,968 
56,181,887 
56,623,104 

57.066.625 

57.512.456 
57,960,603 
58,411,072 
58,863,869 

59.319.000 
59,776,471 
60,236,288 

60.698.457 
61,162,984 
61,629,875 
62,099,136 
62,570,773 
63,044,792 
63,521,199 
64,000,000 
64,481,201 
64,964,808 
65,450,827 
65,939,264 
66,430,125 
66,923,416 
67,419,143 
67,917,312 
68,417,929 

68.921.000 
69,426,531 
69,934,528 
70,444,997 
70,957,944 
71,473,375 
71,991,296 
72,511,713 
73,034,632 
73,560,059 

74.088.000 
74,618,461 
75,151,448 
75,686,967 
76,225,024 

76.765.625 
77,308,776 
77,854,483 
78,402,752 
78,953,589 

79.507.000 
80,062,991 
80,621,568 
81,182,737 

19.2614 

19.2873 

19.3132 

19.3391 

19.3649 

19.3907 

19.4165 

19.4422 

19.4679 

19.4936 

19.5192 

19.5448 

19.5704 

19.5959 

19.6214 

19.6469 

19.6723 

19.6977 

19.7231 

19.7484 

19.7737 

19.7990 

19.8242 

19.8494 

19.8746 

19.8997 

19.9249 

19.9499 

19.9750 

20.0000 

20.0250 

20.0499 

20.0749 

20.0998 

20.1246 

20.1494 

20.1742 

20.1990 

20.2237 

20.2485 

20.2731 

20.2978 

20.3224 

20.3470 

20.3715 

20.3961 

20.4206 

20.4450 

20.4695 

20.4939 

20.5183 

20.5426 

20.5670 

20.5913 

20.6155 

20.6398 

20.6640 

20.6882 

20.7123 

20.7364 

20.7605 

20.7846 

20.8087 

7.1855 

7.1920 

7.1984 

7.2048 

7.2112 

7.2177 

7.2240 

7.2304 

7.2368 

7.2432 

7.2495 

7.2558 

7.2622 

7.2685 

7.2748 

7.2811 

7.2874 

7.2936 

7.2999 

7.3061 

7.3124 

7.3186 

7.3248 

7.3310 

7.3372 

7.3434 

7.3496 

7.3558 

7.3619 

7.3681 

7.3742 

7.3803 

7.3864 

7.3925 

7.3986 

7.4047 

7.4108 

7.4169 

7.4229 

7.4290 

7.4350 

7.4410 

7.4470 

7.4530 

7.4590 

7.4650 

7.4710 

7.4770 

7.4829 

7.4889 

7.4948 

7.5007 

7.5067 

7.5126 

7.5185 

7.5244 

7.5302 

7.5361 

7.5420 

7.5478 

7.5537 

7.5595 

7.5654 

.002695418 

.002688172 

.002680965 

.002673797 

.002666667 

.002659574 

.002652520 

.002645503 

.002638521 

.002631579 

.002624672 

.002617801 

.002610966 

.002604167 

.002597403 

.002590674 

.002583979 

.002577320 

.002570694 

.002564103 

.002557545 

.002551020 

.002544529 

.002538071 

.002531646 

.002525253 

.002518892 

.002512563 

.002506266 

.002500000 

.002493766 

.002487562 

.002481390 

.002475248 

.002469136 

.002463054 

.002457002 

.002450980 

.002444988 

.002439024 

.002433090 

.002427184 

.002421308 

.002415459 

.002409639 

.002406846 

.002398082 

.002392344 

.002386635 

.002380952 

.002375297 

.002369668 

.002364066 

.002358491 

.002352941 

.002347418 

.002341920 

.002336449 

.002331002 

.002325581 

.002320186 

.002314815 

.002309469 

1,165.53 

1,168.67 

1.171.81 
1,174.96 
1,178.10 
1,181.24 
1,184.38 
1,187.52 
1,190.66 

1.193.81 
1,196.95 
1,200.09 
1,203.23 
1,206.37 
1,209.51 

1.212.65 
1,215.80 
1,218.94 
1,222.08 
1,225.22 
1,228.36 

1.231.50 

1.234.65 
1,237.79 
1,240.93 
1,244.07 
1,247.21 

1.250.35 

1.253.50 
1,256.64 
1,259.78 
1,262.92 
1,266.06 
1,269.20 

1.272.35 
1,275.49 
1,278.63 
1,281.77 
1,284.91 
1,288.05 

1.291.19 
1,294.34 
1,297.48 
1,300.62 
1,303.76 
1,306.90 

1.310.04 

1.313.19 
1,316.33 
1,319.47 
1,322.61 
1,325.75 
1,328.89 

1.332.04 
1,335.18 
1,338.32 
1,341.46 
1,344.60 
1,347.74 
1,350.88 
1,354.03 
1,357.17 
1,360.31 

108,102.99 

108.686.54 

109.271.66 

109.858.35 

110.446.62 

111.036.45 

111.627.86 
112,220.83 

112.815.38 
113,411.49 

114.009.18 
114,608.44 
115,209.27 

115.811.67 
116,415.64 

117.021.18 
117,628.30 
118,236.98 

118.847.24 

119.459.06 

120.072.46 

120.687.42 
121,303.96 

121.922.07 

122.541.75 
123,163.00 
123,785.82 
124,410.21 
125,036.17 
125,663.71 
126,292.81 
126,923.48 

127.555.73 

128.189.55 
128,824.93 
129,461.89 

130.100.42 
130,740.52 

131.382.19 

132.025.43 

132.670.24 

133.316.63 
133,964.58 

134.614.10 

135.265.20 

135.917.86 

136.572.10 

137.227.91 
137,885.29 

138.544.24 

139.204.76 

139.866.85 

140.530.51 

141.195.74 
141,862.54 

142.530.92 

143.200.86 

143.872.38 

144.545.46 
145,220.12 

145.896.35 
146,574.15 

147.253.52 

552 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal.  *' 

Circum. 

Area. 

434 

435 

436 

437 

438 

439 

440 

441 

442 

443 

444 

445 

446 

447 

448 

449 

450 

451 

452 

453 

454 

455 

456 

457 

458 

459 

460 

461 

462 

463 

464 

465 

466 

467 

468 

469 

470 
171 

472 

473 

474 

475 

476 

477 

478 

479 

480 

481 

482 

483 

484 

485 

486 

487 

488 

489 

490 

491 

492 

493 

494 

495 

496 

188,356 

189.225 
190,096 
190,969 
191,844 
192,721 

193.600 
194,481 
195,364 
196,249 
197,136 

198.025 
198,916 
199,809 
200,704 

201.601 
202,500 
203,401 
204,304 
205,209 
206,116 

207.025 
207,936 
208,849 
209,764 
210,681 
211,600 
212,521 
213,444 
214,369 
215,296 

216.225 
217,156 
218,089 

219.024 
219,961 
220,900 
221,841 
222,784 
223,729 
224,676 
225,625 
226,576 
227,529 
228,484 
229,441 
230,400 
231,361 
232,324 
233,289 
234,256 

235.225 
236,196 
237,169 
238,144 
239,121 
240,100 
241,081 
242,064 
243,049 
244.036 

245.025 
246,016 

81,746,504 

82,312,875 

82,881,856 

83,453,453 

84,027,672 

84,604,519 

85.184.000 
85,766,121 
86,350,888 
86,938,307 
87,528,384 
88,121,125 
88,716,536 
89,314,623 
89,915,392 
90,518,849 

91.125.000 
91,733,851 
92,345,408 
92,959,677 
93,576,664 
94,196,375 
94,818,816 
95,443,993 
96,071,912 
96,702,579 

97.336.000 
97,972,181 
98,611,128 
99,252.847 
99,897,344 

100,544,625 

101,194,696 

101,847,563 

102,503,232 

103,161,709 

103.823.000 
104,487,111 
105,154,048 
105,823,817 
106,496,424 
107,171,875 
107,850,176 
108,531,333 
109,215,352 
109,902,239 

110.592.000 
111,284,641 

111.980.168 
112,678,587 
113,379,904 
114,084,125 
114,791,256 
115,501,303 
116,214,272 

116.930.169 

117.649.000 
118,370,771 
119,095,488 
119,823,157 
120,553,784 
121,287,375 
122,023,936 

20.8327 

20.8567 

20.8806 

20.9045 

20.9284 

20.9523 

20.9762 

21.0000 

21.0238 

21.0476 

21.0713 

21.0950 

21.1187 

21.1424 

21.1660 

21.1896 

21.2132 

21.2368 

21.2603 

21.2838 

21.3073 

21.3307 

21.3542 

21.3776 

21.4009 

21.4243 

21.4476 

21.4709 

21.4942 

21.5174 

21.5407 

21.5639 

21.5870 

21.6102 

21.6333 

21.6564 

21.6795 

21.7025 

21.7256 

21.7486 

21.7715 

21.7945 

21.8174 

21.8403 

21.8632 

21.8861 

21.9089 

21.9317 

21.9545 

21.9775 

22.0000 

22.0227 

22.0454 

22.0681 

22.0907 

22.1133 

22.1359 

22.1585 

22.1811 

22.2036 

22.2261 

22.2486 

22.2711 

7.5712 

7.5770 

7.5828 

7.5886 

7.5944 

7.6001 

7.6059 

7.6117 

7.6174 

7.6232 

7.6289 

7.6346 

7.6403 

7.6460 

7.6517 

7.6574 

7.6631 

7.6688 

7.6744 

7.6801 

7.6857 

7.6914 

7.6970 

7.7026 

7.7082 

7.7188 

7.7194 

7.7250 

7.7306 

7.7362 

7.7418 

7.7473 

7.7529 

7.7584 

7.7639 

7.7695 

7.7750 

7.7805 

7.7860 

7.7915 

7.7970 

7.8025 

7.8079 

7.8134 

7.8188 

7.8243 

7.8297 

7.8352 

7.8406 

7.8460 

7.8514 

7.8568 

7.8622 

7.8676 

7.8730 

7.8784 

7.8837 

7.8891 

7.8944 

7.8998 

7.9051 

7.9105 

7.9158 

.002304147 

.002298851 

.002293578 

.002288330 

.002283105 

.002277904 

.002272727 

.002267574 

.002262443 

.002257336 

.002252252 

.002247191 

.002242152 

.002237136 

.002232143 

.002227171 

.002222222 

.002217295 

.002212389 

.002207506 

.002202643 

.002197802 

.002192982 

.002188184 

.002183406 

.002178649 

.002173913 

.002169197 

.002164502 

.002159827 

.002155172 

.002150538 

.002145923 

.002141328 

.002136752 

.002132196 

.002127660 

.002123142 

.002118644 

.002114165 

.002109705 

.002105263 

.002100840 

.002096486 

.002092050 

.002087683 

.002083333 

.002079002 

.002074689 

.002070393 

.002066116 

.002061856 

.002057613 

.002053388 

.002049180 

.002044990 

.002040816 

.002036660 

.002032520 

.002028398 

.002024291 

.002020292 

.002016129 

1,363.45 

1,366.59 

1.369.73 
1,372.88 
1,376.02 
1,379.16 
1,382.30 
1,385.44 

1.388.58 

1.391.73 
1,394.87 
1,398.01 
1,401.15 
1,404.29 
1,407.43 

1.410.58 
1,413.72 
1,416.86 
1,420.00 
1,423.14 
1,426.28 

1.429.42 
1,432.57 
1,435.71 
1,438.85 
1,441.99 
1,445.13 

1.448.27 

1.451.42 
1,454.56 
1,457.70 
1,460.84 
1,463.98 
1,467.12 

1.470.27 
1,473.41 
1,476.55 
1,479.69 
1,482.83 
1,485.97 

1.489.11 
1,492.26 
1,495.40 
1,498.54 
1,501.68 
1,504.82 

1.507.96 

1.511.11 
1,514.25 
1.517.39 
1,520.53 
1,523.67 

1.526.81 

1.529.96 
1,533.10 
1,536.24 
1,539.38 
1,542.52 
1,545.66 

1.548.81 
1,551.95 
1,555.09 
1,558.23 

147.934.46 

148.616.97 

149.301.05 

149.986.70 
150,673.93 

151.362.72 

152.053.08 

152.745.02 

153.438.53 

154.133.60 

154.830.25 

155.528.47 

156.228.26 

156.929.62 

157.632.55 

158.337.06 

159.043.13 

159.750.77 
160,459.99 

161.170.77 

161.883.13 

162.597.05 

163.312.55 

164.029.62 

164.748.26 

165.468.47 
166,190.25 

166.913.60 

167.638.53 

168.365.02 

169.093.08 

169.822.72 
170,553.92 

171.286.70 

172.021.05 

172.756.97 

173.494.45 
174,233.51 

174.974.14 
175,716.35 
176,460.12 

177.205.46 
177,952.37 

178.700.86 
179,450.91 

180.202.54 

180.955.74 

181.710.50 
182,466.84 

183.224.75 

183.984.23 
184,745.28 
185,507.90 

186.272.10 

187.037.86 
187,805.19 

188.574.10 
189,344.57 

190.116.62 

190.890.24 
191,665.43 
192,442.18 

193.220.51 

CIRCUMFERENCES,  AND  AREAS. 


553 


No. 

Square. 

* Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

497 

498 

499 

500 

501 

502 

503 

504 

505 

506 

507 

508 

509 

510 

511 

512 

513 

514 

515 

516 

517 

518 

519 

520 

521 

522 

523 

524 

525 

526 

527 

528 

529 

530 

531 

532 

533 

534 

535 

536 

537 

538 

539 

540 

541 

542 

543 

544 

545 

546 

547 

548 

549 

550 

551 

552 

553 

554 
5^5 

556 

557 

558 

559 

247.009 

248.004 
249,001 

250.000 

251.001 

252.004 

253.009 
254,016 
255,025 
256,036 
257,049 
258,064 
259,081 
260,100 
261,121 
262,144 
263,169 
264,196 

265.225 
266,256 
267,289 
268,324 
269,361 

270.400 
271,411 
272,484 
273,529 
274,576 
275,625 
276,676 
277,729 
278,784 
279,841 
280,900 
281,961 

283.024 
284,089 
285,156 

286.225 
287,296 
288,369 
289,444 
290,521 

291.600 
292,681 
293,764 
294,849 
295,936 

297.025 
298,116 
299,209 
300,304 

301.401 
302,500 

303.601 
304,704 
305,809 
306,916 

308.025 
309,136 
310,249 
311,364 
312,481 

122,763,473 

123,505,992 

124,251,499 

125,000,000 

125,751,501 

126,506,008 

127,263,527 

128,024,064 

128.787.625 
1^9,554,216 
130,323,843 
131,096,512 
131,872.229 

132.651.000 

133.432.831 
134,217,728 
135,005,697 
135,796,744 

136.590.875 
137,388,096 
138,188,413 

138.991.832 
139,798,359 

140.608.000 
141,420,761 
142,236,648 
143,055,667 
143,877,824 
144,703,125 
145,531,576 

146.363.183 
147,197,952 
148,035,889 

148.877.001 
149,721,291 
150,568,768 
151,419,437 
152,273,304 
153,130,375 
153,990,656 
154,854,153 
155,720,872 
156,590,819 

157.464.000 
158,340,421 
159,220,088 
160,103,007 

160.989.184 

161.878.625 
162,771,336 
163,667,323 
164,566,592 
165,469,149 

166.375.000 
167,284,151 
168,196,608 
169,112,377 
170,031,464 

170.953.875 
171,879,616 
172,808,693 
173,741,112 
174,676,879 

22.2935 

22.3159 

22.3383 

22.3607 

22.3830 

22.4054 

22.4277 

22.4499 

22.4722 

22.4944 

22.5167 

22.5389 

22.5610 

22.5832 

22.6053 

22.6274 

22.6495 

22.6716 

22.6936 

22.7156 

22.7376 

22.7596 

22.7816 

22.8035 

22.8254 

22.8473 

22.8692 

22.8910 

22.9129 

22.9347 

22.9565 

22.9783 

23.0000 

23.0217 

23.0434 

23.0651 

23.0868 

23.1084 

23.1301 

23.1517 

23.1733 

23.1948 

23.2164 

23.2379 

23.2594 

23.2809 

23.3024 

23.3238 

23.3452 

23.3666 

23.3880 

23.4094 

23.4307 

23.4521 

23.4734 

23.4947 

23.5160 

23.5372 

23.5584 

23.5797 

23.6008 

23.6220 

23.6432 

7.9211 

7.9264 

7.9317 

7.9370 

7.9423 

7.9476 

7.9528 

7.9581 

7.9634 

7.9686 

7.9739 

7.9791 

7.9843 

7.9895 

7.9948 

8.0000 

8.0052 

8.0104 

8.0156 

8.0208 

8.0260 

8.0311 

8.0363 

8.0415 

8.0466 

8.0517 

8.0569 

8.0620 

8.0671 

8.0723 

8.0774 

8.0825 

8.0876 

8.0927 

8.0978 

8.1028 

8.1079 

8.1130 

8.1180 

8.1231 

8.1281 

8.1332 

8.1382 

8.1433 

8.1483 

8.1533 

8.1583 

8.1633 

8.1683 

8.1733 

8.1783 

8.1833 

8.1882 

8.1932 

8.1982 

8.2031 

8.2081 

8.2130 

8.2180 

8.2229 

8.2278 

8.2327 

8.2377 

.002012072 

.002008032 

.002004008 

.002000000 

.001996008 

.001992032 

.001988072 

.001984127 

.001980198 

.001976285 

.001972387 

.001968504 

.001964637 

.001960785 

.00L956947 

.001953125 

.001949318 

.001945525 

.001941748 

.001937984 

.001934236 

.001930502 

.001926782 

.001923077 

.001919386 

.001915709 

.001912046 

.001908397 

.001904762 

.001901141 

.001897533 

.001893939 

.001890359 

.001886792 

.001883239 

.001879699 

.001876173 

.001872659 

.001869159 

.001865672 

.001862197 

.001858736 

.001855288 

.001851852 

.001848429 

.001845018 

.001841621 

.001838235 

.001834862 

.001831502 

.001828154 

.001824818 

.001821494 

.001818182 

.001814882 

.001811594 

.001808318 

.001805054 

.001801802 

.001798561 

.001795332 

.001792115 

.001788909 

1,561.37 

1,564.51 

1.567.65 
1,570.80 
1,573.94 
1,577.08 
1,580.22 
1,583.36 

1.586.50 

1.589.65 
1,592.79 
1,595.93 
1,599.07 
1,602.21 
1,605.35 

1.608.50 
1,611.64 
1,614.78 
1,617.92 
1,621.06 
1,624.20 

1.627.34 
1,630.49 
1,633.63 
1,636.77 
1,639.91 
1,643.05 

1.646.19 

1.649.34 
1,652.48 
1,655.62 
1,658.76 
1,661.90 

1.665.04 

1.668.19 
1,671.33 
1,674.47 
], 677.61 
1,680.75 
1,683.89 

1.687.04 
1,690.18 
1,693.32 
1,696.46 
1,699.60 
1,702.74 

1.705.88 
1,709.03 
1,712.17 
1,715.31 
1,718.45 
1,721.59 

1.724.73 

1.727.88 
1,731.02 
1,734.16 
1,737.30 
1,740.44 
1,743.58 

1.746.73 
1,749.87 
1,753.01 
1,756.15 

194,000.41 

194.781.89 

195.564.93 
196,349.54 
197,135.72 

197.923.48 

198.712.80 

199.503.70 

200.296.17 

201.090.20 

201.885.81 
202,682.99 

203.481.74 
204,282.06 

205.083.95 

205.887.42 
206,692.45 
207,499.05 
208,307.23 

209.116.97 
209,928.29 

210.741.18 
211,555.63 
212,371.66 

213.189.26 

214.008.43 
214,829.17 

215.651.49 
216,475.37 

217.300.82 

218.127.85 

218.956.44 
219,786.61 
220,618.34 

221.451.65 
222,286.53 

223.122.98 

223.961.00 

224.800.59 

225.641.75 
226,484.48 

227.328.79 

228.174.66 
229,022.10 
229,871.12 

230.721.71 

231.573.86 

232.427.59 

233.282.89 

234.139.76 

234.998.20 

235.858.21 

236.719.79 

237.582.94 

238.447.67 

239.313.96 

240.181.83 

241.051.26 

241.922.27 
242,794.85 

243.668.99 

244.544.71 

245.422.00 

554 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 


No. 

Square. 

Cube. 

Sq.  Root 

. Cu.  Root 

Reciprocal. 

Circum. 

Area. 

560 

561 

562 

563 

564 

565 

566 

567 

568 

569 

570 

571 

572 

573 

574 

575 

576 

577 
.578 

579 

580 

581 

582 

583 

584 

585 

586 

587 

588 

589 

590 

591 

592 

593 

594 

595 

596 

597 

598 

599 

600 
601 
602 

603 

604 

605 

606 

607 

608 

609 

610 
611 
612 

613 

614 

615 

616 

617 

618 

619 

620 
621 
622 

313,600 

314,721 

315,844 

316,969 

318,096 

319.225 
320,356 
321,489 

322.624 
323,761 
324,900 
326,041 
327,184 
328,329 
329,476 

330.625 
331,776 
332,929 
334,084 
335,241 

336.400 
337,561 
338,724 
339,889 
341,056 

342.225 
343,396 
344,569 
345,744 
346,921 

348.100 
349,281 
350,464 
351,649 
352,836 

354.025 
355,216 
356,409 
357,604 
358,801 
360,000 
361,201 
362,404 
363,609 
364,816 

366.025 
367,236 
368,449 
369,664 
370,881 

372.100 
373,321 
374,544 
375,769 
376,996 

378.225 
379,456 
380,689 
381,924 
383,161 

384.400 
385,641 
386,884 

175.616.000 
176,558,481 
177,504,328 
178,453,547 
179,406,144 
180,362,125 
181,321,496 
182,284,263 
183,250,432 
184,220,009 

185.193.000 
186,169,411 
187,149,248 
188,132,517 
189,119,224 
190,109,375 
191,102,976 
192,100,033 
193,100,552 
194,104,539 

195.112.000 
196,122,941 
197,137,368 
198,155,287 
199,176,704 
200,201,625 
201,230,056 
202,262,003 
203,297,472 
204,336,469 

205.379.000 
206,425,071 
207,474,688 
208,527,857 
209,584,584 
210,644,875 
211,708,736 
212,776,173 
213,847,192 
214,921,799 
216,000,000 
217,081,801 
218,167,208 
219,256,227 
220,348,864 
221,44.5,125 
222,545,016 

223.648.543 
224,755,712 
225,866,529 

226.981.000 
228,099,131 
229,220,928 
230,346,397. 

231.475.544 
232,608,375 
233,744,896 
234,885,113 
236,029,032 
237,176,659 

238.328.000 
239,483,061 
240,641,848 

23.6643 

23.6854 

23.7065 

23.7276 

23.7487 

23.7697 

23.7908 

23.8118 

23.8328 

23.8537 

23.8747 

23.8956 

23.9165 

23.9374 

23.9583 

23.9792 

24.0000 

24.0208 

24.0416 

24.0624 

24.0832 

24.1039 

24.1247 

24.1454 

24.1661 

24.1868 

24.2074 

24.2281 

24.2487 

24.2693 

24.2899 

24.3105 

24.3311 

24.3516 

24.3721 

24.3926 

24.4131 

24.4336 

24.4540 

24.4745 

24.4949 

24.5153 

24.5357 

24.5561 

24.5764 

24.5968 

24.6171 

24.6374 

24.6577 

24.6779 

24.6982 

24.7184 

24.7386 

24.7588 

24.7790 

24.7992 

24.8193 

24.8395 

24.8596 

24.8797 

24.8998 

24.9199 

24.9399 

8.2426 

8.2475 

8.2524 

8.2573 

8.2621 

8.2670 

8.2719 

8.2768 

8.2816 

8.2865 

8.2913 

8.2962 

8.3010 

8.3059 

8.3107 

8.3155 

8.3203 

8.3251 

8.3300 

8.3348 

8.3396 

8.3443 

8.3491 

8.3539 

8.3587 

8.3634 

8.3682 

8.3730 

8.3777 

8.3825 

8.3872 

8.3919 

8.3967 

8.4014 

8.4061 

8.4108 

8.4155 

8.4202 

8.4249 

8.4296 

8.4343 

8.4390 

8.4437 

8.4484 

8.4530 

8.4577 

8.4623 

8.4670 

8.4716 

8.4763 

8.4809 

8.4856 

8.4902 

8.4948 

8.4994 

8.5040 

8.5086 

8.5132 

8.5178 

8.5224 

8.5270 

8.5316 

8.5362 

.001785714 
.001782531 
.001779359 
.001776199 
.001773050 
.001769912 
.001766784 
.001763668 
.001760563 
.001757469 
.001754386 
.001751313 
.001748252 
.001745201 
.001742164 
.001739130 
.001736111 
.001733102 
.001730104 
.001727116 
.001724138 
.001721170 
.001718213 
.001715266 
.001712329 
.001709402 
.001706485 
.001703578 
.001700680 
.001697793 
.001694915 
.001692047 
.001689189 
.001686341 
.001683502 
.001680672 
.001677852 
.001675042 
.001672241 
.001669449 
.001666667 
.001663894 
.001661130 
.001658375 
.001655629 
.001652893 
.001650165 
.001047446 
.001644737 
.001642036 
.001639344 
.001636661 
.001633987 
.001631321  : 
.001628664  : 
.001626016  ; 
.001623377  ; 
.001620746  : 
.001618123  : 
.001615509  : 
.001612903  ] 
.001610306  ] 
.001607717  ] 

1 

1,759.29  246,300.86 
1,762.43  247,181.30 
1,765.58  248,063.30 
1,768.72  248,946.87 
1,771.86  249,832.01 
1,775.00  250,718.73 
1,778.14  251,607.01 
1,781.28  252,496.87 

1.784.42  253,388.30 
1,787.57  254,281.29 
1,790.71  255,175.86 
1,793.85  256,072.00 
1,796.99  256,969.71 
1,800.13  257,868.99 

1.803.27  258,769.85 

1.806.42  259,672.27 
1,809.56  260,576.26 
1,812.70  261,481.83 
1,815.84  262,388.96 
1,818.98  263,297.67 
1,822.12  264,207.94 

1.825.27  265,119.79 
1,828.41  266,033.21 
1,831.55  266.948.20 
1,834.69  267,864.76 
1,837.83  268,782.89 
1,840.97  269,702.59 

1.844.11  270,623.86 
1,847,26  271,546.70 
1,850.40  272,471.12 
1,853.54  273,397.10 
1,856.68  274,324.66 
1,859.82  275,253.78 

1.862.96  276,184.48 

1.866.11  277,116.75 
1,869.25  278,050.58 
1,872.39  278,985.99 
1,875.53  279.922.97 
1,878.67  280,861.52 

1.881.81  1281,801.65 

1.884.96  282,743.34 
1,888.10  283,686.60 
1,891.24  284,631.44 
1,894.38  1285,577.84 
1,897.52  286,525.82 
1,900.66  '287,475.36 

1.903.81  1288,426.48 
1,906.95  ,289,379.17 
1,910.09  290,333.43 
1,913.23  291,289.26 
1,916.37  1292,246.66 
1,919.51  293,205.63 

1.922.65  294,166.17 
1,925.80  295,128.28 
1,928.94  296,091.97 
1,932.08  297,057.22 
1,935.22  298,024.05 
1,938.36  298,992.44 
1,941.50  299,962.41 

1.944.65  300.933.95 
L,947.79  301,907.05 
L,950.93  302,881.73 
L,954.07  |303,857.98 

CIRCUMFERENCES,  AND  AREAS. 


555 


No. 

Square. 

Cube. 

Sq.  Root, 

. Cu.  Root, 

Reciprocal. 

Circum. 

Area. 

623 

,624 

625 

626 

627 

628 

629 

630 

631 

632 

633 

634 

635 

636 

637 

638 

639 

640 

641 
842 

643 

644 

645 

646 

647 

648 

649 

650 

651 

652 

653 

654 

655 

656 

657 

658 

659 

660 
661 
662 

663 

664 

665 

666 

667 

668 

669 

670 

671 

672 

673 

674 

675 

676 

677 

678 

679 

680 
681 
682 

683 

684 

685 

388.129 
389,376 
390,625 
391,876 

393.129 
394,384 
395,641 
396,900 
398,161 
399,424 
400,689 
401,956 

403.225 
404,496 
405,769 
407,044 
408,321 

409.600 
410,881 
412,164 
413,449 
414,736 
416,125 
417,316 
418,609 
419,904 
421,201 
422,500 
423,801 
425,104 
426,409 
427,716 
429,025 
430,336 
431,639 
432,964 
434,281 

435.600 
436,921 
438,244 
439,569 
440,896 

442.225 
443,556 

444.899 

446.224 
447,561 

448.900 
450,241 
451,584 
452,929 
454,276 
455,625 
456,976 
458,329 
459,684 
461,041 
462,400 
463,761 
465,124 
466,489 
467,856 

469.225 

241,804,367 

242.970.624 

244.140.625 
245,314,376 
246,491,883 
247,673,152 
248,858,189 

250.047.000 
251,239,591 
252,435,968 
253,636,137 
254,840,104 

256.047.875 
257,259,456 
258,474,853 
259,694,072 
260,917,119 

262.144.000 
263,374,721 
264,609,288 
265,847,707 
267,089,984 

268.336.125 
269,585,136 

270.840.023 
272,097,792 
273,359,449 

274.625.000 
275,894,451 
277,167,808 
278,445,077 
279,726,264 
281,011,375 
282,300,416 
283,593,393 
284,890,312 
286,191,179 

287.496.000 
288,804,781 
290,117,528 
291,434,247 
292,754,944 
294,079,625 
295,408,296 
296,740,963 
298,077,632 
299,418,309 

300.763.000 
302,111,711 
303,464,448 
304,821,217 

306.182.024 

307.546.875 
308.915,776 
310,288,733 
311,665,752 
313,046,839 

314.432.000 
315,821,241 
317,214,568 
318,611,987 
320,013,504 

321.419.125 

24.9600 

24.9800 

25.0000 

25.0200 

25.0400 

25.0599 

25.0799 

25.0998 

25.1197 

25.1396 

25.1595 

25.1794 

25.1992 

25.2190 

25.2389 

25.2587 

25.2784 

25.2982 

25.3180 

25.3377 

25.3574 

25.3772 

25.3969 

25.4165 

25.4362 

25.4558 

25.4755 

25.4951 

25.5147 

25.5343 

25.5539 

25.5734 

25.5930 

25.6125 

25.6320 

25.6515 

25.6710 

25.6905 

25.7099 

25.7294 

25.7488 

25.7682 

25.7876 

25.8070 

25.8263 

25.8457 

25.8650 

25.8844 

25.9037 

25.9230 

25.9422 

25.9615 

25.9808 

26.0000 

26.0192 

26.0384 

26.0576 

26.0768 

26.0960 

26.1151 

26.1343 

26.1534 

26.1725 

8.5408 

8.5453 

8.5499 

8.5544 

8.5589 

8.5635 

8.5681 

8.5726 

S.5772 

8.5817 

8.5862 

8.5907 

8.5952 

8.5997 

8.6043 

8.6088 

8.6132 

8.6177 

8.6222 

8.6267 

8.6312 

8.6357 

8.6401 

8.6446 

8.6490 

8.6535 

8.6579 

8.6624 

8.6668 

8.6713 

8.6757 

8.6801 

8.6845 

8.6890 

8.6934 

8.6978 

8.7022 

8.7066 

8.7110 

8.7154 

8.7198 

8.7241 

8.7285 

8.7329 

8.7373 

8.7416 

8.7460 

8.7503 

8.7547 

8.7590 

8.7634 

8.7677 

8.7721 

8.7764 

8.7807 

8.7850 

8.7893 

8.7937 

8.7980 

8.8023 

8.8066 

8.8109 

8.8152 

.001605136 
.001602564 
.001600000 
.001597444 
.001594896 
.001592357 
.001589825 
.001587302 
.001584786 
.001582278 
.001579779 
.001577287 
.001574803 
.001572327 
.001569859 
.001567398 
.001564945 
.001562500 
.001560062 
.001557632 
.001555210 
.001552795 
.001550388 
.001547988 
.001545595 
.001543210 
.001540832 
.001538462 
.001536098 
.001533742 
.001531394 
.001529052 
.001526718 
.001524390 
.001522070 
.001519751 
.001517451 
.001515152 
.001512859 
.001510574 
.001508296 
.001506024 
.001503759 
.001501502 
.001499250 
.001497006 
.001494768 
.001492537 
.001490313 
.001488095 
.001485884 
.001483680 
.001481481 
.001479290 
.001477105 
.001474926 
.001472754 
.001470588  : 
.001468429  : 
.001466276  ! 
.001464129  ; 
.001461988  : 
.001459854  : 

1,957.21 

1.960.35 
1,963.50 
1,966.64 
1,969.78 
1,972.92 
1,976.06 
1,979.20 

1.982.35 
1,985.49 
1,988.63 
1,991.77 
1,994.91 
1,998.05 

2.001.19 
2,004.34 
2,007.48 
2,010.62 
2,013.76 
2,016.90 

2.020.04 

2.023.19 
2,026.33 
2,029.47 
2,032.61 
2,035.75 
2,038.89 

2.042.04 
2,045.18 
2,048.32 
2,051.46 
2,054.60 
2,057.74 
2,060.88 
2,064.03 
2,067.17 
2,070.31 
2,073.45 
2,076.59 

2.079.73 
2,082.88 
2,086.02 
2,089.16 
2,092.30 
2,095.44 

2.098.58 

2.101.73 
2,104.87 
2,108.01 
2,111.15 
2,114.29 
2,117.43 

2.120.58 
2,123.72 
2,126.86  : 
2,130.00  : 
2,133.14  : 
2,136.28  : 
2,139.42  ; 
2,142.57  ; 
2,145.71  : 
2,148.85  : 
2,151.99  : 

304,835.80 

305,815.20 

306.796.16 
307,778.69 
308,762.79 
309,748.47 

310.735.71 

311.724.53 
312,714.92 

313.706.88 
314,700.40 
315,695.50 

316.692.17 
317,690.42 

318.690.23 
319,691.61 
320,694.56 

321.699.09 

322.705.18 

323.712.85 

324.722.09 

325.732.89 
326,745.27 
327,759.22 

328.774.74 
329,791.83 

330.810.49 

331.830.72 

332.852.53 

333.875.90 

334.900.85 
335,927.36 
336,955.45 

337.985.10 
339,016.33 
340,049.13 

341.083.50 

342.119.44 
343,156.95 

344.196.03 

345.236.69 

346.278.91 

347.322.70 
348,368.07 
349,415.00 

350.463.51 

351.513.59 

352.565.24 

353.618.45 

354.673.24 

355.729.60 

356.787.54 

357.847.04 

358.908.11 

359.970.75 
361,034,97 

362.100.75 

363.168.11 

364.237.04 

365.307.54 

366.379.60 

367.453.24 

368.528.45 

556 


SQUARES,  CVBES,  SQUARE  AND  CUBE  ROOTS, 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

686 

470,596 

322,828,856 

26.1916 

8.8194 

.001457726 

2,155.13 

369,605.23 

687 

471,969 

324,242,703 

26.2107 

8.8237 

.001455604 

2,158.27 

370,683.59 

688 

473,344 

325,660,672 

26.2298 

8.8280 

.001453488 

2,161.42 

371,763.51 

689 

474,721 

327,082,769 

26.2488 

8.8323 

.001451379 

2,164.56 

372,845.00 

690 

476,100 

328,509,000 

26.2679 

8.8366 

.001449275 

2,167.70 

373,928.07 

691 

477,481 

329,939,371 

26.2869 

8.8408 

.001447178 

2,170.84 

375,012.70 

692 

478,864 

331,373,888 

26.3059 

8.8451 

.001445087 

2,173.98 

376,098.91 

693 

480,249 

332,812,557 

26.3249 

8.8493 

.001443001 

2,177.12 

377,186.68 

694 

481,636 

334,255,384 

26.3439 

8.8536 

.001440922 

2,180.27 

378,276.03 

695 

483,025 

335,702,375 

26.3629 

8.8578 

.001438849 

2,183.41 

379,366.95 

696 

484,416 

337,153,536 

26.3818 

8.8621 

.001436782 

2,186.55 

380,459.44 

697 

485,809 

338,608,873 

26.4008 

8.8663 

.001434720 

2,189.69 

381,553.50 

698 

487,204 

340,068,392 

26.4197 

8.8706 

.001432665 

2,192.83 

382,649.13 

699 

488,601 

341,532,099 

26.4386 

8.8748 

.001430615* 

2,195.97 

383,746.33 

700 

490,000 

343,000,000 

26.4575 

8.8790 

.001428571 

2,199.11 

384,845.10 

701 

491,401 

344,472,101 

26.4764 

8.8833 

.001426534 

2,202.26 

385,945.44 

702 

492,804 

345,948,408 

26.4953 

8.8875 

.001424501 

2,205.40 

387,047.36 

703 

494,209 

347,428,927 

26.5141 

8.8917 

.001422475 

2,208.54 

388,150.84 

704 

495,616 

348,913,664 

26.5330 

8.8959 

.001420455 

2,211.68 

389,255.90 

705 

497,025 

350,402,625 

26.5518 

8.9001 

.001418440 

2,214.82 

390,362.52 

706 

498,436 

351,895,816 

26.5707 

8.9043 

.001416431 

2,217.96 

391,470.72 

707 

499,849 

353,393,243 

26.5895 

8.9085 

.001414427 

2,221.11 

392,580.49 

708 

501,264 

354,894,912 

26.6083 

8.9127 

.001412429 

2,224.25 

393,691.82 

709 

502,681 

356,400,829 

26.6271 

8.9169 

.001410437 

2,227.39 

394,804.73 

710 

504,100 

357,911,000 

26.6458 

8.9211 

.001408451 

2,230.53 

395,919.21 

711 

505,521 

359,425,431 

26.6646 

8.9253 

.001406470 

2,233.67 

397,035.26 

712 

506,944 

360,944,128 

26.6833 

8.9295 

.001404494 

2,236.81 

398,152.89 

713 

508,369 

362,467,097 

26.7021 

8.9337 

.001402525 

2,239.96 

399,272.08 

714 

509,796 

363,994,344 

26.7208 

8.9378 

.001400560 

2,243.10 

400,392.84 

715 

511,225 

365,525,875 

26.7395 

8.9420 

.001398601 

2,246.24 

401,515.18 

716 

512,656 

367,061,696 

26.7582 

8.9462 

.001396648 

2,249.38 

402,639.08 

717 

514,089 

368,601,813 

26.7769 

8.9503 

.001394700 

2,252.52 

403,764.56 

718 

515,524 

370,146,232 

26.7955 

8.9545 

.001392758 

2,255.66 

404,891.60 

719 

516,961 

371,694,959 

26.8142 

8.9587 

.001390821 

2,258.81 

406,020.22 

720 

518,400 

373,248,000 

26.8328 

8.9628 

.001388889 

2,261.95 

407,150.41 

721 

519,841 

374,805,361 

26.8514 

8.9670 

.001386963 

2,265.09 

408,282.17 

722 

521,284 

376,367,048 

26.8701 

8.9711 

.001385042 

2,268.23 

409,415.50 

723 

522,729 

377,933,067 

26.8887 

8.9752 

.001383126 

2,271.37 

410,550.40 

724 

524,176 

379,503,424 

26.9072 

8.9794 

.001381215 

2,274.51 

411,686.87 

725 

525,625 

381,078,125 

26.9258 

8.9835 

.001379310 

2,277.65 

412,824.91 

726 

527.076 

382,657,176 

26.9444 

8.9876 

.001377410 

2,280.80 

413,964.52 

727 

528,529 

384,240,583 

26.9629 

8.9918 

.001375516 

2,283.94 

415,105.71 

728 

529,984 

385,828,352 

26.9815 

8.9959 

.001373626 

2,287.08 

416,248.46 

729 

531,441 

387,420,489 

27.0000 

9.0000 

.001371742 

2,290.22 

417,392.79 

730 

532,900 

389,017,000  . 

27.0185 

9.0041 

.001369863 

2,293.36 

418,538.68 

731 

534,361 

390,617,891 

27.0370 

9.0082 

.001367989 

2,296.50 

419,686.15 

732 

535,824 

392,223,168 

27.0555 

9.0123 

.001366120 

2,299.65 

420,835.19 

733 

537,289 

393,832,837 

27.0740 

9.0164 

.001364256 

2,302.79 

421,985.79 

734 

538,756 

395,446,904 

27.0924 

9.0205 

.001362398 

2,305.93 

423,137.97 

735 

540,225 

397,065,375 

27.1109 

9.0246 

.001360544 

2,309.07 

424,291.72 

736 

541,696 

398,688,256 

27.1293 

9.0287 

.001358696 

2,312.21 

425,447.04 

737 

543,169 

400,315,553 

27.1477 

9.0328 

.001356852 

2,315.35 

426,603.94 

738 

544,644 

401,947,272 

27.1662 

9.0369 

.001355014 

2,318.50 

427,762.40 

739 

546,121 

403,583,419 

27.1846 

9.0410 

.001353180 

2,321.64 

428,922.43 

740 

547,600 

405,224,000 

27.2029 

9.0450 

.001351351 

2,324.78 

430,084.03 

741 

549,801 

406,869,021 

27.2213 

9.0491 

.001349528 

2,327.92 

431,247.21 

742 

550,564 

408,518,488 

27.2397 

9.0532 

.001347709 

2,331.06 

432,411.95 

743 

552,049 

410,172,407 

27.2580 

9.0572 

.001345895 

2,334.20 

433,578.27 

744 

553,536 

411,830,784 

27.2764 

9.0613 

.001344086 

2,337.34 

434,746.16 

745 

555,025 

413,493,625 

27.2947 

9.0654 

.001342282 

2,340.49 

435,915.62 

746 

556.516 

415,160,936 

27.3130 

9.0694 

.001340483 

2,343.63 

437,086.64 

747 

558,009 

416,832,723 

27.3313 

9.0735 

.001338688 

2,346.77 

438,259.24 

748 

559,504 

418,50^,992 

27.3496 

9.0775 

.001336898 

2,349.91 

439,433.41 

CmCVMFERENCES,  AND  AREAS. 


557 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

749 

750 

751 

752 

753 

754 

755 

756 

757 

758 

759 

760 

761 

762 

763 

764 

765 

766 

767 

768 

769 

770 

771 

772 

773 

774 

775 

776 

777 

778 

779 

780 

781 

782 

783 

784 

785 

786 

787 

788 

789 

790 

791 

792 

793 

794 

795 

796 

797 

798 

799 

800 
801 
802 

803 

804 

805 

806 

807 

808 
'809 
810 
811 

561.001 
562,500 

564.001 
565,504 
567.009 
568,516 

570.025 
571,536 
573,049 
574,564 
576,081 

577.600 
579,121 
580,644 
582,169 
583,696 

585.225 
586,756 
588,289 
589,824 
591,361 
592,900 
594,441 
595,984 
597,529 
599,076 
600,625 
602,176 
603,729 
605,284 
606,841 

608.400 
609,961 
611,524 
613,089 
614,656 

616.225 
617,796 
619,369 
620,944 
622,521 

624.100 
625,681 
627,264 
628,849 
630,436 

632.025 
633,616 
635,209 
636,804 

638.401 
640,000 

641.601 
643,204 
644,809 
646,416 

648.025 
649,636 
651,249 
652,864 
654,481 

656.100 
657,721 

420,189,749 

421.875.000 
423,564,751 
425,259,008 
426,957,777 
428,661,064 

430.368.875 
432,081,216 
433,798,093 
435,519,512 
437,245,479 

438.976.000 
440,711,081 
442,450,728 
444,194,947 
445,943,744 

447.697.125 
449,455,096 
451,217,663 
452,984,832 
454,756,609 

456.533.000 
458,314,011 
460,099.648 
461,88£  917 
463,684,824 
465,484,375 
467,288,576 
469,097,433 
470,910,952 
472,729,139 

474.552.000 
476,379,541 
478,211,768 
480,048,687 
481,890,304 
483,736,625 
485,587,656 
487,443,403 
489,303,872 
491,169,069 

493.039.000 
494,913,671 
496,793,088 
498,677,257 
500,566,184 

502.459.875 
504,358,336 
506,261,573 
508,169,592 
510,082,399 
512,000,000 
513,922,401 
515,849,608 
517,781,627 
519,718,464 

521.660.125 
523,606,616 
525,557,943 
527,514,112 
529,475,129 

531.441.000 
533,411,731 

27.3679 

27.3861 

27.4044 

27.4226 

27.4408 

27.4591 

27.4773 

27.4955 

27.5136 

27.5318 

27.5500 

27.5681 

27.5862 

27.6043 

27.6225 

27.6405 

27.6586 

27.6767 

27.6948 

27.7128 

27.7308 

27.7489 

27.7669 

27.7849 

27.8029 

27.8209 

27.8388 

27.8568 

27.8747 

27.8927 

27.9106 

27.9285 

27.9464 

27.9643 

27.9821 

28.0000 

28.0179 

28.0357 

28.0535 

28.0713 

28.0891 

28.1069 

28.1247 

28.1425 

28.1603 

28.1780 

28.1957 

28.2135 

28.2312 

28.2489 

28.2666 

28.2843 

28.3019 

28.3196 

28.3373 

28.3549 

28.3725 

28.3901 

28.4077 

28.4253 

28.4429 

28.4605 

28.4781 

9.0816 

9.0856 

9.0896 

9.0937 

9.0977 

9.1017 

9.1057 

9.1098 

9.1138 

9.1178 

9.1218 

9.1258 

9.1298 

9.1338 

9.1378 

9.1418 

9.1458 

9.1498 

9.1537 

9.1577 

9.1617 

9.1657 

9.1696 

9.1736 

9.1775 

9.1815 

9.1855 

9.1894 

9.1933 

9.1973 

9.2012 

9.2052 

9.2091 

9.2130 

9.2170 

9.2209 

9.2248 

9.2287 

9.2326 

9.2365 

9.2404 

9.2443 

9.2482 

9.2521 

9.2560 

9.2599 

9.2638 

9.2677 

9.2716 

9.2754 

9.2793 

9.2832 

9.2870 

9.2909 

9.2948 

8.2986 

9.3025 

9.3063 

9.3102 

9.3140 

9.3179 

9.3217 

9.3255 

.001335113 

.001333333 

.001331558 

.001329787 

.001328021 

.001326260 

.001324503 

.001322751 

.001321004 

.001319261 

.001317523 

.001315789 

.001314060 

.001312336 

.001310616 

.001308901 

.001307190 

.001305483 

.001303781 

.001302083 

.001300390 

.001298701 

.001297017 

.001295337 

.001293661 

.001291990 

.001290323 

.001288660 

.001287001 

.001285347 

.001283697 

.001282051 

.001280410 

.001278772 

.001277139 

.001275510 

.001273885 

.001272265 

.001270648 

.001269036 

.001267427 

.001265823 

.001264223 

.001262626 

.001261034 

.001259446 

.001257862 

.001256281 

.001254705 

.001253133 

.001251364 

.001250000 

.001248439 

.001246883 

.001245330 

.001243781 

.001242236 

.001240695 

.001239157 

.001237624 

.001236094 

.001234568 

.001233046 

2,353.05 

2.356.19 
2,359.34 
2,362.48 
2,365.62 
2,368.76 
2,371.90 

2.375.04 

2.378.19 
2,381.33 
2,384.47 
2,387.61 
2,390.75 
2,393.89 

2.397.04 
2,400.18 
2,403.32 
2,406.46 
2,409.60 
2,412.74 

2.415.88 
2,419.03 
2,422.17 
2,425.31 
2,428.45 
2,431.59 

2.434.73 

2.437.88 
2,441.02 
2,444.16 
2,447.30 
2,450.44 

2.453.58 

2.456.73 
2,459.87 
2,463.01 
2,466.15 
2,469.29 
2,472.43 

2.475.58 
2,478.72 
2,481.86 
2,485.00 
2,488.14 
2,491.28 

2.494.42 
2,497.57 
2,500.71 
2,503.85 
2,506.99 
2,510.13 

2.513.27 

2.516.42 
2,519.56 
2,522.70 
2,525.84 
2,528.98 
2,532.12 

2.535.27 
2,538.41 
2,541.55 
2,544.69 
2,547.83 

440,609.16 

441,786.47 

442,965.35 

444.145.80 

445.327.83 
446,511.42 
447,696.59 
448.883.32 

450.071.63 
451,261.51 

452.452.96 

453.645.98 

454.840.57 

456.036.73 
457,234.46 

458.433.77 

459.634.64 
460,837.08 
462,041.10 

463.246.69 

464.453.84 

465.662.57 

466.872.87 

468.084.74 

469.298.18 

470.513.19 

471.729.77 

472.947.92 

474.167.65 

475.388.94 

476.611.81 

477.836.24 

479.062.25 

480.289.83 

481.518.97 

482.749.69 

483.981.98 

485.215.84 

486.451.28 

487.688.28 

488.926.85 

490.166.99 
491,408.71 

492.651.99 

493.896.85 

495.143.28 
496,391.27 
497,640.84 

498.891.98 

500.144.69 
501,398.97 

502.654.82 

503.912.25 
505,171.24 
506,431.80 

507.693.94 
508,957.64 

510.222.92 

511.489.77 

512.758.19 
514,028.18 

515.299.74 

516.572.87 

558 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

812 

813 

814 

815 

816 

817 

818 

819 

820 
821 
822 

823 

824 

825 

826 

827 

828 

829 

830 

831 

832 

833 

834 

835 

836 

837 

838 

839 

840 

841 

842 

843 

844 

845 
.846 

847 

848 

849 

850 

851 

852 

853 

854 

855 

856 

857 

858 

859 

860 
861 
862 

863 

864 

865 

866 

867 

868 

869 

870 

871 

872 

873 

874 

659,344 

660,969 

662,596 

664,225 

665,856 

667,489 

669,124 

670,761 

672,400 

674,041 

675.584 
677,329 
678,976 
680,625 
682,276 
683,929 

685.584 
687,241 

688.900 
690,561 

692.224 
693,889 
695,556 

697.225 
698,896 
700.569 
702;  244 
703,921 

705.600 
707,281 
708,964 
710,649 
712,336 

714.025 
715,716 
717,409 
719,104 
720,801 
722,500 
724,201 
725,904 
727,609 
729,316 

731.025 
732,736 
734,449 
736,164 
737,881 

739.600 
741,321 
743,044 
744,769 
746,496 

748.225 
749,956 
751,689 
753,424 
755,161 

756.900 
758,641 
760,384 
762,129 
763,876 

535,387,328 

537,367,797 

539,353,144 

541.343.375 
543,338,496 
545,338,513 
547,343,432 
549,353,259 

551.368.000 
553,387,661 
555,412,248 
557,441,767 
559,476,224 

561.515.625 
563,559,976 
565,609,283 
567,663,552 
569,722,789 

571.787.000 

573.856.191 
575,930,368 
578,009,537 
580,093,704 
582,182,875 
584,277,056 
586,376,253 
588,480,472 
590,589,719 

592.704.000 
594,823,321 
596,947,688 
599,077,107 
601,211,584 
603,351,125 
605,495,736 
607,645,423 

609.800.192 
611,960,049 

614.125.000 
616,295,051 
618,470,208 
620,650,477 
622,835,864 

625.026.375 
627,222,016 
629,422,793 
631,628,712 
633,839,779 

636.056.000 
638,277,381 
640,503,928 
642,735,647 
644,972,541 

647.214.625 
649,461,896 
651,714,363 
653,972,032 
656,234,909 

658.503.000 
660,776,311 
663,054,848 
665,338,617 
667,627,624 

28.4956 

28.5132 

28.5307 

28.5482 

28.5657 

28.5832 

28.6007 

28.6182 

28.6356 

28.6531 

28.6705 

28.6880 

28.7054 

28.7228 

28.7402 

28.7576 

28.7750 

28.7924 

28.8097 

28.8271 

28.8444 

28.8617 

28.8791 

28.8964 

28.9137 

28.9310 

28.9482 

28.9655 

28.9828 

29.0000 

29.0172 

29.0345 

29.0517 

29.0689 

29.0861 

29.1033 

29.1204 

29.1376 

29.1548 

29.1719 

29.1890 

29.2062 

29.2233 

29.2404 

29.2575 

29.2746 

29.2916 

29.3087 

29.3258 

29.3428 

29.3598 

29.3769 

29.3939 

29.4109 

29.4279 

29.4449 

29.4618 

29.4788 

29.4958 

29.5127 

29.5296 

29.5466 

29.5635 

9.3294 

9.3332 

9.3370 

9.3408 

9.3447 

9.3485 

9.3523 

9.3561 

9.3599 

9.3637 

9.3675 

9.3713 

9.3751 

9.3789 

9.3827 

9.3865 

9 3902 
9.3940 
9.3978 
9.4016 
9.4053 
9.4091 
9.4129 
9.4166 
9.4204 
9.42^11 
9.4279 
9.4316 
9.4354 
9.4391 
9.4429 
9.4466 
9.4503 
9.4541 
9.4578 
9.4615 
9.4652 
9.4690 
9.4727 
9.4764 
9.4801 
9.4838 
9.4875 
9.4912 
9.4949 
9.4986 
9.5023 
9.5060 
9.5097 
9.5135 
9.5171 
9.5207 
9.5244 
9.5281 
9.5317 
9.5354 
9.5391 
9.5427 
9.5464 
9.5501 
9.5537 
9.5574 
9.5610 

.001231527 

.001230012 

.001228501 

.001226994 

.001225490 

.001223990 

.001222494 

.001221001 

.001219512 

.001218027 

.001216545 

.001215067 

.001213592 

.001212121 

.001210654 

.001209190 

.001207729 

.001206273 

.001204819 

.001203369 

.001201923 

.001200480 

.001199041 

.001197605 

.001196172 

.001194743 

.001193317 

.001191895 

.001190476 

.001189061 

.001187648 

.001186240 

.001184834 

.001183432 

.001182033 

.001180638 

.001179245 

.001177856 

.001176471 

.001175088 

.001173709 

.001172333 

.001170960 

.001169591 

.001168224 

.001166861 

.001165501 

.001164144 

.001162791 

.001161440 

.001160093 

.001158749 

.001157407 

.001156069 

.001154734 

.001153403 

.001152074 

.001150748 

.001149425 

.001148106 

.001146789 

.001145475 

.001144165 

2,550.97 

2,554:11 

2,557.26 

2,560.40 

2,563.54 

2,566.68 

2,569.82 

2.572.96 
2,576.11 
2,579.25 
2,582.39 
2,585.53 
2,588.67 

2.591.81 

2.594.96 
2,598.10 
2,601.24 
2,604.38 
2,607.52 
2,610.66 

2.613.81 
2,616.95 
2,620.09 
2,623.23 
2,626.37 
2,629.51 

2.632.65 
2,635.80 
2,638.94 
2,642.08 
2,645.22 
2,648.36 

2.651.50 

2.654.65 
2,657.79 
2,660.93 
2,664.07 
2,667.21 
2,670.35 

2.673.50 
2,676.64 
2,679.78 
2,682.92 
2,686.06 
2,689.20 

2.692.34 
2,695.49 
2,698.63 
2,701.77 
2,704.91 
2,708.05 

2.711.19 

2.714.34 
2,717.48 
2,720.62 
2,723.76 
2,726.90 
2,730.04 

2.733.19 
2,736.33 
2,739.47 
2,742.61 
2,745.75 

517.847.57 

519.123.84 

520.401.68 
521,681.10 
522,962.08 
524,244.63 

525.528.76 

526.814.46 
528,101.73 
529,390.56 
530,680.97 

531.972.95 

533.266.50 

534.561.62 
535,858.32 

537.156.58 

538.456.41 

539.757.82 
541,060.79 
542,365.34 

543.671.46 

544.979.15 
546,288.40 
547,599.23 

548.911.63 
550,225.61 

551.541.15 
552,858.26 
554,176.94 

555.497.20 

556.819.02 

558.142.42 
559,467.39 
560,793.92 

562.122.03 

563.451.71 

564.782.96 
566;  115.78 
567,450.17 

568.786.14 
570,123.67 

571.462.77 
572,803.45 

574.145.69 

575.489.51 
576,834.90 

578.181.85 

579.530.38 
580,880.48 

582.232.15 

583.585.39 

584.940.20 

586.296.59 
587,654.54 
589,014.07 

590.375.16 

591.737.83 
593,102.06 
594,467.87 
595,835.25 

597.204.20 

598.574.72 
599,946.81 

CIRCVMFERENCES,  AND  AREAS. 


559 


No. 

Square. 

Cube. 

Sq.  Boot. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

875 

876 

877 

878 

879 

880 
881 
882 

883 

884 

885 

886 

887 

888 

889 

890 

891 

892 

893 

894 

895 

896 

897 

898 

899 

900 

901 

902 

903 

904 

905 

906 

907 

908 

909 

910 

911 

912 

913 

914 

915 

916 

917 

918 

919 

920 

921 

922 

923 

924 

925 

926 

927 

928 

929 

930 

931 

932 

933 

934 

935 

936 

937 

765.625 
767,376 
769,129 
770,884 
772,641 

774.400 
776,161 
777,924 
779,689 
781,456 

783.225 
784,996 
786,769 
788,544 
790,321 

792.100 
793,881 
795,664 
797,449 
799,236 

801.025 
802,816 
804,609 
806,404 
808,201 
810,000 
811,801 
813,604 
815,409 
817,216 

819.025 
820,836 
822,649 
824,464 
826,281 

828.100 
829,921 
831,744 
833,569 
835,396 

837.225 
839,056 
840,889 
842,724 
844,561 

846.400 
848,241 
850,084 
851,929 
853,776 

855.625 
857,476 
859,329 
861,184 
863,041 
864,900 
866,761 
868,624 
870,489 
872,356 

874.225 
876,096 
877,969 

669.921.875 
672,221,376 
674,526,133 
676,836,152 
679,151,439 

681.472.000 
683,797.841 
686,128,968 
688,465,387 
690,807,104 

693.154.125 
695,506,456 
697,864,103 
700,227,072 
702,595,369 

704.969.000 
707,347,971 
707,932,288 
712,121,957 
714,516,984 

716.917.375 
719,323,136 
721,734,273 
724,150,792 
726,572,699 
729,000,000 
731,432,701 
733,870,808 
736,314,327 
738,763,264 
741,217,625 
743,677,416 
746,142,643 
748,613,312 
751,089,429 

753.571.000 
756,058,031 
758,550,825 
761,048,497 
763,551,944 

766.060.875 
768,575,296 
771,095,213 
773,620,632 
776,151,559 

778.688.000 
781,229,961 
783.777,448 
786;330,467 
788,889,024 

791.453.125 
794,022,776 
796,597,983 
799,178,752 
801,765,089 

804.357.000 
806,954,491 
809,557,568 
812,166,237 
814,780,504 

817.400.375 
820,025,856 
822,656,953 

29.5804 

29.5973 

29.6142 

29.6311 

29.6479 

29.6648 

29.6816 

29.6985 

29.7153 

29.7321 

29.7489 

29.7658 

29.7825 

29.7993 

29.8161 

29.8329 

29.8496 

29.8664 

29.8831 

29.8998 

29.9166 

29.9333 

29.9500 

29.9666 

29.9833 

30.0000 

30.0167 

30.0333 

30.0500 

30.0666 

30.0832 

30.0998 

30.1164 

30.1330 

30.1496 

30.1662 

30.1828 

30.1993 

30.2159 

30.2324 

30.2490 

30.2655 

30.2820 

30.2985 

30.3150 

30.3315 

30.3480 

30.3645 

30.3809 

30.3974 

30.4138 

30.4302 

30.4467 

30.4631 

30.4795 

30.4959 

30.5123 

30.5287 

30.5450 

30.5614 

30.5778 

30.5941 

30.6105 

9.5647 

9.5683 

9.5719 

9.5756 

9.5792 

9.5828 

9.5865 

9.5901 

9.5937 

9.5973 

9.6010 

9.6046 

9.6082 

9.6118 

9.6154 

9.6190 

9.6226 

9.6262 

9.6298 

9.6334 

9.6370 

9.6406 

9.6442 

9.6477 

9.6513 

9.6549 

9.6585 

9.6620 

9.6656 

9.6692 

9.6727 

9.6763 

9.6799 

9.6834 

9.6870 

9.6905 

9.6941 

9.6976 

9.7012 

9.7047 

9.7082 

9.7118 

9.7153 

9.7188 

9.7224 

9.7259 

9.7294 

9.7329 

9.7364 

9.7400 

9.7435 

9.7470 

9.7505 

9.7540 

9.7575 

9.7610 

9.7645 

9.7680 

9.7715 

9.7750 

9.7785 

9.7829 

9.7854 

.001142857 

.001141553 

.001140251 

.001138952 

.001137656 

.001136364 

.001135074 

.001133787 

.001132503 

.001131222 

.001129944 

.001128668 

.001127396 

.001126126 

.001124859 

.001123596 

.001122334 

.001121076 

.001119821 

.001118568 

.001117818 

.001116071 

.001114827 

.001113586 

.001112347 

.001111111 

.001109878 

.001108647 

.001107420 

.001106195 

.001104972 

.001103753 

.001102536 

.001101322 

.001100110 

.001098901 

.001091695 

.001096491 

.001095290 

.001094092 

.001092896 

.001091703 

.001090513 

.001089325 

.001088139 

.001086957 

.001085776 

.001084599 

.001083423 

.001082251 

.001081081 

.001079914 

.001078749 

.001077586 

.001076426 

.001075269 

.001074114 

.001072961 

.001071811 

.001070664 

.001069519 

.001068376 

.001067236 

2,748.89 

2,752.04 

2,755.18 

2,758.32 

2,761.46 

2,764.60 

2,767.74 

2.770.88 
2,774.03 
2,777.17 
2,780.31 
2,783.45 
2,786.59 

2.789.73 

2.792.88 
2,796.02 
2,799.16 
2,802.30 
2,805.44 

2.808.58 

2.811.73 
2,814.87 
2,818.01 
2,821.15 
2,824.29 
2,827.43 

2.830.58 
2,833.72 
2,836.86 
2,840.00 
2,843.14 
2,846.28 

2.849.42 
2,852.57 
2,855.71 
2,858.85 
2,861.99 
2,865.13 

2.868.27 

2.871.42 
2,874.56 
2,877.70 
2,880.84 
2,883.98 
2.887.12 

2.890.27 
2,893.41 
2,896.55 
2,899.69 
2,902.83 
2,905.97 

2.909.11 
2,912.26 
2,915.40 
2,918.54 
2,921.68 
2,924.82 
2,927.96 

2.931.11 
2,934.25 
2,937.39 
2,940.53 
2,943.67 

601.320.47 

602.695.70 

604.072.50 

605.450.88 

606.830.82 
608,212.34 

609.595.42 

610.980.08 
612,366.31 
613,754.11 

615.143.48 

616.534.42 
617,926.93 

619.321.01 

620.716.66 

622.113.89 

623.512.68 

624.913.04 

626.314.98 

627.718.49 

629.123.56 

630.530.21 

631.938.43 

633.348.22 

634.759.58 

636.172.51 

637.587.01 

639.003.09 

640.420.73 
641,839.95 

643.260.73 

644.683.09 

646.107.01 

647.532.51 

648.959.58 

650.388.22 

651.818.43 
653,250.21 

654.683.56 
656,118.48 

657.554.98 

658.993.04 

660.432.68 
661,873.88 

663.316.66 

664.761.01 
666,206.92 

667.654.41 
669,103.47 

670.554.10 
672,006.30 
673,460.08 

674.915.42 
676,372.33 

677.830.82 
679,290.87 

680.752.50 

682.215.69 
683,680.46 
685,146.80 

686.614.71 
688,084.19 
689,555.24 

560 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 


No. 

Square. 

Cube. 

Sq.  Root. 

Cu.  Root. 

Reciprocal. 

Circum. 

Area. 

938 

939 

940 

941 

942 

943 

944 

945 

946 

947 

948 

949 

950 

951 

952 

953 

954 

955 

956 

957 

958 

959 

960 

961 

962 

963 

964 

965 

966 

967 

968 

969 

970 

971 

972 

973 

974 

975 

976 

977 

978 

979 

980 

981 

982 

983 

984 

985 

986 

987 

988 

989 

990 

991 

992 

993 

994 

995 

996 

997 

998 

999 
1000 

879,844 

881,721 

883.600 
885,481 
887,364 
889,249 
891,136 

893.025 
894,916 
896;808 
898,704 

900.601 
902,500 
904,401 
906,304 
908,209 
910,116 

912.025 
913,936 
915,849 
917,764 
919,681 
921,600 
923,521 
925,444 
927,369 
929,296 

931.225 
933,156 
935,089 

937.024 
938,961 
940,900 
942,841 
944,784 
946,729 
948,676 
950,625 
952,576 
954,529 
956,484 
958,441 
960,400 
962,361 
964,324 
966,289 
968,256 

970.225 
972,196 
974,169 
976,144 
978,121 
980,100 
982,081 
984,064 
986,049 
988,036 

990.025 
992,016 
994,009 
996,004 
998,001 

1,000,000 

825,293,672 

827,936,019 

830.584.000 
833,237,621 
835,896,888 
838,561,807 
841,232,384 

843.908.625 
846,590,536 
849,278,123 
851,971,392 
854,670,349 

857.375.000 

860.085.351 
862,801,408 
865,523,177 
868,250,664 

870.983.875 
873,722,816 
876,467,493 
879,217,912 
881,974,079 

884.736.000 
887,503,681 
890,277,128 
893,056,347 
895,841,344 
898,632,125 
901,428,696 
904,231,063 
907,039,232 
909,853,209 

912.673.000 
915,498,611 
918,330,048 
921,167,317 
924,010,424 
926,859,375 
929,714,176 
932,574,833 

935.441.352 
938,313,739 

941.192.000 
944,076,141 
946,966,168 
949,862,087 
952,763,904 

955.671.625 
958,585,256 
961,504,803 
964,430,272 
967,361,669 

970.299.000 
973,242,271 
976,191,488 
979,146,657 
982,107,784 

985.074.875 
988,047,936 
991,026,973 
994,011,992 
997,002,999 

1,000,000,000 

30.6268 

30.6431 

30.6594 

30.6757 

30.6920 

30.7083 

30.7246 

30.7409 

30.7571 

30.7734 

30.7896 

30.8058 

30.8221 

30.8383 

30.8545 

30.8707 

30.8869 

30.9031 

30.9192 

30.9354 

30.9516 

30.9677 

30.9839 

31.0000 

31.0161 

31.0322 

31.0483 

31.0644 

31.0805 

31.0966 

31.1127 

31.1288 

31.1448 

31.1609 

31.1769 

31.1929 

31.2090 

31.2250 

31.2410 

31.2570 

31.2730 

31.2890 

31.3050 

31.3209 

31.3369 

31.3528 

31.3688 

31.3847 

31.4006 

31.4166 

31.4325 

31.4484 

31.4643 

31.4802 

31.4960 

31.5119 

31.5278 

31.5436 

31.5595 

31.5753 

31.5911 

31.6070 

31.6228 

9.7889 

9.7924 

9.7959 

9.7993 

9.8028 

9.8063 

9.8097 

9.8132 

9.8167 

9.8201 

9.8236 

9.8270 

9.8305 

9.8339 

9.8374 

9.8408 

9.8443 

9.8477 

9.8511 

9.8546 

9.8580 

9.8614 

9.8648 

9.8683 

9.8717 

9.8751 

9.8785 

9.8819 

9.8854 

9.8888 

9.8922 

9.8956 

9.8990 

9.9024 

9.9058 

9.9092 

9.9126 

9.9160 

9.9194 

9.9228 

9.9261 

9.9295 

9.9329 

9.9363 

9.9396 

9.9430 

9.9464 

9.9497 

9.9531 

9.9565 

9.9598 

9.9632 

9.9666 

9.9699 

9.9733 

9.9766 

9.9800 

9.9833 

9.9866 

9.9900 

9.9933 

9.996r 

10.0000 

.001066098 

.001064963 

.001063830 

.001062699 

.001061571 

.001060445 

.001059322 

.001058201 

.001057082 

.001055966 

.001054852 

.001053741 

.001052632 

.001051525 

.001050420 

.001049318 

.001048218 

.001047120 

.001046025 

.001044932 

.001043841 

.001042753 

.001041667 

.001040583 

.001039501 

.001038422 

.001037344 

.001036269 

.001035197 

.001034126 

.001033058 

.001031992 

.001030928 

.001029866 

.001028807 

.001027749 

.001026694 

.001025641 

.001024590 

.001023541 

.001022495 

.001021450 

.001020408 

.001019168 

.001018330 

.001017294 

.001016260 

.001015228 

.001014199 

.001013171 

.001012146 

.001011122 

.001010101 

.001009082 

.001008065 

.001007049 

.001006036 

.001005025 

.001004016 

.001003009 

.001002004 

.001001001 

.001000000 

2.946.81 
2,949.96 
2,953.10 
2,956.24 
2,959.38 
2,962.52 
2,965.66 

2.968.81 
2,971.95 
2,975.09 
2,978.23 
2,981.37 
2,984.51 

2.987.65 
2,990.80 
2,993.94 
2,997.08 
3,000.22 
3,003.36 

3.006.50 

3.009.65 
3,012.79 
3,015.93 
3,019.07 
3,022.21 
3,025.35 

3.028.50 
3,031.64 
3,034.78 
3,037.92 
3,041.06 
3,044.20 

3.047.34 
3,050.49 
3,053.63 
3,056.77 
3,059.91 
3,063.05 

3.066.19 

3.069.34 
3,072.48 
3,075.62 
3,078.76 
3,081.90 

3.085.04 

3.088.19 
3,091.33 
3,094.47 
3,097.61 
3,100.75 
3,103.89 

3.107.04 
3,110.18 
3,113.32 
3,116.46 
3,119.60 
3,122.74 
3,125.88 
3,129.03 
3,132.17 
3,135.31 
3,138.45 
3,141.59 

691,027.86 

692.502.05 

693.977.82 

695.455.15 

696.934.06 

698.414.53 

699.896.58 
701,380.19 

702.865.38 

704.352.14 

705.840.47 

707.330.37 

708.821.84 
710,314.88 
711,809.50 
713,305.68 

714.803.43 

716.302.76 

717.803.66 

719.306.12 

720.810.16 

722.315.77 

723.822.95 

725.331.70 
726,842.02 
728,353.91 

729.867.37 
731,382.40 
732,899.01 
734,417.18 

735.936.93 
737,458.24 

738.981.13 

740.505.59 
742,031.62 
743,559.22 

745.088.39 

746.619.13 

748.151.44 
749,685.32 

751.220.78 
752,757.80 

754.296.40 
755,836.56 
757,378.30 

758.921.61 

760.466.48 

762.012.93 

763.560.95 

765.110.54 

766.661.70 

768.214.44 
769,768.74 

771.324.61 

772.882.06 

774.441.07 

776.001.66 

777.563.82 

779.127.54 

780.692.84 

782.259.71 

783.828.15 

785.398.16 

CIRCUMFERENCES  AND  AREAS  OF  CIRCLES. 


561 


CIRCUMFERENCES  AND  AREAS  OF  CIRCLES 
FROM  1-64  TO  100. 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Bi 

.0491 

.0002 

6 

18.8496 

28.2744 

13f 

41.2335 

135.297 

35 

.0982 

.0008 

6f 

19.2423 

29.4648 

13i 

41.6262 

137.887 

TB 

.1963 

.0031 

6f 

19.CC30 

30.6797 

13| 

42.0189 

140.501 

h 

.3927 

.0123 

6f 

20.02V7 

31.9191 

13i 

42.4116 

143.139 

.5890 

.0276 

6i 

20.4204 

33.1831 

13t 

42.8043 

145.802 

.7854 

.0491 

6f 

20.8131 

34.4717 

13f 

43.1970 

148.490 

.9817 

.0767 

6f 

21.2058 

35.7848 

13f 

43.5897 

151.202 

1.1781 

.1104 

6f 

21.5985 

37.1224 

14 

43.9824 

153.938 

TB 

1.3744 

.1503 

7 

21.9912 

38.4846 

14f 

44.3751 

156.700 

h 

1.5708 

.1963 

7f 

22.3839 

39.8713 

14i 

44.7678 

159.485 

1.7671 

.2485 

Vi 

22.7766 

41.2826 

14f 

45.1605 

162.296 

1 

1.9635 

.3068 

Vf 

23.1693 

42.7184 

14i 

45.5532 

165.130 

H 

2.1598 

.3712 

Vf 

23.5620 

44.1787 

14f 

45.9459 

167.990 

i 

2.3562 

.4418 

Vf 

23.9547 

45.6636 

14f 

46.3386 

170.874 

H 

2.5525 

.5185 

Vf 

24.3474 

47.1731 

14f 

46.7313 

173.782 

i 

2.7489 

.6013 

Vf 

24.7401 

48.7071 

15 

47.1240 

176.715 

11 

2.9452 

.6903 

8 

25.1328 

50.2656 

15i 

47.5167 

179.673 

1 

3.1416 

.7854 

8f 

25.5255 

51.8487 

15i 

47.9094 

182.655 

n 

3.5343 

.9940 

8i 

25.9182 

53.4563 

15t 

48.3021 

185.661 

li 

3.9270 

1.2272 

8f 

26.3109 

55.0884 

15f 

48.6948 

188.692 

If 

4.3197 

1.4849 

8i 

26.7036 

56.7451 

151 

49.0875 

191.748 

H 

4.7124 

1.7671 

8f 

27.0963 

58.4264 

15f 

49.4802 

194.828 

If 

5.1051 

2.0739 

8f 

27.4890 

60.1322 

15f 

49.8729 

197.933 

If 

5.4978 

2.4053 

8f 

27.8817 

61.8625 

16 

50.2656 

201.062 

If 

5.8905 

2.7612 

9 

28.2744 

63.6174 

16i 

50.6583 

204.216 

2 

6.2832 

3.1416 

9f 

28.6671 

65.3968 

16i 

51.0510 

207.395 

2f 

6.6759 

3.5466 

9i 

29.0598 

67.2008 

161 

51.4437 

210.598 

2i 

7.0686 

3.9761 

9f 

29.4525 

69.0293 

16i 

51.8364 

213.825 

2f 

7.4613 

4.4301 

9i 

29.8452 

70.8823 

16f 

52.2291 

217.077 

21 

7.8540 

4.9087 

9f 

30.2379 

72.7599 

16f 

52.6218 

220.354 

2f 

8.2467 

5.4119 

9f 

30.6306 

74.6621 

16f 

53.0145 

223.655 

2f 

8.6394 

5.9396 

9f 

31.0233 

76.589 

17 

53.4072 

226.981 

2f 

9.0321 

6.4918 

10 

31.4160 

78.540 

IVf 

53.7999 

230.331 

3 

9.4248 

7.0686 

lOf 

31.8087 

80.516 

17i 

54.1926 

233.706 

3f 

9.8175 

7.6699 

lOi 

32.2014 

82.516 

17f 

54.5853 

237.105 

3i 

10.2102 

8.2958 

lOf 

32.5941 

84.541 

17i 

54.9780 

240.529 

3f 

10.6029 

8.9462 

lOi 

32.9868 

86.590 

171 

55.3707 

243.977 

31 

10.9956 

9.6211 

lOf 

33.3795 

88.664 

17f 

65.7634 

247.450 

3f 

11.3883 

10.3206 

lOf 

33.7722 

90.763 

17| 

56.1561 

250.948 

3f 

11.7810 

11.0447 

lOf 

34.1649 

92.886 

18 

56.5488 

254.470 

3f 

12.1737 

11.7933 

11 

34.5576 

95.033 

18f 

56.9415 

258.016 

4 

12.5664 

12.5664 

Ilf 

34.9503 

97.205 

18i 

57.3342 

261.587 

41 

12.9591 

13.3641 

Ilf 

35.3430 

99.402 

18f 

57.7269 

265.183 

41 

13.3518 

14.1863 

Ilf 

35.7357 

101.623 

18i 

58.1196 

268.803 

4f 

13.7445 

15.0330 

Ilf 

36.1284 

103.869 

181 

58.5123 

272.448 

41 

14.1372 

15.9043 

Ilf 

36.5211 

106.139 

18f 

58.9050 

276.117 

4f 

14.5299 

16.8002 

Ilf 

36.9138 

108.434 

18f 

59.2977 

-279.811 

4f 

14.9226 

17.7206 

Ilf 

37.3065 

110.754 

19 

59.6904 

283.529 

4f 

15.3153 

18.6555 

12 

37.6992 

113.098 

19f 

60.0831 

287.272 

5 

15.7080 

19.6350 

12f 

38.0919 

115.466 

19i 

60.4758 

291.040 

5f 

16.1007 

20.6290 

12i 

38.4846 

117.859 

19| 

60.8685 

294.832 

51 

16.4934 

21.6476 

12f 

38.8773 

120.277 

19i 

61.2612 

298.648 

5f 

16.8861 

22.6907 

12i 

39.2700 

122.719 

19f 

61.6539 

302.489 

51 

17.2788 

23.7583 

12f 

39.6627 

125.185 

19f 

62.0466 

306.355 

5f 

17.6715 

24.8505 

12f 

40.0554 

127.677 

19f 

62.4393 

310.245 

5f 

18.0642 

25.9673 

12f 

40.4481 

130.192 

20 

62.8320 

314.160 

5f 

18.4569 

27.1086 

13 

40.8408 

132.733 

20i 

63.2247 

318.099 

562 


CIRCUMFERENCES  AND  AREAS  OF  CIRCLES. 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

20i 

63.6174 

322.063 

28i 

88.3575 

621.264 

36 

113.098 

1,017.878 

20f 

64.0101 

326.051 

28i 

88.7502 

626.798 

36} 

113.490 

1,024.960 

20i 

64.4028 

330.064 

28f 

39.1429 

632.357 

36} 

113.883 

1,032.065 

201 

64.7955 

334.102 

28i 

89.5356 

637.941 

36} 

114.276 

1,039.195 

20^ 

65.1882 

338.164 

281 

89.9283 

643.549 

36} 

114.668 

1,046.349 

20| 

65.5809 

342.250 

28f 

90.3210 

649.182 

36} 

115.061 

1,053.528 

21 

65.9736 

346.361 

28^ 

90.7137 

654.840 

36} 

115.454 

1,060.732 

2ii 

66.3663 

350.497 

29 

91.1064 

660.521 

36} 

115.846 

1,067.960 

21i 

66.7590 

354.657 

29} 

91,4991 

666.228 

37 

116.239 

1,075.213 

21f 

67.1517 

358.842 

29} 

91,8918 

671.959 

37} 

116.632 

1,082.490 

21i 

67.5444 

363.051 

291 

92.2845 

677.714 

37} 

117.025 

1,089.792 

2H 

67.9371 

367.285 

29} 

92.6772 

683.494 

37} 

117.417 

1,097.118 

21| 

68.3298 

371.543 

291 

93.0699 

689.299 

37} 

117.810 

1,104.469 

21i 

68.7225 

375.826 

29} 

93.4626 

695.128 

37} 

118.203 

1,111.844 

22 

69.1152 

380.134 

29} 

93.8553 

700.982 

37} 

118.595 

1,119.244 

22f 

69.5079 

384.466 

30 

94.2480 

706.860 

37} 

118.988 

1,126.669 

22i 

69.9006 

388.822 

30} 

94.6407 

712.763 

38 

119.381 

1,134.118 

22i 

70.2933 

393.203 

30} 

95.0334 

718.690 

38} 

119.773 

1,141.591 

22i 

70.6860 

397.609 

30| 

95.4261 

724.642 

38} 

120.166 

1,149.089 

22f 

71.0787 

402.038 

30} 

95.8188 

730.618 

38} 

120.559 

1,156.612 

22f 

71.4714 

406.494 

301 

96.2115 

736.619 

38} 

120.952 

1,164.159 

22^ 

71.8641 

410.973 

30} 

96.6042 

742.645 

38} 

121.344 

1,171.731 

25 

72.2568 

415.477 

30} 

96.9969 

748.695 

38} 

121.737 

1,179.327 

23i 

72.6495 

420.004 

31 

97.3896 

754.769 

38} 

122.130 

1,186.948 

23i 

73.0422 

424.558 

31} 

97.7823 

760.869 

39 

122.522 

1,194.593 

23f 

73.4349 

429.135 

31} 

98.1750 

766.992 

39} 

122.915 

1,202.263 

23i 

73.8276 

433.737 

31f 

98.5677 

773.140 

39} 

123.308 

1,209.958 

23f 

74.2203 

438.364 

31} 

98.9604 

779.313 

39} 

123.700 

1,217.677 

23f 

74.6130 

443.015 

31} 

99.3531 

785.510 

39} 

124.093 

1,225.420 

231 

75.0057 

447.690  ' 

31} 

99.7458 

791.732 

39} 

124.486 

1,233.188 

24 

75.3984 

452.390 

31} 

100.1385 

797.979 

39} 

124.879 

1,240.981 

24} 

75.7911 

457.115 

32 

100.5312 

804.250 

39} 

125.271 

1,248.798 

24i 

76.1838 

461.864 

32} 

100.9239 

810.545 

40 

125.664 

1,256.640 

241 

76.5765 

466.638 

32} 

101.3166 

816.865 

40} 

126.057 

1,264.510 

241 

76.9692 

471.436 

32} 

101.7093 

823.210 

40} 

126.449 

1,272.400 

241 

77.3619 

476.259 

32} 

102.1020 

829.579 

40} 

126.842 

1,280.310 

241 

77.7546 

481.107 

32} 

102.4947 

835.972 

40} 

127.235 

1,288.250 

241 

78.1473 

485.979 

32} 

102.8874 

842.391 

40} 

127.627 

1,296.220 

26 

78.5400 

490.875 

32} 

103.280 

848.833 

40} 

128.020 

1,304.210 

251 

78.9327 

495.796 

33 

103.673 

855.301 

40} 

128.413 

1,312.220 

251 

79.3254 

500.742 

33} 

104.065 

861.792 

41 

128.806 

1,320.260 

251 

79.7181 

505.712 

33} 

104.458 

868.309 

41} 

129.198 

1,328.320 

251 

80.1108 

510.706 

33} 

104.851 

874.850 

41} 

129.591 

1,336.410 

251 

80.5035 

515.726 

33} 

105.244 

881.415 

41} 

129.984 

1,344.520 

251 

80.8962 

520.769 

33} 

105.636 

888.005 

41} 

130.376 

1,352.660 

251 

81.2889 

525.838 

33} 

106.029 

894.620 

41} 

130.769 

1,360.820 

26 

81.6816 

530.930 

33} 

106.422 

901.259 

41} 

131.162 

1,369.000 

261 

82.0743 

536.048 

34 

106.814 

907.922 

41} 

131.554 

1,377.210 

.261 

82.4670 

541.190 

34} 

107.207 

914.611 

42 

131.947 

1,385.450 

261 

82.8597 

546.356 

34} 

107.600 

921.323 

42} 

132.340 

1,393.700 

261 

83.2524 

551.547 

34} 

107.992 

928.061 

42} 

132.733 

1,401.990 

261 

83.6451 

556.763 

34} 

108.385 

934.822 

42} 

133.125 

1,410.300 

261 

84.0378 

562.003 

34} 

108.778 

941.609 

42} 

133.518 

1,418.630 

261 

84.4305 

567.267 

34} 

109.171 

948.420 

42} 

133.911 

1,426.990 

27 

84.8232 

572.557 

34} 

109.563 

955.255 

42} 

134.303 

1,435.370 

271 

85.2159 

577.870 

35 

109.956 

962.115 

42} 

134.696 

1,443.770 

271 

85.6086 

583.209 

35} 

110.349 

969.000 

43 

135.089 

1,452.200 

271 

86.0013 

588.571 

35} 

110.741 

975.909 

43} 

135.481 

1,460.660 

271 

86.3940 

593.959 

35} 

111.134 

982.842 

43} 

135.874 

1,469.140 

271 

86.7867 

599.371 

35} 

111.527 

989.800 

43} 

136.267 

1,477.640 

271 

87.1794 

604.807 

35} 

111.919 

996.783 

43} 

136.660 

1,486.170 

271 

87.5721 

610.268 

35} 

112.312 

1,003.790 

43} 

137.052 

1,494.730 

28 

87.9648 

615.754 

35} 

112.705 

1,010.822 

43} 

137.445 

1,503.300 

CIRCVMFERENCES  AND  AREAS  OE  CIRCLES. 


563 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

43| 

137.838 

1,511.910 

51} 

162.578 

2,103.35 

59} 

187.318 

2,792.21 

44 

138.230 

1,520.530 

51} 

162.970 

2,113.52 

59} 

187.711 

2,803.93 

441- 

138.623 

1,529.190 

52 

163.363 

2,123.72 

59} 

188.103 

2,815.67 

44i 

139.016 

1,537.860 

52} 

163.756 

2,133.94 

60 

188.496 

2,827.44 

44f 

139.408 

1,546.56 

52} 

164.149 

2,144.19 

60} 

188.889 

2,839.23 

44i 

139.801 

1,555.29 

52} 

164.541 

2,154.46 

60} 

189.281 

2,851.05 

44f 

140.194 

1,564.04 

52} 

164.934 

2,164.76 

60} 

189.674 

2,862.89 

44^ 

140.587 

1,572.81 

52} 

165.327 

2,175.08 

60} 

190.067 

2,874.76 

44i 

140.979 

1,581.61 

52} 

165.719 

2,185.42 

60} 

190.459 

2,886.65 

45 

141.372 

1,590.43 

52} 

166.112 

2,195.79 

60} 

190.852 

2,898.57 

45} 

141.765 

1,599.28 

53 

166.505 

2,206.19 

60} 

191.245 

2,910.51 

45} 

142.157 

1,608.16 

53} 

166.897 

2,216.61 

61 

191.638 

'2,922.47 

451 

142.550 

1,617.05 

53} 

167.290 

2,227.05 

61} 

192.030 

2,934.46 

45} 

142.943 

1,625.97 

53} 

167.683 

2,237.52 

61} 

192.423 

2,946.48 

45| 

143.335 

1,634.92 

53} 

168.076 

2,248.01 

61} 

192.816 

2,958.52 

45} 

143.728 

1,643.89 

53} 

168.468 

2,258.53 

61} 

193.208 

2,970.58 

45} 

144.121 

1,652.89 

53} 

168.861 

2,269.07 

61} 

193.601 

2,982.67 

46 

144.514 

1,661.91 

53} 

169.254 

2,279.64 

61} 

193.994 

2,994.78 

46} 

144.906 

1,670.95 

54 

169.646 

2,290.23 

61} 

194.386 

3,006.92 

46} 

145.299 

1,680.02 

54} 

170.039 

2,300.84 

62 

194.779 

3,019.08 

46} 

145.692 

1,689.11 

54} 

170.432 

2,311.48 

62} 

195.172 

3,031.26 

46} 

146.084 

1,698.23 

54} 

170.824 

2,322.15 

62} 

195.565 

3,043.47 

46} 

146.477 

1,707.37 

54} 

171.217 

2,332.83 

62} 

195.957 

3,055.71 

46} 

146.870 

1,716.54 

54} 

171.610 

2,343.55 

62} 

196.350 

3,067.97 

46} 

147.262 

1,725.73 

54} 

172.003 

2,354.29 

62} 

196.743 

3,080.25 

47 

147.655 

1,734.95 

54} 

172.395 

2,365.05 

62} 

197.135 

3,092.56 

47} 

148.048 

1,744.19 

55 

172.788 

2,375.83 

62} 

197.528 

3,104.89 

47} 

148.441 

1,753.45 

55} 

173.181 

2,386.65 

63 

197.921 

3,117.25 

47} 

148.833 

1,762.74 

55} 

173.573 

2,397.48 

63} 

198.313 

3,129.64 

47} 

149.226 

1,772.06 

55} 

173.966 

2,408.34 

63} 

198.706 

3,142.04 

47} 

149.619 

1,781.40 

55} 

174.359 

2,419.23 

63} 

199.099 

3,154.47 

47} 

150.011 

1,790.76 

55} 

174.751 

2,430.14 

63} 

199.492 

3,166.93 

47} 

150.404 

1,800.15 

55} 

175.144 

2,441.07 

631 

199.884 

3,179.41 

48 

150.797 

1,809.56 

55} 

175.537 

2,452.03 

63} 

200.277 

3,191.91 

48} 

151.189 

1,819.00 

56 

175.930 

2,463.01 

63} 

200.670 

3,204.44 

48} 

151.582 

1,828.46 

56} 

176.322 

2,474.02 

64 

201.062 

3,217.00 

48} 

151.975 

1,837.95 

56} 

176.715 

2,485.05 

64} 

201.455 

3,229.58 

48} 

152.368 

1,847.46 

56} 

177.108 

2,496.11 

64} 

201.848 

3,242.18 

48} 

152.760 

1,856.99 

56} 

177.500 

2,507.19 

64} 

202.240 

3,254.81 

48} 

153.153 

1,866.55 

56} 

177.893 

2,518.30 

64} 

202.633 

3,267.46 

48} 

153.546 

1,876.14 

56} 

178.286 

2,529.43 

64} 

203.026 

3,280.14 

49 

153.938 

1,885.75 

56} 

178.678 

2,540.58 

64} 

203.419 

3,292.84 

49} 

154.331 

1,895.38 

57 

179.071 

2,551.76 

64} 

203.811 

3,305.56 

49} 

154.724 

1,905.04 

57} 

179.464 

2,562.97 

65 

204.204 

3,318.31 

49} 

155.116 

1,914.72 

57} 

179.857 

2,574.20 

65} 

204.597 

3,331.09 

49} 

155.509 

1,924.43 

57} 

180.249 

2,585.45 

65} 

204.989 

3,343.89 

49} 

155.902 

1,934.16 

57} 

180.642 

2,596.73 

65} 

205.382 

3,356.71 

49} 

156.295 

1,943.91 

57} 

181.035 

2,608.03 

65} 

205.775 

3,369.56 

49} 

156.687 

1,953.69 

57} 

181.427 

2,619.36 

65} 

206.167 

3,382.44 

50 

157.080 

1,963.50 

57} 

181.820 

2,630.71 

65} 

206.560 

3,395.33 

50} 

157.473 

1,973.33 

58 

182.213 

2,642.09 

65} 

206  953 

3,408.26 

50} 

157.865 

1,983.18 

58} 

182.605 

2,653.49 

66 

207.346 

3,421.20 

50} 

158.258 

1,993.06 

58} 

182.998 

2,664.91 

66} 

207.738 

3,434.17 

50} 

158.651 

2,002.97 

58} 

183.391 

2,676.36 

66} 

208.131 

3,447.17 

50} 

159.043 

2,012.89 

58} 

183.784 

2,687.84 

66} 

208.524 

3,460.19 

50} 

159.436 

2,022.85 

58} 

184.176 

2,699.33 

66} 

208.916 

3,473.24 

50} 

159.829 

2,032.82 

58} 

184.569 

2,710.86 

66} 

209.309 

3,486.30 

51 

160.222 

2,042.83 

58} 

184.962 

2,722.41 

66} 

209.702 

3,499.40 

51} 

160.614 

2,052.85 

59 

185.354 

2,733.98 

66} 

210.094 

3,512.52 

51} 

161.007 

2,062.90 

59} 

185.747 

2,745.57 

67 

210.487 

3,525.66 

51} 

161.400 

2,072.98 

59} 

186.140 

2,757.20 

67} 

210.880 

3,538.83 

51} 

161.792 

2,083.08 

59} 

186.532 

2,768.84 

67} 

211.273 

3,552.02 

51} 

162.185 

2,093.20 

59} 

186.925 

2,780.51 

67} 

211.665 

3,565.24 

564 


CIRCUMFERENCES  AND  AREAS  OF  CIRCLES. 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

67i 

212.058 

3,578.48 

75} 

236.798 

4,462.16 

83} 

261.538 

5,443.26 

67| 

212.451 

3,591.74 

75} 

237.191 

4,476.98 

83} 

261.931 

5,459.62 

G7f 

212.843 

3,605.04 

75} 

237.583 

4,491.81 

83} 

262.324 

5,476.01 

67  j 

213.236 

3,618.35 

75} 

237.976 

4,506.67 

83} 

262.716 

5,492.41 

68 

213.629 

3,631.69 

75} 

238.369 

4,521.56 

83} 

263.109 

5,508.84 

68i 

214.021 

3,645.05 

76 

238.762 

4,536.47 

83} 

263.502 

5,525.30 

68i 

214.414 

3,658.44 

76} 

239.154 

4,551.41 

84 

263,894 

5,541.78 

68i 

214.807 

3,671.86 

76} 

239.547 

4,566.36 

84} 

264.287 

5,558.29 

68i 

215.200 

3,685.29 

76} 

239.940 

4,581.35 

84} 

264.680 

5,574.82 

68f 

215.592 

3,698.76 

76} 

240.332 

4,596.36 

84} 

265.072 

5,591.37 

68^ 

215.985 

3,712.24 

76} 

240.725 

4,611.39 

84} 

265.465 

5,607.95 

681- 

216.378 

3,725.75 

76} 

241.118 

4,626.45 

84} 

265.858 

5,624.56 

69 

216.770 

3,739.29 

76} 

241.510 

4,641.53 

84} 

266.251 

5,641.18 

69} 

217.163 

3,752.85 

77 

241.903 

4,656.64 

84} 

266.643 

5,657.84 

69i 

217.556 

3,766.43 

m 

242.296 

4,671.77 

85 

267.036 

5,674.51 

691 

217.948 

3,780.04 

77} 

242.689 

4,686.92 

85} 

267.429 

5,691.22 

69i 

218.341 

3,793.68 

77f 

243.081 

4,702.10 

85} 

267.821 

5,707.94 

69i 

218.734 

3,807.34 

77} 

243.474 

4,717.31 

85} 

268.214 

5,724.69 

69J 

219.127 

3,821.02 

77} 

243.867 

4,732.54 

85} 

268.607 

5,741.47 

69f 

219.519 

3,834.73 

111 

244.259 

4,747.79 

85} 

268.999 

5,758.27 

70 

219.912 

3,848.46 

77} 

244.652 

4,763.07 

85} 

269.392 

5,775.10 

70i 

220.305 

3,862.22 

78 

245.045 

4,778.37 

85} 

269.785 

5,791.94 

70^ 

220.697 

3,876.00 

78} 

245.437 

4,793.70 

86 

270.178 

5,808.82 

70| 

221.090 

3,889.80 

78} 

245.830 

4,809.05 

86} 

270.570 

5,825.72 

70i 

221.483 

3,903.63 

78} 

246.223 

4,824.43 

86} 

270.963 

5,842.64 

70f 

221.875 

3,917.49 

78} 

246.616 

4,839.83 

86} 

271.356 

5,859.59 

70^ 

222.268 

3,931.37 

78} 

247.008 

4,855.26 

86} 

271.748 

5,876.56 

70^ 

222.661 

3,945.27 

78} 

247.401 

4,870.71 

86} 

272.141 

5,893.55 

71 

223.054 

3,959.20 

78} 

247.794 

4,886.18 

86} 

272.534 

5,910.58 

223.446 

3,973.15 

79 

248.186 

4,901.68 

86} 

272.926 

5,927.62 

71i 

223.839 

3,987.13 

79} 

248.579 

4,917.21 

87 

273.319 

5,944.69 

71f 

224.232 

4,001.13 

79} 

248.972 

4,932.75 

87} 

273.712 

5,961.79 

71i 

224.624 

4,015.16 

79} 

249.364 

4,948.33 

87} 

274.105 

5,978.91 

71| 

225.017 

4,029.21 

79} 

249.757 

4,963.92 

87} 

274.497 

.5,996.05 

7U 

225.410 

4,043.29 

79} 

250.150 

4,979.55 

87} 

274.890 

6,013.22 

7H 

225.802 

4,057.39 

79} 

250.543 

4,995.19 

87} 

275.283 

6,030.41 

72 

226.195 

4,071.51 

79} 

250.935 

5,010.86 

87} 

275.675 

6,047.63 

72i 

226.588 

4,085.66 

80 

251.328 

5,026.56 

87} 

276.068 

6,064.87 

72i 

226.981 

4,099.84 

80} 

251.721 

5,042.28 

88 

276.461 

6,082.14 

72f 

227.373 

4,114.04 

80} 

252.113 

5,058.03 

88} 

276.853 

6,099.43 

72i 

227.766 

4,128.26 

80} 

252.506 

5,073.79 

88} 

277.246 

6,116.74 

72f 

228.159 

4,142.51 

80} 

252.899 

5,089.59 

88} 

277.629 

6,134.08 

72f 

228.551 

4,156.78 

80} 

253.291 

5,105.41 

88} 

278.032 

6,151.45 

72i 

228.944 

4,171.08 

80} 

253.684 

5,121.25 

88} 

278.424 

6,168.84 

73 

229.337 

4,185.40 

80} 

254.077 

5,137.12 

00 

00 

278.817 

6,186.25 

73} 

229.729 

4,199.74 

81 

254.470 

5,153.01 

88}  ■ 

279.210 

6,203.69 

73} 

230.122 

4,214.11 

81} 

254.862 

5,168.93 

89 

279.602 

6,221.15 

73| 

230.515 

4,228.51 

81} 

255.255 

5,184.87 

89} 

279.995 

6,238.64 

73} 

230.908 

4,242.93 

81} 

255.648 

5,200.83 

89} 

280.388 

6,256.15 

731 

231.300 

4,257.37 

81} 

256.040 

5,216.82 

89} 

280.780 

6,273.69 

73^ 

231.693 

4,271.84 

81} 

256.433 

5,232.84 

89} 

281.173 

6,291.25 

73} 

232.086 

4,286.33 

81} 

256.826 

5,248.88 

89} 

281.566 

6,308.84 

74 

232.478 

4,300.85 

81} 

257.218 

5,264.94 

89} 

281.959 

6,326.45 

74} 

232.871 

4,315.39 

82 

257.611 

5,281.03 

89} 

282.351 

6,344.08 

74} 

233.264 

4,329.96 

82} 

258.004 

5,297.14 

90 

282.744 

6,361.74 

74} 

233.656 

4,344.55 

82} 

258.397 

5,313.28 

90} 

283.137 

6,379.42 

74} 

234.049 

4,359.17 

82} 

258.789 

5,329.44 

90} 

283.529 

6,397.13 

74} 

234.442 

4,373.81 

82} 

259.182 

5,345.63 

90} 

283.922 

6,414.86 

74} 

234.835 

4,388.47 

82} 

259.575 

5,361.84 

90} 

284.315 

6,432.62 

74} 

235.227 

4,403.16 

82} 

259.967 

5,378.08 

90} 

284.707 

6,450.40 

75 

235.620 

4,417.87 

82} 

260.360 

5,394.34 

90} 

285.100 

6,468.21 

75} 

236.013 

4,432.61 

83 

250.753 

5,410.62 

90} 

285.493 

6,486.04 

75} 

236.405 

4,447.38 

83} 

261.145 

5,426.93 

91 

285.886 

6,503.90 

CIRCUMFERENCES  AND  AREAS  OF  CIRCLES. 


565 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

91i 

286.278 

6,521.78 

94i 

295.703 

6,958.26 

97i 

305.128 

7,408.89 

91i 

286.671 

6,539.68 

94i 

296.096 

6,976.76 

m 

305.521 

7,427.97 

91| 

287.064 

6,557.61 

94t 

296.488 

6,995.28 

97f 

305.913 

7,447.08 

91i 

287.456 

6,575.56 

94i 

296.881 

7,013.82 

97i 

306.306 

7,466.21 

91| 

287.849 

6,593.54 

94f 

297.274 

7,032.39 

971 

306.699 

7,485.37 

m 

288.242 

6,611.55 

94^ 

297.667 

7,050.98 

m 

307.091 

7,504.55 

9H 

288.634 

6,629.57 

94^ 

298.059 

7,069.59 

97i 

307.484 

7,523.75 

92 

289.027 

6,647.63 

95 

298.452 

7,088.24 

98 

307.877 

7,542.98 

92i 

289.420 

6,665.70 

95^ 

298.845 

7,106.90 

98i 

308.270 

7,562.24 

92i 

289.813 

6,683.80 

95i 

299.237 

7,125.59 

98i 

308.662 

7,581.52 

92| 

290.205 

6,701.93 

95| 

299.630 

7,144.31 

98f 

309.055 

7,600.82 

92i 

290.598 

6,720.08 

95i 

300.023 

7,163.04 

m 

309.448 

7,620.15 

92| 

290.991 

6,738.25 

95t 

300.415 

7,181.81 

981 

309.840 

7,639.50 

92^ 

291.383 

6,756.45 

95f 

300.808 

7,200.60 

98f 

310.233 

7,658.88 

92i 

291.776 

6,774.68 

95i 

301.201 

7,219.41 

98| 

310.626 

7,678.28 

93 

292.169 

6,792.92 

96 

301.594 

7,238.25 

99 

311.018 

7,697.71 

93i 

292.562 

6,811.20 

961- 

301.986 

7,257.11 

99i 

311.411 

7,717.16 

93i 

292.954 

6,829.49 

96i 

302.379 

7,275.99 

99i 

311.804 

7,736.63 

93f 

293.347 

6,847.82 

96f 

302.772 

7,294.91 

99i 

312.196 

7,756.13 

93i 

293.740 

6,866.16 

96i 

303.164 

7,313.84 

99i 

312.589 

7,775.66 

931 

294.132 

6,884.53 

96| 

303.557 

7,332.80 

m 

312.982 

7,795.21 

m 

294.525 

6,902.93 

96^ 

303.950 

7,351.79 

313.375 

7,814.78 

93i 

294.918 

6,921.35 

96^ 

304.342 

7,370.79 

m 

313.767 

7,834.38 

94 

295.310 

6,939.79 

97 

304.735 

7,389.83 

100 

314.160 

7,854.00 

The  preceding  table  may  be  used  to  determine  the  diameter  when 
the  circumference  or  area  is  known.  Thus,  the  diameter  of  a circle  having 
an  area  of  7,200  sq.  in.  is  approximately  95f  in. 


A GLOSSARY  OF  MINING  TERMS. 


The  present  glossary  is  a combination  of  glossaries  of  mining  terms  con- 
tained in  the  following  works:  Coal  and  Metal  Miners’  Pocketbook,  Fifth 
Edition;  Raymond’s  Glossary  of  Mining  and  Metallurgical  Terms;  Powers’ 
Pocketbook  for  Miners  and  Metallurgists;  Locke’s  Miners’  Pocketbook; 
Vol.  AC,  Second  Pennsylvania  Geological  Survey;  Ilhseng’s  Manual  of 
Mining;  Chism’s  Encyclopedia  of  Mexican  Mining  Law;  a Glossary  of  Terms 
as  Used  in  Coal  Mining,  by  W.  S.  Gresley;  11th  Annual  Report  of  the  State 
Mine  Inspector  of  Missouri;  Bullman’s  Colliery  Working  and  Management; 
Reynolds’  Handbook  of  Mining  Laws;  Report  of  the  Mine  Inspector  of 
Tennessee  for  1897;  Smithsonian  Report  for -1886;  together  with  a large  num- 
ber of  words  which  have  been  added  from  various  stray  sources.  It  is 
impossible  to  quote  the  authority  for  each  definition,  as  many  of  the  defini- 
tions are  combinations  from  a number  of  authors.  Where  such  different 
definitions  have  given  distinctly  different  meanings,  each  one  has  been 
included,  but  where  there  has  been  expressed  merely  a slight  shade  of 
difference,  the  definition  agreeing  most  closely  with  current  American 
practice  has  been  taken,  or  else  modified  to  suit  such  practice.  The  foreign 
words  selected  are  those  with  which  an  American  is  most  likely  to  come 
in  contact,  and  this  portion  of  the  glossary  is,  of  course,  not  exhaustive.  For 
the  large  number  of  purely  local  terms  used  in  the  several  coal  fields  of  Great 
Britain,  the  reader  is  referred  to  Mr.  Gresley ’s  glossary. 


566 


Aba 


GLOSSARY, 


Air 


GLOSSARY. 


Abattis  (Leicester).— Cross-packing  of  branches  or  rough  wood,  used  to  keep 
roads  open  for  ventilation. 

Ahra  (Spanish).— Fissure  in  a lode,  unfilled  or  only  partially  filled. 

Ahronziado  (Spanish).— Copper  sulphides. 

Absolute  Pressure— pressure  reckoned  from  a vacuum. 

Absolute  Temperature— The  temperature  reckoned  from  the  absolute  zero, 
-459.2°  F.  or  —273°  C. 

Accompt  (Cornish).— Settling  day  or  place. 

Achicar  (Mexican). — To  diminish  the  quantity  of  water  in  any  gallery  or 
working,  generally  by  carrying  it  out  in  buckets  or  in  leather  bags. 
Achicadores— Labor ers  employed  for  said  purpose.  Achichinques.— Same 
as  Achicadores.  Also  applied  to  hangers-on  about  police  courts,  etc. 
Such  people  as  are  generally  called  strikers  in  the  United  States. 

Acreage  Rent  (English).— Royalty  or  rent  for  working  minerals. 

Adarme  (Mexican).— A weight  for  gold,  about  1.8  grams. 

Addlings  (North  of  England).— Earnings. 

Ademador  (Spanish). — Mine  carpenter,  or  timberman. 

Ademar  (Spanish).— To  timber. 

Adit. — A nearly  horizontal  passage  from  the  surface,  by  which  a mine  is 
entered  and  unwatered  with  just  sufficient  slope  to  insure  drainage. 
In  the  United  States,  an  adit  driven  across  the  measures  is  usually  called 
a tunnel,  though  the  latter,  strictly  speaking,  passes  entirely  through  a 
hill,  and  is  open  at  both  ends. 

Adobe.- Sun-dried  brick. 

Adventurers.— Original  prospectors. 

Adverse.— To  oppose  the  granting  of  a patent  to  mining  claim. 

Adze.— A.  curved  cutting  instrument  for  dressing  timber. 

Aerac/e  (French).— Ventilation. 

Aerometers.— The  air  pistons  of  a Struve  ventilator. 

Aerop/iore.— The  name  given  to  an  apparatus  that  will  enable  a man  to  enter 
places  in  mines  filled  with  explosive  or  other  deadly  gases,  with  safety. 

Afinar  (Mexican).— Refining  gold  and  silver. 

A/terdamp.— The  gaseous  mixture  resulting  from  an  explosion  of  firedamp. 

Agent— The  manager  of  a mining  property. 

Agitator.— A mechanical  stirrer  used  in  pan  amalgamation. 

Ahondar  (Spanish). — To  sink. 

Air.— The  current  of  atmospheric  air  circulating  through  and  ventilating  the 
workings  of  a mine. 

Air  Box. — Wooden  tubes  used  to  convey  air  for  ventilating  headings  or 
sinkings  or  other  local  ventilation. 

Air  Compartment. — An  air-tight  portion  of  any  shaft,  winze,  rise,  or  level, 
used  for  improving  ventilation. 

Air-Cowrse.— See  Airway. 

Air  Crossing.— A bridge  that  carries  one  air-course  over  another. 

Air  Cushion.— A spring  caused  by  confined  air. 

Air  Door. — A door  for  the  regulation  of  currents  of  air  through  the  workings 
of  a mine. 

Air-End  Way  (Locke).— Ventilation  levels  run  parallel  with  main  level. 

Air  Furnace. — A reverberatory  furnace  in  which  to  smelt  lead. 

Air  Gates  (Locke).— (1)  Underground  roadways,  used  principally  for  venti- 
lating purposes.  (2)  An  air  regulator. 

Air  Head  (Staff).— Ventilation  ways. 

Air  Heading.— An  airway. 

Air  (Powers).— A hole  drilled  in  advance  to  improve  ventilation  by 

communication  with  other  workings  or  the  surface. 

Airless  End.— The  extremity  of  a stall  in  long:wall  workings  in  which  there 
is  no  current  of  air,  or  circulation  of  ventilation,  but  which  is  kept  pure 
by  diffusion  and  by  the  ingress  and  egress  of  cars,  men,  etc. 


Air 


GLOSSARY, 


Aqu 


567 


Air  Level.— K level  or  airway  of  former  workings  made  use  of  in  subsequent 
deeper  mining  operations  for  ventilating  purposes. 

Air  Oven. — A heated  chamber  for  drying  samples  of  ore,  etc. 

Air  Pipe.— A pipe  made  of  canvas  or  metal,  or  a wooden  box  used  in  con- 
veying air  to  the  workmen,  or  for  rock  drills  or  air  locomotives. 

Air-Shaft. — A shaft  or  pit  used  expressly  for  ventilation. 

Air  Slit  (Yorks).— A short  head  between  other  air  heads. 

Air  SoUar.—A  brattice  carried  beneath  the  tram  rails  or  road  bed  in  a head- 
ing or  gangway. 

Air  Stack.— A stack  or  chimney  built  over  a shaft  for  ventilation. 

Airway. — ^Any  passage  through  which  air  is  carried. 

Aitch  Piece. — Parts  of  a pump  in  which  the  valves  are  fixed.  - 

Albanil  (Spanish). — Mason. 

Albayalde  (Spanish).— White  lead. 

Alberti  Furnace. — A continuous  reverberatory  for  mercury  ores. 

Alcam  (Wales). — Tin. 

Alive  (Cornish).— Productive. 

Alloy.— A homogeneous  mixture  of  two  or  more  metals  by  fusion. 

Alluvial  6r0?d.— Gold  found  associated  with  water-worn  material. 

Alluvium. — Gravel,  sand,  and  mud  deposited  by  streams. 

Almadeneta  (Spanish).— Stamp  head. 

Almagre  (Spanish).— Red  ocher. 

Alternating  Motion.— and  down,  or  backward  and  forward  motion. 

Alto  (Mexican). — ^The  hanging  wall  of  a vein.  See  Respaldos. 

Aludel  (Spanish).— Earthen  condenser  for  mercury. 

Amalgam.— An  alloy  of  quicksilver  with  some  other  metal. 

Amalgamation. — Absorption  of  gold  and  silver  by  mercury. 

Amalgamator. — One  that  amalgamates  gold  and  silver  ores. 

Amygdaloidal.-Almond-sheiped. 

Analysis.— The  determination  of  the  original  elements  and  the  proportions 
of  each  in  a substance. 

Anemometer.— An  instrument  used  for  measuring  the  velocity  of  a ventilating 
current. 

Angle  Beam.— A two-limbed  beam  used  for  turning  angles  in  shafts,  etc. 

Without  water  in  its  composition. 

Anneal.— To  toughen  metals,  glass,  etc.  by  first  heating  and  then  cooling 
very  slowly. 

Anthracite.— Coa\  containing  a small  percentage  of  volatile  matter. 

Anticline.— A flexure  or  fold  in  which  the  rocks  on  the  opposite  sides  of  the 
fold  dip  away  from  each  other,  like  the  two  legs  of  the  letter  A.  The 
inclination  on  one  side  may  be  much  greater  than  on  the  opposite  side. 
An  anticlinal  is  said  to  be  overturned  when  the  rocks  on  both  sides 
dip  in  the  same  direction. 

Anticlinal  A.r^s.— The  ridge  of  a saddle  in  a mineral  vein,  or  the  line  along 
the  summit  of  a vein,  from  which  the  vein  dips  in  opposite  directions. 

Anticlinal  Flexure;  Anticlinal  Fold. — An  anticline. 

Antiguos,  Los  (Mexican).— The  Spanish  or  Indian  miners  of  colonial  times. 

Antimony  Star.— The  metal  antimony  when  crystallized,  showing  fern-like 
markings  on  the  surface. 

Aparadores  ( Mexican)  .—Persons  that  re  wash  or  rework  tailings  from  silver 
mills. 

Aparejo  (Mexican).— A rigid  pair  of  large  stuffed  pads  connected  over  back  of 
pack  mule  by  an  unpadded  portion  to  protect  body  of  mule  when  heavy 
or  irregularly  shaped  loads  are  carried. 

Aperos  (Mexican). — All  kinds  of  mining  supplies  in  general.  Aperador. — A 
storekeeper. 

Apex. — The  landing  point  at  the  top  of  a slope  or  inclined  plane,  the 
knuckle;  also,  the  top  of  an  anticlinal.  In  the  U.  S.  Revised  Statutes, 
the  end  or  edge  of  a vein  nearest  the  surface. 

A pique  (Mexican).— Perpendicular. 

Apolvillados  (Spanish). — Superior  ores. 

Apron  (English).— (1)  A covering  of  timber,  stone,  or  metal,  to  protect  a sur- 
face against  the  action  of  water  flowing  over  it.  (2)  A hinged  extension 
to  a loading  chute. 

Aprons.— Stamp-battery  copper  plates. 

Aqua  Fortis.—lSlitnc  acid. 

Aqua  Regia.— A mixture  of  hydrochloric  acid  and  nitric  acid. 

Aqueduct.— An  artificial  elevated  way  for  carrying  water. 


568 


Ara 


GLOSSARY. 


AZO 


Araw  (Mexican).— See  Hatajo. 

Arch  (Cornish).— Portion  of  lode  left  standing  to  support  hanging  wall,  or 
because  too  poor. 

Archean.—An  early  period  of  geological  time. 

ArcMTi^.— Brickwork  or  stonework  forming  the  roof  of  any  underground 
roadway. 

Arenaceous.— Sandy;  rocks  are  arenaceous  when  they  contain  a considerable 
percentage  of  sand. 

Arends  Tap.— An  inverted  siphon  for  drawing  molten  lead  from  a crucible 
or  furnace. 

Arenillas  (Spanish).— Refuse  earth. 

Ar5'en^^/erons.— Silver-bearing. 

Argillaceous.— rocks  are  argillaceous  when  they  contain  a consid- 
erable percentage  of  clay,  or  have  some  of  the  characteristics  of  clay. 

Argol.— Crude  tartar  deposited  from  wine. 

Arian  (Wales).— Silver. 

Arm. — The  inclined  leg  of  a set  of  timber. 

Arrage  (North  England).— Sharp  corner. 

Arrastre.—A  circular  trough  in  which  drags  are  pulled  round  by  being  con- 
nected with  a central  revolving  shaft  by  an  arm  and  chain.  Used  for 
grinding  and  amalgamating  ores.  Arrastre  de  cuchara,  spoon  arrastre; 
de  marca,  large  arrastre;  de  mula,  mule-power  arrastre. 

Arrastrar  (Mexican).— To  drag  along  the  ground.  Arrastrar  el  Agua. — To 
almost  completely  exhaust  the  water  in  a sump  or  working. 

Arroha  (Mexican).— 25  lb. 

Artesian  Well. — An  artificial  channel  of  escape,  made  by  a bore  hole,  for  a 
subterranean  stream,  subject  to  hydrostatic  pressure. 

Ascensional  Ventilation. — The  arrangement  of  the  ventilating  currents  in 
such  a manner  that  the  air  shall  continuously  rise  until  reaching  the 
bottom  of  the  upcast  shaft.  Particularly  applicable  to  steep  seams. 

Ashlar.— A facing  of  cut  stone  applied  to  a backing  of  rubble  or  rough 
masonry  or  brickwork. 

Aspirail  (French).— Opening  for  ventilation. 

Assa?/.— The  determination  of  the  quality  and  quantity’ of  any  particular 
substance  in  a mineral.  Assay er.— One  who  performs  assays. 

Assessment  Work.— The  annual  work  necessary  to  hold  a mining  claim. 

Asfe^.— Overhead  boarding  in  a gallery. 

Astyllen  (Cornish).— Small  dam  in  an  adit;  partition  between  ore  and  deads 
on  grass. 

Atacador  (Mexican).— A tamping  bar  or  tamping  stick. 

Atecas  (Mexican).— Same  as  Achicadores,  etc. 

Atierres  (Spanish).— Refuse  rock  or  dirt  inside  a mine. 

Attle  (Cornish).— Refuse  rock. 

Attle  (Addle). — The  waste  of  a mine. 

Attrition. — The  act  of  wearing  away  by  friction. 

Auger  Stem.— The  iron  rod  or  bar  to  which  the  bit  is  attached  in  rope  drilling. 

A wgfef. —Priming  tube. 

Aur  (Wales).— Gold. 

Attn/eroas.- Gold-bearing. 

Ausscharen  (German).— Junction  of  lodes. 

Auszimmern  ( German) . — Timbering. 

Average  Produce  (Cornish).— Percentage  of  fine  copper  in  ore. 

Average  Standard  (Cornish). — Price  of  pure  copper  in  ore. 

Aviador  (Spanish). — One  who  provides  the  capital  to  work  a mine. 
Avio. — Money  furnished  to  the  proprietors  of  a mine  to  work  the  mine, 
by  another  person,  the  Aviador.  Avio  Contract.— A contract  between 
two  parties  for  working  a mine  by  which  one  of  the  parties,  the  aviador^ 
furnishes  the  money  to  the  proprietors  for  working  the  mine. 

Axis.— An  imaginary  line  passing  through  a body  that  may  be  supposed  to 
revolve  around  it. 

Azimuth. — The  azimuth  of  a body  is  that  arc  of  the  horizon  that  is  included 
between  the  meridian  circle  at  the  given  place  and  a vertical  plane 
passing  through  the  body.  It  is  always  measured  from  due  north  around 
to  the  right. 

Azogue  (Spanish). — Mercury.  Azogueria. — Amalgamating  works.  Azoguero. 
Amalgamator.  The  person  in  charge  of  a patio  works.  Azogues.—Yree 
milling  ores. 

Azoic.— The  age  of  rocks  that  were  formed  before  animal  life  existed. 


Bac 


GLOSSARY, 


Ban 


569 


Back.— (1)  A plane  or  cleavage  in  coal,  etc.,  having  frequently  a smooth 
parting  and  some  sooty  coal  included  in  it.  (2)  The  inner  end  of  a 
heading  or  gangway.  (3)  To  throw  back  into  the  gob  or  waste  the  small 
slack,  dirt,  etc.  (4)  To  roll  large  coals  out  of  a waste  for  loading  into  cars. 

Back  Balance. — A self-acting  incline  in  the  mine,  where  a balance  car  and  a 
carriage  in  which  the  mine  car  is  placed  are  used.  The  loaded  car  upon 
the  carriage  will  hoist  the  balance  car,  and  the  balance  car  will  hoist  the 
carriage  and  empty  car. 

Backbye  Work.— Work  done  between  the  shaft  and  the  working  face^  in 
contradistinction  to  face  work,  or  work  done  at  the  face. 

Back  Casing. — A wall  or  lining  of  dry  bricks  used  in  sinking  through  drift 
deposits,  the  permanent  walling  being  built  up  within 'it.  The  use  of 
timber  cribs  and  planking  serves  the  same  purpose. 

Back  End  (England).— The  last  portion  of  a jud. 

Backing. — (1)  The  rough  masonry  of  a wall  faced  with  finer  work.  (2)  Earth 
deposited  behind  a retaining  wall,  etc.  (3)  Timbers  let  into  notches  in 
the  rock  across  the  top  of  a level. 

Backing  Deals.— DobX  boards  or  planking  placed  at  the  back  of  curbs  for 
supporting  the  sides  of  a shaft  that  is  liable  to  run. 

Back  Joint. — ^Joint  plane  more  or  less  parallel  to  the  strike  of  the  cleavage, 
and  frequently  vertical. 

Backlash.— {1)  Backward  suction  of  air-currents  produced  after  an  explosion 
of  firedamp.  (2)  Reentry  of  air  into  a fan. 

Back  of  Ore.— The  ore  between  two  levels  which  has  to  be  worked  from  the 
lower  level. 

Back  Pressure.-YYio  loss,  expressed  in  pounds  per  square  inch,  due  to  getting 
the  steam  out  of  the  cylinder  after  it  has  done  its  work. 

Back  Shift. — Afternoon  shift. 

Back  Skin  (North  of  England).— A leather  jacket  for  wet  workings. 

Backstay.— A wrought-iron  forked  bar  attached  to  the  back  of  cars  when 
ascending  an  inclined  plane,  which  throws  them  off  the  rails  if  the  rope 
or  coupling  breaks. 

Bajf  Ends. — Long  wooden  edges  for  adjusting  linings  in  sinking  shafts  dur- 
ing the  operation  of  fixing  the  lining. 

Baffle.— To  brush  out  firedamp. 

Raif.— Provisions. 

Bajo  (Mexican).— The  footwall  of  a vein.  See  Respaldo. 

Bal  (Cornish). — A mine. 

Balance. — (1)  The  counterpoise  or  weights  attached  to  the  drum  of  a winding 
engine,  to  assist  the  engine  in  lifting  the  load  out  of  a shaft  bottom  and 
in  helping  it  to  slacken  speed  when  the  cage  reaches  the  surface.  It 
consists  often  of  a bunch  of  heavy  chains  suspended  in  a shallow  shaft, 
the  chains  resting  on  the  shaft  bottom  as  unwound  off  the  balance  drum 
attached  to  the  main  shaft  of  the  engine.  (2)  Scales  used  in  chemical 
analysis  and  assaying. 

Balance  Bob.— A large  beam  or  lever  attached  to  the  main  rods  of  a Cornish 
pumping  engine,  carrying  on  its  outer  end  a counterpoise. 

Balance  Box. — A large  box  placed  on  one  end  of  a balance  bob  and  filled 
with  old  iron,  rock,  etc.  to  counterbalance  the  weight  of  pump  rods. 

Balance  Brow.— An  inclined  plane  in  steep  seams  on  which  a platform  on 
wheels  travels  and  carries  the  cars  of  coal. 

Balance  Car.— A small  weighted  truck  mounted  upon  a short  inclined  track, 
and  carrying  a sheave  around  which  the  rope  of  an  endless  haulage 
system  passes  as  it  winds  off  the  drum. 

Balance  Pit.— A pit  or  shaft  in  which  a balance  rises  or  falls. 

Balanzon  (Mexican).— The  balance  bob  of  a Cornish  pump. 

Balk.—{1)  A more  or  less  sudden  thinning  out  of  a seam  of  coal.  (2)  Irregu- 
lar-shaped masses  of  stone  intruding  into  a coal  seam,  or  bulgings  out 
of  the  stone  roof  into  the  seam.  (3)  A bar  of  timber  supporting  the  roof 
of  a mine,  or  for  carrying  any  heavy  load. 

Balland  (Derbyshire). — Pulverulent  lead  ore. 

Broken  stone,  gravel,  sand,  etc.  used  for  keeping  railroad  ties  ^tead3^ 

Bancos  (Spanish).— Horses  in  a vein  or  cross-courses. 

Band. — A seam  or  thin  stratum  of  stone  or  other  refuse  in  a seam  of  coal. 

Bank. — (1)  The  top  of  the  shaft,  or  out  of  the  shaft.  (2)  The  surface  around 
the  mouth  of  a shaft.  (3)  To  manipulate  coals,  etc.  on  the  bank. 
(4)  The  whole  or  sometimes  only  one  side  or  one  end  of  a working 
place  underground.  (5)  A large  heap  of  mineral  on  the  surface. 


570 


Ban 


GLOSSARY. 


Bas 


Bank  Chain— A.  chain  that  includes  the  bank  of  a river  or  creek. 

Bank  Claim  (Australian).— Mining  right  on  bank  of  stream. 

.BawM.— Auriferous  conglomerate  of  South  Africa. 

Bank  Head. — The  upper  end  of  an  inclined  plane,  next  to  the  engine  or  drum, 
made  nearly  level. 

Bank  Right  (Australian). — Right  to  divert  water  to  bank  claim. 

Banksman.— man  in  attendance  at  the  top  of  the  shaft,  superintending 
the  work  of  banking. 

Bankwork.—A  system  of  working  coal  in  South  Yorkshire. 

Bank  to  Bank. — A shift. 

Bannocking. — See  Kirving. 

Bano  (Spanish). — Excess  of  mercury  used  in  torta. 

Bar. — A length  of  timber  placed  horizontally  for  supporting  the  roof.  In 
some  cases,  bars  of  wrought  iron,  about  3 in.  X 1 m.  X 5 ft.  are  used. 

Bar  I>iggmgs.—{1)  River  placers  subject  to  overflow.  (2)  Auriferous  claims 
on  shallow  streams. 

Bargain.— Portion  of  mine  worked  by  a gang  on  contract. 

Barilla  (Spanish).— Grains  of  native  copper  disseminated  through  ores. 

Baring.— Soo  Stripping. 

Barmaster  (Derbyshire)- Mine  manager,  agent,  and  engineer. 

Bar  Mining.— The  mining  of  river  bars,  usually  between  low  and  high  water, 
although  the  stream  is  sometimes  deflected  and  the  bar  worked  below 
water  level. 

Barney. — A small  car,  used  on  inclined  planes  and  slopes  to  push  the  mine 
car  up  the  slope.  Barney  Pit.— A pit  at  the  bottom  of  a slope  or  plane 
into  which  the  barney  runs  to  allow  the  mine  car  to  pass  over  it. 

Barra  (Mexican). — (1)  A bar,  as  of  gold,  silver,  iron,  steel,  etc.  (2)  A cer- 
tain share  in  a mine.  The  ancient  Spanish  laws,  from  time  immemorial, 
considered  a mine  as  divided  into  24  parts,  and  each  part  was  called  a 
“ barra.” 

Barra  Viuda,  or  Aviada  (Mexican).— These  are  “barras”  or  shares  that  par- 
ticipate in  the  profits,  but  not  in  the  expenses,  of  mining  concerns. 
Their  share  of  the  expenses  is  paid  by  the  other  shares.  Non-assessable 
shares. 

Barranca  (Mexican).— A ravine,  a gulch.  What  is  improperly  called  in  the 
United  States  a canyon  or  canon. 

Barrel  Amalgamation. — Amalgamating  ores  in  revolving  barrels. 

Barrel  Work. — (1)  Native  copper  that  can  be  hand-sorted  ready  for  smelt- 
ing. (2)  Barrel  amalgamation. 

Ran’ena  (Mexican).— A hand  drill  for  opening  holes  in  rocks  for  blasting 
purposes. 

Barrenarse  (Mexican). — When  two  mines  or  two  workings  (as  a shaft  or 
winze,  or  a gallery)  communicate  with  each  other. 

Barren  Ground.— Strata  unproductive  of  seams  of  coal,  etc.  of  a workable 
thickness. 

Barreno  ( Mexican! . — (1)  A drill  hole  for  blasting  purposes.  In  mechanics,  any 
bored  hole.  (2)  A communication  between  two  mines  or  two  workings. 

Barretero  (Mexican). — A miner  of  the  first  class:  one  that  knows  how  to 
point  his  holes,  drill,  and  blast,  or  work  with  a gad. 

Barrier  Pillar.— A solid  block  or  rib  of  coal,  etc.,  left  un worked  between  two 
collieries  or  mines  for  security  against  accidents  arising  from  influx  of 
water. 

Barrier  System.— The  method  of  working  a colliery  by  pillar  and  stall,  where 
solid  ribs  or  barriers  of  coal  are  left  in  between  a set  or  series  of  working 
places. 

Barrow.— {\)  A box  with  two  handles  at  one  end  and  a wheel  at  the  other. 
(2)  Heap  of  waste  stuff  raised  from  a mine;  a dump. 

Bar  Timbering.— A system  of  supporting  a tunnel  roof  by  long  top  bars, 
while  the  whole  lower  tunnel  core  is  taken  out,  leaving  an  open  space 
for  the  masons  to  run  up  the  arching.  Under  certain  conditions,  the 
bars  are  withdrawn  after  the  masonry  is  completed,  otherwise  they  are 
bricked  in  and  not  drawn. 

Base  Bullion. — Lead  combined  with  precious  metals. 

Base  Metal.— ^letai  not  classed  with  the  precious  metals,  gold,  silver,  plat- 
inum, etc.,  that  are  not  easily  oxidized. 

Basin. — (1)  A coal  field  having  some  resemblance  in  form  to  a basin.  (2) 
The  synclinal  axis  of  a seam  of  coal  or  stratum  of  rock 

Basket.— A measure  of  weight  = 2 cwt. 


Bas 


GLOSSARY. 


Ben 


571 


Crucible  or  furnace  lining. 

Bass  (Derbyshire).— Indurated  clay. 

Basset.— Outcrop  of  a lode  or  stratum. 

Bastard.— A particularly  hard  massive  rock  or  boulder. 

Batch.— An  assorted  parcel  of  ore,  sometimes  called  doles,  when  divided 
into  equal  quantities. 

Batea.—A  shallow  wooden  bowl  used  for  washing  out  gold,  etc. 

Batt  (English).— (1)  A highly  bituminous  shale  found  in  the  coal  measures. 
(2)  Hardened  clay,  but  not  fireclay.  Same  as  Bend  and  Bind. 

Batten.— A piece  of  thin  board  less  than  12  in.  in  width. 

Batter.— YYiq  inclination  of  a face  of  masonry  or  of  any  inclined  portion  of 
a frame  or  metal  structure. 

Battery. — (1)  A structure  built  to  keep  coal  from  sliding  down  a chute  or 
breast.  (2)  An  embankment  or  platform  on  which  miners  work.  (3) 
A set  of  stamps. 

Bay. — An  open  space  for  waste  between  two  packs  in  a longwall  working. 
See  Board. 

Bay  of  Biscay  CowTifr?/.— (Geological).— See  Crab  Holes. 

Beach  Combing. — Working  the  sands  on  a beach  for  gold,  tin,  or  platinum. 

Beans  (North  of  England). — All  coal  that  will  pass  through  about 
screen. 

Bean  Copper  granulated  by  pouring  into  hot  water. 

Bear. — A deposit  of  iron  at  the  bottom  of  a furnace. 

Bear;  to  Bear  In. — Underholding  or  undermining;  driving  in  at  the  top  or  at 
the  side  of  a working. 

Bearers.— Pieces  of  timber  3 or  4 ft.  longer  than  the  breadth  of  a shaft, 
which  are  fixed  into  the  solid  rock  at  the  sides  at  certain  intervals  apart; 
used  as  foundations  for  sets  of  timber. 

Bearing. — (1)  The  course  by  a compass.  (2)  The  span  or  length  in  the  clear 
between  the  points  of  support  of  a beam,  etc.  (3)  The  points  of  support 
of  a beam,  shaft,  axle,  etc. 

Bearing  Door. — A door  placed  for  the  purpose  of  directing  and  regulating  the 
amount  of  ventilation  passing  through  an  entire  district  of  a mine. 

Bearing  7?i.— The  depth  or  distance  under  of  the  undercut  or  holing. 

Bearing-up  Pulley.— A pulley  wheel  fixed  in  a frame  and  arranged  to  tighten 
up  or  take  up  the  slack  rope  in  endless-rope  haulage. 

Bearing-up  Stop.— A partition  of  brattice  or  plank  that  serves  to  conduct  air 
to  a face. 

Beat  (Cornish).— To  cut  away  a lode. 

Beataway. — Working  hard  ground  by  means  of  wedges  and  sledge  hammers. 

Bed. — (1)  The  level  surface  of  a rock  upon  which  a curb  or  crib  is  laid.  (2)  A 
stratum  of  coal,  ironstone,  clay,  etc. 

Bed  Claim  (Australian).— A claim  that  includes  the  bed  of  a river  or  creek. 

Bede. — Miners’  pickax. 

Bedplate. — A large  plate  of  iron  used  as  a foundation  for  an  engine. 

Bed  Bocfc.— The  solid  rock  underlying  the  soil,  drift,  or  alluvial  deposits. 

Before-Breast— Bock  or  vein,  which  still  lies  ahead. 

Belgian  Zinc  Furnace. — A furnace  for  the  production  of  zinc,  in  which  the 
calcined  ore  is  distilled  in  tubular  retorts. 

BeZZ.— Overhanging  rock  or  slate,  of  a bell-like  form,  disconnected  from  the 
main  roof. 

Belland.—A  form  of  lead  poisoning  to  which  lead  miners  are  subject. 

Belly. — A swelling  mass  of  ore  in  a lode. 

Ben,  Benhayl  (Cornish).— Productive.  The  productive  portion  of  a tin 
stream. 

Bench. — (1)  A natural  terrace  marking  the  outcrop  of  any  stratum.  (2)  A 
stratum  of  coal  forming  a portion  of  the  vein. 

Bench  Diggings.— Bi\cv  placers  not  subject  to  overfiow. 

Benching.— Yo  break  up  with  wedges  the  bottom  coals  when  the  holing  is 
done  in  the  middle  of  the  seam. 

Benching  Up  (North  of  England).— Working  on  top  of  coal. 

Bench  Mark. — A mark  cut  in  a tree  or  rock  whose  elevation  is  known.  Used 
by  surveyors  for  reference  in  determining  elevations. 

Bench  Working.— The  system  of  working  one  or  more  seams  or  beds  of 
mineral  by  open  working  or  stripping,  in  stages  or  steps. 

Bend  (Derbyshire). — Indurated  clay. 

Beneficiar  (Mexican).— To  treat  ores  for  the  purpose  of  extracting  the 
metallic  contents. 


572 


Ben 


GLOSSARY. 


Blo 


Beneficio  (Mexican).— Any  metallurgical  process. 

Benheyl  (Cornish).— Flowing  tin  stream. 

Bessemer  Steel— made  by  the  Bessemer  process. 

Beton  (English).— Concrete  of  hydraulic  cement  with  broken  stone,  bricks, 
gravel,  etc. 

Bevel.— slope  formed  by  trimming  away  on  edge. 

Bevel  Gear. — A gear-wheel  whose  teeth  are  inclined  to  the  axis  of  the  wheel. 

Biche.—A  hollow-ended  tool  for  recovering  boring  rods. 

Billy  Boy.— A boy  who  attends  a Billy  Playfair. 

Billy  Playfair.— A.  mechanical  contrivance  for  weighing  coal,  consisting  of 
an  iron  trough  with  a sort  of  hopper  bottom,  into  which  all  the  small 
coal  passing  through  the  screen  is  conducted  and  weighed  off  and 
emptied  from  time  to  time. 

Bin.— A box  with  cover,  used  for  tools,  stones,  ore,  etc. 

Bind,  or  Bmder.— Indurated  argillaceous  shales  or  clay,  very  commonly 
forming  the  roof  of  a coal  seam  and  frequently  containing  clay  iron- 
stone. See  Batt. 

Binding.— Riring  men. 

Bing  (North  of  England).— 8 cwt.  of  ore. 

Bing  Hole  (Derbyshire).— An  ore  shoot. 

Bing  Ore  (Derbyshire).— Lead  ore  in  lumps. 

Bing  Tale  (North  of  England).— Ore  given  to  the  miner  for  his  labor. 

Bit.— A piece  of  steel  placed  in  the  cutting  edge  of  a drill  or  point  of  a pick. 

BtocA:6a7id.— Carbonaceous  ironstone  in  beds,  mingled  with  coaly  matter 
sufficient  for  its  own  calcination. 

Black  Batt,  or  Black  Stone.— Black  carbonaceous  shale. 

Black  Copper.— Impure  smelted  copper. 

^tocfcdamp.— Carbonic-acid  gas. 

Black  Diamonds. — Coal. 

Black  Ends.— Refuse  coke. 

Black  Flux.— ChavcooX  and  potassium  carbonate. 

Black  Jack.—{1)  Properly  speaking,  dark  varieties  of  zinc  blende,  but  many 
miners  apply  it  to  any  black  mineral.  (2)  Crude  black  oil  used  to  oil 
mine  cars. 

Black  Lead.- Graphite. 

Black  Ore  (English).— Partly  decomposed  pyrites  containing  copper. 

Black  Sand. — Dark  minerals  found  with  alluvial  gold. 

Black  Stone.— A carbonaceous  shale. 

Black  Tin.— Dressed  cassiterite;  oxide  of  tin. 

Blanch. — (1)  A piece  of  ore  found  isolated  in  the  hard  rock.  (2)  Lead  ore 
mixed  with  other  minerals. 

Blanched  Copper.— Copper  alloyed  with  arsenic. 

Blanket  Strake  (Australian).— Sloping  tables  or  sluices  lined  with  baize,  for 
catching  gold. 

Blanket  Tafttos.- Inclined  planes  covered  with  blankets,  to  catch  the  heavier 
minerals  passing  over  them. 

.Btosf.— (1)  The  sudden  rush  of  fire,  gas,  and  dust  of  an  explosion  through  the 
workings  and  roadways  of  a mine.  (2)  To  cut  or  bring  down  coal, 
rocks,  etc.  by  the  explosion  of  gunpowder,  dynamite,  etc. 

Blasting  Barrel.— A small  pipe  used  for  blasting  in  wet  or  gaseous  places. 

Blast  Pipe.— A pipe  for  supplying  air  to  furnaces. 

J5tonde.— Sulphide  of  zinc;  sphalerite. 

Blick  (Germany).— Iridescence  on  gold  and  silver  at  end  of  cupeling. 

Blind  Coal.— Coal  altered  by  the  heat  of  a trap  dike. 

Blind  Creek. — (1)  A creek  in  which  water  flows  only  in  very  wet  weather. 
(2)  (Australasian)  Dry  watercourse. 

Blind  Drift— A horizontal  passage  in  the  mine  not  yet  connected  with  the 
other  workings. 

Blind  Obscure  bedding  plane. 

Blind  Lead,  or  Blind  Lode.— A vein  having  no  visible  outcrop. 

Blind  Level.— {!)  An  incomplete  level.  (2)  A drainage  level. 

Blind  Shaft,  or  Blind  Pit— A shaft  not  coming  to  the  surface. 

Bloat. — A hammer  swelled  at  the  eye. 

Block  Claim  (Australian). — A square  mining  claim. 

Block  Coat— Coal  that  breaks  in  large  rectangular  lumps. 

Blocking^  Out.—{l)  Working  deep  leads  in  blocks;  somewhat  like  horizontal 
stoping.  (2)  (Australian)  Washing  gold  gravel  in  sections. 

Block  Re^s.— Reefs  showing  frequent  contractions  longitudinally. 


Blo 


GLOSSARY. 


Bon 


573 


Block  Cast  tin. 

Bloomary.— K forge  for  making  wrought  iron. 

Blossom.— YhQ  decomposed  outcrop,  float,  surface  stain,  or  any  indicating 
traces  of  a coal  bed  or  mineral  deposit.  Blossom  Rock. — (ij  Colored 
veinstone  detached  from  an  outcrop.  (2)  The  rock  detached  from 
a vein,  but  which  has  not  been  transported. 

Blow.—{l)  To  blast  with  gunpowder,  etc.  (2)  A dam  or  stopping  is  said  to 
blow  when  gas  escapes  through  it. 

Blower.— [1)  A sudden  emission  or  outburst  of  gas  in  a mine.  (2)  Any 
emission  of  gas  from  a coal  seam  similar  to  that  from  an  ordinary  gas 
burner.  (3)  A type  of  centrifugal  fan  used  largely  to  force  air  into 
furnaces.  (4)  A blowdown  ventilating  fan. 

Blow  Fan.— A small  centrifugal  fan  used  to  force  air  through  canvas  pipes 
or  wooden  boxes  to  the  workmen. 

Blowdown  Fan. — A force  fan. 

Blow  In.—Yo  commence  a smelting  process. 

Blown- Out  Shot.— A shot  that  has  blown  out  the  tamping,  but  not  broken  the 
coal  or  rock. 

Blow  Off.— To  let  off  excess  of  steam  from  a boiler. 

Blow  Out.—{l)  To  finish  a smelting  campaign.  (2)  A blown-out  shot. 
(3)  The  decomposed  mineral  exposure  of  a vein. 

Blowpipe. — An  instrument  for  creating  a blast  whereby  the  heat  of  a flame 
or  lamp  can  be  better  utilized. 

Blue  Residue  of  copper  pyrites  after  roasting  with  salt. 

Blue  Cap.— The  blue  halo  of  ignited  gas  (firedamp  and  air)  on  the  top  of  the 
flame  in  a safety  lamp,  in  an  explosive  mixture. 

Blue  Elvan  (Cornish).— Greenstone. 

Blue  Jb/iTi.— Fluorspar. 

Blue  Lead.— A blue-stained  stratum  of  gravel  of  great  extent  and  richness. 

Blue  Metal. — A local  term  for  shale  possessing  a bluish  color. 

Blue  Peach  (Cornish). — A slate-blue  fine-grained  schorl. 

Ri^esto7ie.—(1)  Sulphate  of  copper.  (2)  Lapis  lazuli.  (3)  Basalt.  (4)  Maryland, 
a gray  gneiss;  in  Ohio,  a gray  sandstone;  in  the  District  of  Columbia, 
a mica  schist;  in  New  York,  a blue-gray  sandstone;  in  Pennsylvania,  a 
blue-gray  sandstone.  (5)  A popular  term  among  stone  men  not  suf- 
ficiently" definite  to  be  of  value. 

Bluff.— B\\mt. 

Board.— A wide  heading  usually  from  3 to  5 yd.  wide. 

Board-and-Pillar.—A  system  of  working  coal  where  the  first  stage  of  exca- 
vation is  accomplished  with  the  roof  sustained  by  pillars  of  coal  left 
between  the  breasts;  often  called  Breast-and- Pillar. 

Bob.— An  oscillating  bell-crank,  or  lever,  through  which  the  motion  of  an 
engine  is  transmitted  to  the  pump  rods  in  an  engine  or  pumping  pit. 
There  are  i bobs,  L bobs,  and  V bobs. 

Boca  or  Boca  Mina  (Mexican). — Mouth  or  mine  mouth.  This  is  the  name 
applied  to  the  principal  or  first  opening  of  a mine,  or  to  the  one  where 
the  miners  are  accustomed  to  descend. 

Bochorno  (Mexican).— Excessive  heat,  with  want  of  ventilation,  so  that  the 
lights  go  out.  See  Vapores. 

Body.—{l)  An  ore  body,  or  pocket  of  mineral  deposit.  (2)  The  thickness  of 
a lubricating  oil  or  other  liquid;  also  the  measure  of  that  thickness 
expressed  in  the  number  of  seconds  in  which  a given  quantity  of  the 
oil  at  a given  temperature  flows  through  a given  aperture. 

Bog  Iron  Ore.— Loose  earthy  brown  hematite  recently  formed  in  swampy 
ground. 

Boleo  (Mexican).— A dump  pile  for  waste  rock. 

Boliche  (Spanish).— Concentrating  bowl. 

Bollos  (Spanish). — Triangular  blocks  of  amalgam. 

Bolsa  (Spanish).— Small  bunch  of  ore. 

Bonanza.— An  aggregation  of  rich  ore  in  a mine. 

Bond. — (1)  The  arrangement  of  blocks  of  stone  or  brickwork  to  form  a firm 
structure  by  a judicious  overlapping  of  each  other  so  as  to  break  joint. 
(2)  An  agreement  for  hiring  men. 

Bone.— Slaty  coal  or  carbonaceous  shale  found  in  coal  seams. 

Bone  Ash.— Burnt  bones  pulverized  and  sifted. 

Bonnet.— {!)  The  overhead  cover  of  a cage.  (2)  A cover  for  the  gauze  of 
a safety  lamp.  (3)  A cap  piece  for  an  upright  timber, 

Bonney  (Cornish).— An  isolated  body  of  ore, 


574 


Bon 


GLOSSARY, 


Bee 


JSoTise.— Undressed  lead  ore. 

Booming.— Ground  sluicing  on  a large  scale  by  emptying  the  contents  of  a 
reservoir  at  once  on  material  collected  below,  thus  removing  boulders. 

Bord  (English). — A narrow  breast. 

Bord-and-Pillar  (English).— See  Pillar-and-Breast. 

Bord  Room. — The  space  excavated  in  driving  a bord.  The  term  is  used  in 
connection  with  the  “ridding”  of  the  fallen  stone  in  old  bords  when 
driving  roads  across  them  in  pillar  working;  thus,  “ ridding  across  the 
old  bord  room.” 

Bord  Ways  Course. — The  direction  at  right  angles  to  the  main  cleavage 
planes.  In  some  mining  districts,  it  is  termed  “on  face.” 

Bore.— To  drill. 

Bore  Hole. — A hole  made  with  a drill,  auger,  or  other  tools,  in  coal,  rock,  or 
other  material. 

Borrasca  (Mexican). — The  reverse  of  bonanza.  When  the  mine  has  a vein, 
but  no  ore,  it  is  said  to  be  “ en  borrasca.” 

Bor^.— Amorphous  dark  diamond. 

Bosh. — The  plane  in  a blast  furnace  where  the  greatest  diameter  is  reached. 

Boss  (English). — (1)  An  increase  of  the  diameter  at  any  part  of  the  shaft. 
(2)  A person  in  charge  of  a piece  of  work. 

Botas  (Mexican). — Buckets  made  of  an  entire  ox  skin,  to  take  out  water. 

Botryoidal.—Gvaipe-like  in  appearance. 

Bottle  Jack  (English). — An  appliance  for  lifting  heavy  weights. 

Bottom.— iX)  The  landing  at  the  bottom  of  the  shaft  or  slope.  (2)  The  lowest 
point  of  mining  operations.  (3)  The  floor,  bottom  rock,  or  stratum 
underlying  a coal  bed.  (4)  In  alluvial,  the  bed  rock  or  reef. 

Bottomery  Bottomman. — The  person  that  loads  the  cages  at  the  pit  bottom 
and  gives  the  signal  to  bank. 

Bottom  Joint. — ^Joint  or  bedding  plane,  horizontal  or  nearly  so. 

Bottom  Lift.—{1)  The  deepest  column  of  a pump.  (2)  The  lowest  or  deepest 
lift  or  level  of  a mine. 

Bottom  Pillars.— Largo  pillars  left  around  the  bottom  of  a shaft. 

Bottoms. — Impure  copper  alloy  below  the  matte  in  smelting. 

Boulders. — Loose  rounded  masses  of  stone  detached  from  the  parent  rock. 

Bounds  (Cornish). — A tract  of  tin  ground. 

Bout  (Derbyshire). — Twenty-four  dishes  of  lead  ore. 

Bow. — The  handle  of  a kibble. 

Bowk. — An  iron  barrel  or  tub  used  for  hoisting  rock  and  other  debris  when 
sinking  a shaft. 

Bowke  (Staffordshire). — A small  wooden  box  for  hauling  ironstone  under- 
ground. 

Bowl  Metal. — The  impure  antimony  obtained  from  doubling. 

Bowse  ( Derbyshire) . — Lead  ore  as  cut  from  the  lode. 

Box. — (1)  A *12'  to  14'  section  of  a sluice.  (2)  A mine  car. 

Box  Bill. — Tool  for  recovering  boring  rods. 

Boxing. — A method  of  securing  shafts  solely  by  slabs  and  wooden  pegs. 

Brace. — (1)  An  inclined  beam,  bar,  or  strut  for  sustaining  compression 
or  tension.  See  Tie-Brace,  Sway-Brace.  (2)  A platform  at  the  top  of  a 
shaft  on  which  miners  stand  to  work  the  tackle.  (3)  (Cornish)  Building 
at  pit  mouth. 

Brace  Beads.— Wooden  handles  or  bars  for  raising  and  rotating  the  rods 
when  boring  a deep  hole. 

B?m2:e.— Charcoal  dust. 

Brake  Seive. — Hand  jigger. 

Brances.—lron  pyrites  in  coal. 

BrancTi.— Small  vein  shooting  off  from  main  lode. 

Brashy. — Short  and  tender. 

Brasque.—A  mixture  of  clay  and  coke  or  charcoal  used  for  furnace  bottoms. 

Brass.— (1)  Iron  pyrites  in  coal.  (2)  An  alloy  of  copper  and  zinc. 

B?’asses  (English).— Fitting  of  brass  in  plummer  blocks,  etc.,  for  diminishing 
the  friction  of  revolving  journals  that  rest  upon  them. 

Brat.— A thin  bed  of  coal  mixed  with  pyrites  or  limestone. 

Brattice. — A lining  or  partition. 

Brattice  CZof/i.-Du  eking  or  canvas  used  for  making  a brattice. 

Brazzil  (North  of  England).— Iron  pyrites  in  coal. 

Breaker. — In  anthracite  mining,  the  structure  in  which  the  coal  is  broken, 
sized,  and  cleaned  for  market.  Known  also  as  Coal  Breaker. 

Breaker  Boy.— A boy  who  works  in  a coal  breaker. 


Bre 


GLOSSARY. 


BUL 


575 


Breakstaff.—Y\iQ  lever  for  blowing  a blacksmiths’  bellows,  or  for  working 
bore  rods  up  and  down. 

Breakthrough.— A.  narrow  passage  cut  through  a pillar  connecting  rooms. 

Breast.— A stall,  board,  or  room  in  which  coal  is  mined.  (2)  The  face  or 
wall  of  a quarry  is  sometimes  called  by  this  name. 

Breast-and- Pillar. —A  system  of  working  coal  by  boards  or  rooms  with  pillars 
of  coal  between  them. 

Breasting  Ore.— The  ore  taken  from  the  face  or  end  of  the  tunnel. 

Breast  Wall  (English).— A wall  built  to  prevent  the  falling  of  a vertical  face 
cut  into  the  natural  soil. 

Breccia.— A rock  composed  of  angular  fragments  cemented  together. 

Breeding  Fire. — See  Gob  Fire. 

Freese.— Fine  slack. 

J5ree2!e.— Small  coke,  probably  same  as  braize  or  braise. 

Brettis  (Derbyshire). — A timber  crib  filled  with  slack. 

Bridge.— {!)  A platform  on  wheels  running  on  rails  for  covering  the  mouth 
of  a shaft  or  slope.  (2)  A track  or  platform  passing  over  an  inclined 
haulageway  and  which  can  be  raised  out  of  the  way  of  ascending  and 
descending  cars.  (3)  An  air  crossing. 

Bridle  Chains.—SYioit  chains  by  which  a cage,  car,  or  gunboat  is  attached  to 
a winding  rope;  of  use  in  case  the  rope  pulls  out  of  its  socket. 

Briquets.— made  of  slack  or  culm  and  pressed  into  brick  form. 

Broaching  Bit.— A tool  for  reopening  a bore  hole  that  has  been  partially 
closed  by  swelling  of  the  walls. 

Brob. — A spike  to  prevent  timber  slipping. 

Broil  (Cornish). — Traces  of  a vein  in  loose  matter. 

Broken.— A district  of  coal  pillars  in  process  of  removal,  so  called  in  contra- 
distinction to  the  first  working  of  a seam  by  bord-and-wall,  or  working 
in  the  “whole.”  See  Whole  Working. 

Broken  CoaZ.— Anthracite  coal  that  will  pass  through  a mesh  or  bars  3i  to 
4i  in.,  and  over  a mesh  2f  in.  square.  (See  page  434.) 

Bronce  (Mexican). — In  mining,  copper  or  iron  pyrites. 

Brooch  (Cornish).— Mixed  ores. 

Brooc/imgr.— Smoothing. 

Brood  (Cornish).— Heavy  waste  from  tin  and  copper  ores. 

Brow. — An  underground  roadway  leading  to  a working  place  driven  either 
to  the  rise  or  to  the  dip. 

Brown  CoaZ.— Lignite.  A fuel  classed  between  peat  and  bituminous  coal. 

Brown  /Spar.— Dolomite  containing  carbonate  of  iron. 

Brownstone. — (1)  Decomposed  iron  pyrites.  (2)  Brown  sandstone. 

Browse. — Imperfectly  smelted  ore  mixed  with  cinder  and  clay. 

Brujula  (Mexican).— A surveyors’  (or  marine)  magnetic  compass. 

Brush.— {i)  To  mix  air  with  the  gas  in  a mine  working  by  swinging  a 
jacket,  etc.,  which  creates  a current.  (2)  To  “6ras/i”  the  roof  of  an 
airway,  is  to  take  down  some  of  the  roof  slate,  to  increase  the  height 
or  headroom. 

Bryle  (Cornish).— Traces  of  a vein  in  loose  matter. 

Bucket— (1)  An  iron  or  wooden  receptacle  for  hoisting  ore,  or  for  raising 
rock  in  shaft  sinking.  (2)  The  top  valve  or  clack  of  a pump. 

Bucket  Pump.— A.  lifting  pump,  consisting  of  buckets  fastened  to  an  endless 
belt  or  chain. 

Bucket  Sword.— A wrought-iron  rod  to  which  the  pump  bucket  is  attached. 

Bucket  Tree.— The  pipe  between  the  working  barrel  and  the  wind  bore. 

Bucking.— Breaking  down  ore  with  a very  broad  hammer,  ready  for  jigmng. 

Bucking  Hammer. — An  iron  disk,  provided  with  a handle,  used  for  breaking 
up  minerals  by  hand. 

Buck  Quartz. — Hard  non-auriferous  quartz. 

Buck  Staff.— Uprights  for  bracing  reverberatory  furnaces  together. 

Buckwheat.— Anthracite  coal  that  will  pass  through  a mesh  i in.  and  over  a 
mesh  i in. 

Buddie.— An  inclined  table,  circular  or  oblong,  on  which  ore  is  concentrated. 

Buddling.—W  ashing. 

Buggy.— A small  mine  car. 

Bug  Hole. — A small  cavity  usually  lined  with  crystals. 

Building.— A built-up  block  or  pillar  of  stone  or  coal  to  support  the  roof. 

Buitron  (Spanish).— A silver  furnace  of  peculiar  form. 

Bulkhead.— {!)  A tight  partition  or  stopping.  (2)  The  end  of  a flume  carry- 
ing water  for  hydraulicking. 


576 


GLOSSARY. 


Bul 


Cal 


Bulldog.—A  refractory  furnace  lining  of  calcined  mill  cinder,  containing 
iron  and  silica. 

Bull  Engine. — A single,  direct-acting  pumping  engine,  the  pump  rods  form- 
ing a continuation  of  the  piston  rod. 

Buller  Shot.— A second  shot  put  in  close  to,  and  to  do  the  work  not  done  by, 
a blown-out  shot,  loose  powder  being  used. 

Bull.— An  iron  rod  used  in  ramming  clay  to  line  a shot  hole. 

Bulling.— Lining  a shot  hole  with  clay. 

Bullion. — Uncoined  gold  and  silver. 

Bull  Pump. — A single-acting  pumping  engine  in  which  the  steam  cylinder  is 
placed  over  the  shaft  or  slope  and  the  pump  rods  are  attached  directly  to 
the  piston  rod.  The  steam  enters  below  the  piston  and  raises  the  pump 
rods;  the  water  is  pumped  on  the  down  stroke  by  the  weight  of  the  rods. 

Bull  Pup.— A worthless  claim. 

Bull  Wheel. — A wheel  on  which  the  rope  carrying  the  boring  rod  is  coiled 
when  boring  by  steam  machinery. 

Bully. — A miners’  hammer. 

Bumping  Table.— A concentrating  table  with  a jolting  motion. 

Bunch.— A small  rich  deposit  of  ore. 

Bunding.— A staging  in  a level  for  carrying  debris. 

Bunkers.— coal  consumed  on  board  ship. 

Bunney.—A  nest  of  ore  not  lying  in  a regular  vein. 

Timbers  placed  horizontally  across  a shaft  or  slope  to  carry  the 
cage  guides,  pump  rods,  column  pipe,  etc.;  also,  to  strengthen  the  shaft 
timbering. 

Burden.— {!)  Earth  overlying  a bed  of  useful  mineral.  (2)  The  proportion 
of  ore  and  flux  to  fuel  in  the  charge  of  a blast  furnace. 

Burr. — Solid  rock. 

Burrow. — Refuse  heap. 

Buscones  (Spanish).— Prospectors,  fossickers,  tribute  workers. 

Bush. — To  line  a circular  hole  with  a ring  of  metal,  to  prevent  the  hole  from 
wearing  out. 

Butt.—{1)  Coal  surface  exposed  at  right  angles  to  the  face;  the  ''ends''  of 
the  coal.  (2)  The  butt  of  a slate  quarry  is  where  the  overlying  rock 
comes  in  contact  with  an  inclined  stratum  of  slate  rock. 

Butt  Entry. — A gallery  driven  at  right  angles  with  the  butt  joint  (see  page  285). 

Butterfly  Valve.— A circular  valve  that  revolves  on  an  axis  passing  through 
its  center. 

Butt  Heading. — See  Butt  Entry. 

Button.— TLq  globule  of  metal,  the  result  of  an  assay. 

Button  Balance. — A small  very  delicate  balance  used  for  weighing  assay 
buttons. 

Butty. — A partner  in  a contract  for  driving  or  mining;  a comrade,  crony. 
Sometimes  called  “ Buddy." 

By  Level.— A side  level  driven  for  some  unusual  but  necessary  purpose. 

Cab.— The  side  parts  of  a lode,  nearest  the  walls,  which  are  generally  hard 
and  deficient  of  ore. 

Caballo  (Mexican).— A “ horse  ” or  mass  of  barren  rock  in  a vein. 

Cabezuela  (Spanish).— Rich  gold  and  silver  concentrates. 

Cabin.— {!)  A miner’s  house.  (2)  A small  room  in  the  mine  for  the  use  of  the 
officials. 

Cable  Drilling. — Rope  drilling. 

Cage.— A platform  on  which  mine  cars  are  raised  to  the  surface. 

Cage  Omdcs.- Vertical  rods  of  pine,  iron,  or  steel,  or  wire  rope,  fixed  in  a 
shaft,  between  which  cages  run,  and  whereby  they  are  prevented  from 
striking  one  another,  or  against  any  portion  of  the  shaft. 

eager. — The  person  that  puts  the  cars  on  the  cage  at  the  bottom  of  the  shaft. 

Cage  Seat. — Scaffolding,  sometimes  fitted  with  strong  springs,  to  take  off  the 
shock,  and  on  which  the  cage  drops  when  reaching  the  pit  bottom. 

Cage  Sheets.— props  or  catches  on  which  cages  stand  during  caging  or 
changing  cars. 

Caking  Coal. — Coal  that  agglomerates  on  the  grate. 

Cal. — Wolfram. 

Cala  (Spanish). — Prospecting  pit. 

Calcareous. — Containing  lime. 

Calcine. — To  heat  a substance;  not  sufficiently  to  melt  it,  but  enough  to  drive 
off  the  volatile  contents. 


Cal 


GLOSSARY. 


Cau 


577 


Calcining  Furnace.— K furnace  used  for  roasting  ore  in  order  to  drive  off 
certain  impurities. 

Caliche  (Spanish). — Feldspar. 

California  Pump. — A rude  pump  made  of  a wooden  box  through  which  an 
endless  belt  with  floats  circulates;  used  for  pumping  water  from  shallow 
ground. 

Callys  (Cornish).— Stratifled  rocks  traversed  by  lodes. 

Caw.— (1)  A curved  arm  attached  to  a revolving  shaft  for  raising  stamps. 
(2)  Carbonate  of  lime  and  fluorspar,  found  on  the  joints  of  lodes. 

Camino  (Mexican).— Any  gallery,  winze,  or  shaft,  inside  of  a mine  used  for 
general  transit. 

Campaign. — The  length  of  time  a furnace  remains  in  blast. 

Canada  (Mexican).— See  Barranca. 

Canch,  or  Caunche.—{1)  A thickness  of  stone  required  to  be  removed  to  make 
height  or  to  improve  the  gradient  of  a road.  If  above  a seam,  it  is 
termed  a “top  canch”;  if  below,  a “bottom  canch.”  (2)  A trend  with 
sloping  sides  and  very  narrow  bottom. 

Cancha  (Spanish).— Space  for  drying  slimes. 

Cand  (Cornish).— Fluorspar. 

Cank  (Derbyshire).— Whinstone. 

Canker.— The  ocherous  sediment  in  coal-pit  waters. 

Cannel  Coal.— See  Classification  of  Coals  (page  170). 

Canon  (Mexican). — A level,  drift,  or  gallery  within  a mine.  Canon  de 
Guia.—A  drift  along  the  vein. 

Cants  (English).— The  pieces  forming  the  ends  of  buckets  of  a waterwheel. 

Cap.— (1)  A piece  of  plank  placed  on  top  of  a prop.  See,  also.  Collar.  (2) 
The  pale  bluish  elongation  of  the  flame  of  a lamp  caused  by  the  presence 
of  gas. 

Capellina  (Mexican).— An  old-style  retort  for  retorting  silver  amalgam. 

Caple  (Cornish). — Hard  rock  lining  tin  lodes. 

Cap  Rock.— The  upper  rock  that  covers  the  bed  rock. 

Capstan. — A vertical  axle  used  for  heavy  hoisting,  and  worked  by  horizontal 
arms  or  bars. 

Captain.— Cornish  name  for  manager  or  boss  of  a mine. 

Car.— Any  car  used  for  the  conveyance  of  coal  along  the  gangways  or 
haulage  roads  of  a mine. 

Carat.— A weight  nearly  equal  to  4 grains. 

Carbon.— A combustible  elementary  substance  forming  the  largest  compo- 
nent part  of  coal. 

Carbona.—{l)  A rich  bunch  of  ore  in  the  country  rock  connected  with  the 
lode  by  a mere  thread  of  mineral.  (2)  ((’ornish)  An  irregular  deposit 
of  tin  ore. 

Carbonaceous.— Coaiy,  containing  carbon  or  coal. 

Carbonate.— Caxhonic  acid  combined  with  a base. 

Carbonates.- Lead  ore.  The  oxide  and  carbonic-acid  compounds  of  lead; 
also  applied  to  lead  sulphate. 

Carbon?/erons.— Containing  or  carrying  coal. 

Carga  (Mexican).— A charge.  A mule  load,  generally  of  300  pounds,  but 
variable  in  different  parts  of  Mexico. 

Carriage.— See  Cage  and  Slope  Cage. 

Cartridge.— Taper  or  waterproof  cylindrical  case  filled  with  gunpowder, 
forming  the  charge  for  blasting. 

Cascajo  (Mexican).— Gravel. 

Case. — A fissure  admitting  water  into  a mine. 

Case-Harden. — To  convert  the  outer  surface  of  wrought  iron  into  steel  by 
heating  it  while  in  contact  with  charcoal. 

Casing. — Tubing  inserted  in  a bore  hole  to  keep  out  water  or  to  protect  the 
sides  from  collapsing. 

Cast  Iron.— Tig  iron  that  contains  carbon  (up  to  5^),  silicon,  sulphur,  phos- 
phorus, etc. 

Cata  (Spanish).— A mine  denounced  but  not  worked. 

Catches. — (1)  Iron  levers  or  props  at  the  top  and  bottom  of  a shaft.  (2)  Stops 
fitted  on  a cage  to  prevent  cars  from  running  off. 

Catch  Pit.— A reservoir  for  saving  tailings  from  reduction  works. 

Cauf  (North  of  England).— A coal  bucket  or  basket. 

Cauldron  Bottoms.— The  fossil  remains  or  the  “ casts”  of  the  trunks  of  sigil- 
laria  that  have  remained  vertical  above  or  below  the  seam. 

Caulk.— To  fill  seams  or  joints  with  something  to  prevent  leaking. 


578 


Cau 


GLOSSARY. 


Cho 


Cannier,  or  Cannier  Lode  (Cornish).— A vein  running  obliquely  across  the 
regular  veins  of  the  district. 

Cave,  or  Cave  In. — A caving-in  of  the  roof  strata  of  a mine,  sometimes  extend- 
ing to  the  surface. 

Cavils.— Lots  drawn  by  the  hewers  each  quarter  year  to  determine  their 
working  places. 

Cawk. — Baryta  sulphate. 

Cazeador  (Spanish). — Amalgamator. 

Cazo  (Mexican).— A vessel  for  hot  amalgamation.  Any  large  copper  or  iron 
vessel. 

Cebar  (Mexican).— (1)  To  melt  rich  ores,  or  lead  bullion,  etc.  in  a smelting 
furnace.  (2)  To  add  small  quantities  of  material,  from  time  to  time,  to 
the  melted  mass  within  a furnace.  (3)  Generally,  to  feed  any  kind  of 
metallurgical  machinery  or  process. 

Cement— {1)  Auriferous  gravel  consolidated  together.  (2)  A finely  divided 
metal  obtained  by  precipitation.  (3)  A binding  material. 

Cementation.— The  process  of  converting  wTOUght  iron  into  steel  by  heating 
it  in  contact  with  charcoal,  or  of  treating  cast  iron  in  a bed  of  hema- 
tite ore. 

Cendrada  (Mexican).— The  cupel  bottom  of  a furnace. 

Cendradilla  (Mexican). — A small  reverberarory  furnace  for  smelting  rich 
silver  ores  in  a rough  way.  Also  called  Galeme. 

Center. — A temporary  support,  serving  at  the  same  time  as  a guide  to  the 
masons,  placed  under  an  arch  during  the  progress  of  its  construction. 

Centrifngal  Force.— A force  drawing  away  from  the  center. 

Centripetal  Force.— A force  drawing  toward  the  center. 

Marsh  gas  (see  page  348). 

Chain.— A measure  66  or  100  ft.  long,  divided  into  100  links. 

Chain-Brow  Way.— An  underground  inclined  plane  worked  on  the  endless- 
chain  system  of  haulage. 

Chain  Pillar.— A pillar  left  to  protect  the  gangway  and  air-course,  and  run- 
ning parallel  to  these  passages. 

Chain  Road.— An  underground  wagonway  worked  on  the  endless-chain 
system  of  haulage. 

C/iair.— Sometimes  applied  to  keeps. 

Chamber. — See  Breast. 

Char  CO  (Mexican).— A pool  of  water. 

Charge.— {1)  The  amount  of  powder  or  other  explosive  used  in  one  blast  or 
shot.  (2)  The  amount  of  flux  used  in  assaying.  (3)  The  material  fed 
into  a furnace  at  one  time. 

Charqnear  (Mexican).— To  dip  out  water  from  pools  within  the  mine, 
throwing  it  into  gutters  or  pipes  that  will  conduct  it  to  the  shaft. 

Chats. — (1)  The  gravel-like  tailings  derived  from  the  concentration  of  ores. 
(2)  A low-grade  ore,  often  too  poor  to  handle;  the  refuse  from  concen- 
tration works.  (3)  (North  of  England)  Small  pieces  of  stone  with  ore. 

Check-Battery.— A battery  to  close  the  lower  part  of  a chute,  acting  as  a 
check  to  the  flow  of  coal  and  as  an  air  stopping. 

Checker  C'oa?.— Anthracite  coal  that  seems  to  be  made  up  of  rectangular 
grains. 

Check-  Weighman.—A  man  appointed  and  paid  by  the  miners  to  check  the 
weighing  of  the  coal  at  the  surface. 

CAeefc.— Wall. 

Chert— A silicious  rock,  often  the  gangue  of  lead  and  zinc. 

Chestnut  CoaZ.- Anthracite  coal  that  will  pass  through  a mesh  If  in.  square 
and  over  a mesh  f in.  square  (see  page  434). 

Chiflon  (Mexican). — A narrow  drift  directed  obliquely  downwards.  Any 
pipe  from  which  issues  water  or  air  under  pressure,  or  at  high  velocity. 

Chile  Bars.— Bars  of  impure  copper,  weighing  about  200  lb.,  imported  from 
Chile,  corresponding  to  the  Welsh  blister  copper,  containing  98^  Cu. 

Chilian  Mill. — A roller  mill  for  crushing  ore. 

Chill  Hardening. — Giving  a greater  hardness  to  the  outside  of  cast  iron  by 
pouring  it  into  iron  molds,  which  causes  the  skin  of  the  casting  to  cool 
rapidly. 

Chimney.— {!)  An  ore  shoot.  (2)  A furnace  or  air  stack. 

Chinese  Pump.— Lihe  a California  pump,  but  made  entirely  of  wood. 

Chock.— A square  pillar  for  supporting  the  roof,  constructed  of  prop  timber 
laid  up  in  alternate  cross-layers,  in  log-cabin  style,  the  center  being  filled 
with  waste. 


Cho 


GLOSSARY. 


COF 


579 


Chokedamp.—See  Blackdamp. 

Churn  Drill.— A.  long  iron  bar  with  a cutting  end  of  steel,  used  in  quarrying, 
and  worked  by  raising  and  letting  it  fall.  When  worked  by  blows  of  a 
hammer  or  sledge,  it  is  called  a “ jumper.” 

Chute  (also  spelled  Shute). — (1)  A narrow  inclined  passage  in  a mine,  down 
which  coal  or  ore  is  either  pushed  or  slides  by  gravity.  (2)  The  load- 
ing chute  of  a tipple. 

Chuza  (Spanish).— A catch  basin  for  mercury. 

Cielo  (Mexican.) — A ceiling.  Trabajar  de  Cielo. — Overhead  stoping. 

Cmr^abar.— Mercury  and  sulphur. 

Clack. — A valve  that  is  opened  and  closed  by  the  force  of  the  water. 

Clack  Door. — The  opening  into  the  valve  chamber  to  facilitate  repairs  and 
renewals  without  unseating  the  pump  or  breaking  the  connections. 

Clack  Piece. — The  casting  forming  the  valve  chamber. 

Clack  The  receptacle  for  the  valve  to  rest  on. 

Claggy  (North  of  England).— When  coal  is  tightly  joined  to  the  roof. 

Claim.— A portion  of  ground  staked  out  and  held  by  virtue  of  a miner’s 
right. 

Clanny.—A  type  of  safety  lamp  invented  by  Dr.  Clanny. 

C'^as^^c.— Constituted  of  rocks  or  minerals  that  are  fragments  derived  from 
other  rocks. 

Clay  Course. — A clay  seam  or  gouge  found  at  the  sides  of  some  veins. 

Claying  Bar.—¥ov  molding  clay  in  a wet  bore  hole. 

Clay  J5and.— Argillaceous  iron  ore;  common  in  many  coal  measures. 

Clean-  Up. — Collecting  the  product  of  a period  of  work  with  battery  or  sluice. 

Clearance.— il)  The  distance  between  the  piston  at  the  end  of  its  stroke  and 
the  end  of  the  cylinder.  (2)  The  volume  or  entire  space  filled  with 
steam  at  end  of  a stroke  including  the  space  between  piston  and 
cylinder  head,  and  the  steam  ducts  to  the  valve  seat. 

Cleat.— {1)  Vertical  cleavage  of  coal  seams,  irrespective  of  dip  or  strike.  (2) 
A small  piece  of  wood  nailed  to  two  planks  to  keep  them  together,  or 
nailed  to  any  structure  to  make  a support  for  something  else. 

Cleavage. — The  property  of  splitting  more  readily  in  some  directions  than  in 
others. 

Clinometer.— An  instrument  used  to  measure  the  angle  of  dip. 

C/od.— Soft  and  tough  shale  or  slate  forming  the  roof  or  floor  of  a coal  seam. 

' Closed  Season.— When  placers  cannot  be  worked. 

Clunch  (English).— Under  clay,  fireclay. 

Clutch.— An  arrangement  at  the  end  of  separate  shafts  by  means  of  which 
they  catch  into  each  other,  so  that  both  can  revolve  together. 

Coal  Breaker.— ^ee  Breaker. 

Coal  Cutter. — A machine  for  holing  or  undercutting  coal. 

Coal  Dust.—Yerj  finely  powdered  coal  suspended  in  the  airways  of  a mine. 

Coal  Measures.— strata  of  coal  with  the  attendant  rocks. 

Coal  Pipes  (North  of  England).— Very  thin  irregular  coal  beds. 

Coal  Road. — An  underground  roadway  or  heading  in  coal. 

Coal  Smut. — See  Blossom. 

Coaly  Rashings.—Soft  dark  shale,  in  small  pieces,  containing  much  carbona- 
ceous matter. 

Coarse  (Chose).— When  lode  stuff  is  not  rich,  the  ore  being  only  thinly  dis- 
seminated throughout  it. 

Coarse  Metal. — In  copper  smelting,  the  compound  containing  the  copper 
concentrated  in  it  after  the  first  smelting  to  get  rid  of  the  bulk  of  the 
gangue  in  the  ore. 

Coaster. — One  that  picks  ore  from  the  dump. 

Coh  (Cornish). — To  break  up  ore  for  sorting. 

Cobbing  Hammer.— A short  double-ended  hammer  for  breaking  minerals  to 
sizes. 

Cobre. — Cuban  copper  ores. 

Cockermeg,  or  ChcA:m.— Timber  used  to  hold  coal  face  while  it  is  being 
undercut. 

Cockle  (Cornish).— Black  tourmaline,  often  mistaken  for  tin. 

Cod  (North  of  England).— The  bearing  of  an  axle. 

Cofer  (Derbyshire). — To  calk  a shaft  by  ramming  clay  behind  the  lining. 

Coffer. — Mortar  box  of  a battery. 

Coffer  Dam. — An  enclosure  built  in  the  water,  and  then  pumped  dry,  so  as  to 
permit  masonry  or  other  work  to  be  carried  on  inside  of  it. 

Coffin  (Cornish).— An  old  pit, 


580 


Cog 


GLOSSARY. 


Cor 


Cog.—K  chock. 

Cohete  (Mexican).— A rocket;  applied  to  a blast  within  a mine  or  outside. 

Coil  Brag— A tool  for  picking  pebbles,  etc.  from  drill  holes. 

Coke— The  fixed  carbon  and  ash  of  coal  sintered  together. 

C'o^as  (Spanish).— Tailings  from  a stamp  mill  or  any  wet  process. 

Collar— {1)  A flat  ring  surrounding  anything  closely.  (2)  Collar  of  a shaft 
is  the  first  wood  frame  of  a shaft.  (3)  The  bar  or  crosspiece  of  a framing 
in  entry  timbering. 

Colliery— The  whole  plant,  including  the  mine  and  all  adjuncts. 

Colliery  Warnings  (English).— Telegraphic  messages  sent  from  signal-service 
stations  to  the  principal  colliery  centers  to  warn  managers  of  mines 
when  sudden  falls  of  the  barometer  occur. 

Colorados  (Spanish).— Decomposed  ores  stained  with  iron. 

Colores  (Mexican).— Metal-stained  ground  or  rocks. 

Colrake—A  shovel  for  stirring  lead  ores  while  washing. 

Co^or.— Minute  traces  or  individual  specks  of  gold. 

Column,  or  Column  Pipe— The  pipe  conveying  the  drainage  water  from  the 
mine  to  the  surface. 

Comer  (Mexican).— To  eat.  Comerse  los  Pilares— To  take  out  the  last  vestiges 
of  mineral  from  the  sides  and  rock  pillars  of  a mine. 

Conchoidal. — Shell-like,  such  as  the  curved  fracture  of  flint. 

Concrete.- Artificial  stone,  formed  by  mixing  broken  stone,  gravel,  etc.  with 
lime,  cement,  tar,  or  other  binder.  When  hydraulic  cement  is  used 
instead  of  lime,  the  mixture  is  called  beton  (English). 

Concretion —A  cemented  aggregation  of  one  or  more  kinds  of  minerals 
around  a nucleus. 

Conduit.— {1)  A covered  waterway.  (2)  An  airway. 

Conduit  Hole.— A flat  hole  drilled  for  blasting  up  a thin  piece  in  the  bottom 
of  a level. 

Conductors  (English). — See  Guides. 

Conformable.— strata  are  conformable  when  they  lie  one  over  the  other  with 
the  same  dip. 

Conglomerate. — The  rock  formation  underlying  the  Coal  Measures;  a rock 
containing  or  consisting  of  pebbles,  or  of  fragments  of  other  rocks 
cemented  together;  English  Pudding  Rock  or  millstone  grit. 

Conical  Drum. — The  rope  roll  or  drum  of  a winding  engine,  constructed  in 
the  form  of  two  truncated  cones  placed  back  to  back,  the  outer  ends 
being  usually  the  smaller  in  diameter. 

Consumido  (Mexican).— The  amount  of  mercury  that  disappears  by  chem- 
ical combination  during  the  treatment  of  ore  by  any  amalgamation 
process. 

Contact.— Ynion  of  different  formations. 

Contact  Load  or  Vein. — A vein  lying  between  two  differently  constituted 
rocks. 

Contour.— {1)  The  line  that  bounds  the  figure  of  an  object.  (2)  In  survey- 
ing, a contour  line  is  a line  every  point  of  which  is  at  an  equal  elevation. 

Conteamwa  (Mexican). — Countermine.  Any  communication  between  two 
or  more  mines.  Also,  a tunnel  communicating  with  a shaft. 

Cope  (Derbyshire). — Lead  mining  on  contract. 

Cope,  or  Coup.— An  exchange  of  working  places  between  hewers. 

Copelilla  ( Spanish ) .-Zinc-blende. 

Copella  (Spanish).— Dry  amalgam. 

Copper  Plate. — A sheet  of  copper  that,  when  coated  with  mercury,  is  used  in 
amalgamation. 

Corbond.—An  irregular  mass  from  a lode. 

Cord.— A cord  weighs  about  8 tons. 

Co?'es.— Cylinder-shaped  pieces  of  rock  produced  by  the  diamond-drill  system 
of  boring. 

Corf.— A mine  wagon  or  tub. 

Cornish  Pumps. — A single-acting  pump,  in  which  the  motion  is  transmitted 
through  a walking  beam;  in  other  respects  similar  to  a Bull  Pump. 

Coro-Coro  (South  American). — Grains  of  native  copper  mixed  with  pyrite, 
chalcopyrite,  mispickel,  etc. 

Cortar  Pillar  (Mexican). — To  form  a rock  support  or  pillar  within  a mine, 
at  the  opening  of  a cross-cut  or  elsewbere. 

Cortar  Sogas  (Mexican). — Literally,  to  cut  the  ropes.  To  abandon  the  mine, 
taking  away  everything  useful  or  movable. 

Corve.—A  mining  wagon  or  tub. 


Cos 


GLOSSARY. 


Cro 


581 


Costean  (Cornish).— To  prospect  a lode  by  sinking  pits  on  its  supposed 
course. 

Trenching  for  a lode. 

Cost  Book  (Cornish).— Mining  accounts. 

Cotton  Rock.— {1)  Decomposed  chert.  (2)  A variety  of  earthy  limestone. 

Coulee.— {1)  A solified  stream  or  sheet  of  lava  extending  down  a volcano, 
often  forming  a ridge  or  spur.  (2)  A deep  gulch  or  water  channel, 
usually  dry. 

Counter.— {1)  A cross-vein.  (2)  (English)  An  apparatus  for  lecording  the 
number  of  strokes  made  by  the  Cornish  pumping  engine.  (3)  A second- 
ary haulageway  in  a coal  mine. 

Counterchute.^X  chute  down  which  coal  is  dumped  to  a lower  level  or 
gangway. 

Counter  gangway. —X  level  or  gangway  driven  at  a higher  level  than  the 
main  one. 

Country.— TYiq  formation  traversed  by  a lode. 

Country  i^ocA;.— The  main  rock  of  the  region  through  which  the  veins  cut, 
or  that  surrounding  the  veins. 

Course.- The  direction  of  a line  in  regard  to  the  points  of  compass. 

Coursing  or  Coursing  the  Air. — Conducting  it  through  the  different  portions 
of  a mine  by  means  of  doors,  stoppings,  and  brattices. 

Cow.—X  self-acting  brake. 

Coyoting.— IrvQgyxlav  mining  by  small  pits. 

Crab.—X  variety  of  windlass  or  capstan  consisting  of  a short  shaft  or  axle, 
either  horizontal  or  vertical,  which  serves  as  a rope  drum  for  raising 
weights;  it  may  be  worked  by  a winch  or  handspikes. 

Crab  Holes.— Roles  often  met  with  in  the  bed  rock  of  alluvial.  Also  depres- 
sions on  the  surface  owing  to  unequal  disintegration  of  the  underlying 
rock. 

Cradle.— X box  with  a sieve  mounted  on  rockers  for  washing  auriferous 
alluvial. 

Cradle  Dump.—X  rocking  tipple  for  dumping  cars.  See  Dump. 

Cramp  (English).— (1)  A short  bar  of  metal  having  its  two  ends  bent  down- 
wards at  right  angles  for  insertion  into  two  adjoining  pieces  of  stone, 
wood,  etc.  to  hold  them  together.  (2)  A pillar  left  for  support  in  a mine. 

Cranch.— Fart  of  a vein  left  by  previous  workers. 

Crane  (English).— A hoisting  machine  consisting  of  a revolving  vertical 
post  or  stalk,  a projecting  jib,  and  a stay  for  sustaining  the  outer  end  of 
the  jib;  these  do  not  change  their  relative  positions  as  they  do  in  a 
derrick.  There  is  also  a rope  drum  with  winding  rope,  etc. 

Create  (Cornish).— (1)  Tin  ore  collected  in  the  middle  of  the  huddle.  (2)  The 
middle  of  a huddle. 

Creep.— The  gradual  upheaval  of  the  floor  or  sagging  of  the  roof  of  mine 
workings  due  to  the  weighting  action  of  the  roof  and  a tender  floor. 

Creston  (Mexican).— The  outcrop  or  apex  of  a vein  or  mineral  deposit. 

Crevice.— X fissure. 

C revicing. —Fieking  out  the  gold  caught  in  cracks  and  crevices  in  the  rocks 
over  which  it  has  been  washed. 

Criadero  (Mexican).— (1)  A mineral  deposit  of  irregular  form,  not  vein-like. 
(2)  A chamber  in  a vein  filled  with  ore  of  more  or  less  richness.  (3)  Any 
mineral  deposit.  This  latter  is  the  more  modern  sense,  and  the  word  is 
so  used  in  the  mining  laws  at  present  in  force  in  Mexico. 

Crib.—{1)  X structure  composed  of  horizontal  timbers  laid  on  one  another, 
or  a iramework  built  like  a log  cabin.  See  Chock.  (2)  A miner’s  lunch- 
eon. (3)  See  Curb. 

Cribbing.— Close  timbering,  as  the  lining  of  a shaft,  or  the  construction  of 
cribs  of  timber,  or  timber  and  earth  or  rock  to  support  a roof. 

Cribble.— X sieve. 

Crisol  (Mexican).— A crucible  of  any  kind. 

Crop. — See  Outcrop. 

Crop  Fall.—X  caving  in  of  the  surface  at  or  near  the  outcrop  of  a bed  of  coal. 

Cropping  Coal. — The  leaving  of  a small  thickness  of  coal  at  the  bottom  of  the 
seam  in  a working  place,  usually  in  order  to  keep  back  water.  The  coal 
so  left  is  termed  “ Cropper  Coal.” 

Croppings.— FoTtions  of  a vein  as  seen  exposed  at  the  surface. 

Cropping  Owi.— Appearing  at  the  surface;  outcropping.  ; 

Cross- Course. —X  vein  lying  more  or  less  at  right  angles  to  the  regular  vein  of 
the  district.  t.;  : 


582 


Cro 


GLOSSARY. 


Deb 


Crosscut. — (1)  A tunnel  driven  tlirough  or  across  the  measures  from  one 
seam  to  another.  (2)  A small  passageway  driven  at  right  angles  to  the 
main  gangway  to  connect  it  with  a parallel  gangway  or  air-course. 

Crosses  and  Holes  (Derbyshire). — Made  in  the  ground  ijy  the  discoverer  of  a 
lode  to  tempoiarily  secure  possession. 

Cross-Heading. — A passage  driven  for  ventilation  from  the  airway  to  the  gang- 
way, or  from  one  breast  through  the  pillar  to  the  adjoining  working. 

Cross-Heading,  or  Cross-Gateway. — A road  kept  through  goaf  and  cutting  off 
the  gateways  at  right  angles  or  diagonally. 

Cross- Hole. — See  Crosscut  (2). 

Cross- Latches. — See  Latches. 

Cross-Spur.— A vein  of  quartz  that  crosses  the  reef. 

Cross-  rein.— An  intersecting  vein. 

Crouan  (Cornish).— Granite. 

Crowbar.— A strong  iron  bar  with  a slightly  curved  and  flattened  end. 

Crowfoot.— A tool  for  drawing  broken  boring  rods. 

Crown  Tree.— A piece  of  timber  set  on  props  to  support  the  roof. 

Crucero  (Mexican).— A crosscut  for  ventilation  to  get  around  a horse,  or  to 
prospect  for  the  vein. 

Cru^le.—{1)  The  bottom  of  a cupola  furnace  in  which  the  molten  materials 
collect.  (2)  Pots  for  smelting  assays  in. 

Crush. — See  ^ueeze,  Thrust. 

Crusher.— A machine  used  for  crushing  ores  and  rock. 

Crushing.— Reduction  of  mineral  in  size  by  machinery. 

Crystal.— A solid  of  definite  geometrical  form,  which  mineral  (or  sometimes 
organic)  matter  has  assumed. 

Cu^m.— Anthracite-coal  dirt. 

Culm  Bank,  or  Culm  Dump. — Heaps  of  culm  now  generally  kept  separate 
from  the  rock  and  slate  dumps. 

Cuha  (Mexican). — Literally,  a wedge.  A short  drill  or  picker  generally 
known  in  the  United  States  as  a “gad.” 

Cupel. — A cup  made  of  bone  ash  for  absorbing  litharge. 

Curb.— (1}  A timber  frame  intended  as  a support  or  foundation  for  the  lining 
of  a snaft.  (2)  The  heavy  frame  or  sill  at  the  top  of  a shaft. 

Curbing.— TRe  wooden  lining  of  a shaft. 

Cut. — (1)  To  strike  or  reach  a vein.  (2)  To  excavate  in  the  side  of  a hill. 

Cutter. — A term  employed  in  speaking  of  any  coal-cutting  or  rock-cutting 
machines;  the  men  operating  them,  or  the  men  engaged  in  underholing 
by  pick  or  drill. 

Cutting  Dovm.—To  cut  down  a shaft  is  to  increase  its  sectional  area. 

Dim.— A timber  bulkhead,  or  a masonry  or  brick  stopping  built  to  prevent 
the  water  in  old  workings  from  flooding  other  workings,  or  to  confine 
the  water  in  a mine  flooded  to  dro^vn  out  a mine  fire. 

Damu. —Mine  gases  and  gaseous  mixtures  are  called  dami)s.  See  also  After- 
damp, Blackdamp,  Firedamp,  Stinkdamp. 

Dan  (North  of  England).— A truck  without  wheels. 

Danger  Board. — See  Fireboard. 

Dant  (North  of  England). — Soft  inferior  coal. 

Datum  Water  Level.— The  level  at  which  water  is  first  struck  in  a shaft 
sunk  on  a reef  or  gutter. 

Davy.— A safety  lamp  invented  by  Sir  Humphrey  Davy. 

Day.— Light  se'en  at  the  top  of  a shaft. 

Day  Fall. — See  Crop  Fall. 

Day  Shift. — The  relay  of  men  working  in  the  daytime. 

Dead. — The  air  of  a mine  is  said  to  be  dead  or  heavy  when  it  contains  car- 
bonic-acid gas,  or  when  the  ventilation  is  sluggish. 

Dead. — (1)  Unproductive.  (2)  Unventilated. 

Dead  Men's  Graves  (Australian). — Grave-like  mounds  in  the  basalt  under- 
l3ring  auriferous  gravels. 

Dead  Quartz. — Quartz  canying  no  mineral. 

Dead  Riches.— t^d  carrying  much  bullion. 

Dead  RoaM.— To  completely  drive  off  all  volatile  substances. 

Deads. — Waste  or  rubbish  from  a mine. 

Dead  TUarfc.- Exploratory  or  prospecting  work  that  is  not  directly  productive. 
Brushing  roof,  lifting  bottom,  cleaning  up  falls,  blowing  roek,  etc. 

Dean  (Cornish). — The  end  of  a level. 

D^rw.- Fragments  from  any  kind  of  disintegration. 


Dee 


GLOSSARY. 


Dip 


583 


Deep  (English).—"  To  the  deep,”  toward  the  lower  portion  of  a mine;  hence, 
the  lower  workings. 

Delta.— A.  triangularly  shaped  piece  of  alluvial  land  at  the  mouth  of  the 
river. 

Demasia  (Mexican).— A piece  of  unoccupied  ground  between  two  mining 
concessions. 

Denudation. — The  laying  bare  by  water  or  other  agency. 

Denuncio  (Mexican).— Denouncement.  The  act  of  applying  for  a mining 
concession  under  the  old  mining  laws. 

Deposit. — (1)  Irregular  ore  bodies  not  veins.  (2)  A bed  or  any  sedimentary 
formation. 

Deputy  (English).— (1)  A man  who  fixes  and  withdraws  the  timber  sup- 
porting the  roof  of  a mine,  and  attends  to  the  safety  of  the  roof  and 
sides,  builds  stoppings,  puts  up  bratticing,  and  looks  after  the  safety  of 
the  hewers,  etc.  (2)  An  underground  official  who  sees  to  the  general 
safety  of  a certain  number  of  stalls  or  of  a district,  but  does  not  set 
the  timber  himself,  although  he  has  to  see  that  it  is  properly  and  suffi- 
ciently done.  (3)  (American)  A deputy  sheriff. 

Derrick. — (1)  A crane  in  which  the  rope  or  chain  forming  the  stay  can  be 
let  out  or  hauled  in  at  pleasure,  thus  altering  the  inclination  of  the  jib. 
(2)  The  structure  erected  to  sink  a drill  hole  and  the  framework  above 
shafts  are  sometimes  called  by  this  name. 

Derrumbe,  or  Derrumbamineto  (Mexican). — The  caving  in  of  the  whole  or  a 
portion  of  a mine. 

Desaguador  (Spanish).— A water  pipe  or  drain. 

Desague  (Mexican).— Drainage  of  a mine  by  any  means. 

Descargar  (Mexican). — Literally,  ‘‘to  unload.”  Descargar  un  Homo. — To 
tear  down  a furnace. 

Descubridora  (Mexican).— The  first  mine  opened  in  a new  district  or  on  a 
new  mineral  deposit. 

Desecho  (Spanish). — Foul  red  mercury. 

Desfrute  (Mexican). — Taking  out  ore.  'Ohras  de  Desfrute. — Stopes,  etc. 

Desmontar  (Mexican).— Literally,  to  clear  away  underbrush.  In  mining,  to 
take  away  useless  and  barren  rocks;  to  remove  rubbish. 

Desmontes  (Spanish). — Poor  ores. 

Despmsa  (Mexican). — (1)  A pantry  or  storeroom.  (2)  A secure  room  to  lock 
up  rich  ore. 

Despoblado  (Spanish).— Ore  with  much  gangue. 

Despoblar  (Mexican).— To  suspend  work  in  a mine. 

Dessue  (Cornish).— To  cut  away  the  ground  beside  a thin  vein  so  as  to 
remove  the  latter  whole. 

Destajo  (Mexican).— (1)  A contract  to  do  any  kind  of  work  in  or  about  a 
mine  or  elsewhere  for  a fixed  price.  (2)  Piece  work,  as  distinguished 
from  time  work.  Destajero. — A contractor  for  piece  work. 

Detaching  Hook.— A self-acting  mechanical  contrivance  for  setting  free  a 
winding  rope  from  a cage  when  the  latter  is  raised  beyond  a certain 
point  in  the  head-gear;  the  rope  being  released,  the  cage  remains 
suspended  in  the  frame. 

Devil's  Dice.— Cubes  of  limonite,  pseudomorphs  after  pyrites. 

Diagonal  Joints  diagonal  to  the  strike  of  the  cleavage. 

Dial  (English).— An  instrument  similar  to  a surveyor’s  compass,  with 
vernier  attached. 

Surveying. 

Die.— The  bottom  iron  block  of  a battery,  or  grinding  pan  on  which  the 
shoe  acts. 

Digging. — Mining  operations  in  coal  or  other  minerals. 

Diggings.— here  gold  and  other  minerals  are  dug  out  from  shallow 
alluvials. 

Dike.—^ee  also  Dyke. 

Dillits,  or  Ginneys.— Short  self-acting  inclines  where  one  or  two  tubs  at  a 
time  are  run. 

Dillueing  (Cornish). — Dressing  tin  slimes  in  a fine  sieve. 

Dip.—{i)  To  slope  downwards.  (2)  The  inclination  of  strata  with  a hori- 
zontal plane.  (3)  The  lower  workings  of  a mine. 

Dip  Joint. — Vertical  joints  about  parallel  to  the  direction  of  the  cleavage  dip. 

Dippa  (Cornish).— A small  catch-water  pit. 

Dipping  Needle.— A magnetic  needle  suspended  in  a vertical  plane;  for 
locating  iron  deposits. 


584 


Dir 


GLOSSARY, 


Dbe 


Dirt  FauU.^A  confusion  in  a seam  of  coal,  the  toj)  and  bottom  of  the  seam 
being  well  defined,  but  the  body  of  the  vein  being  soft  and  dirty. 

Dish  (Cornish).— An  ore  measure;  in  lead  mines,  a trough  28  in.  long,  4 in. 
deep,  and  6 in.  broad;  sometimes  1 gallon,  sometimes  14  to  16  pints. 

Disintegration.— Sep&rsition  by  mechanical  means,  not  by  decomposition. 

Ditch.— {1)  The  drainage  gutter  in  a mine.  (2)  A drainage  gutter  on  the 
surface.  (3)  An  open  conveyor  of  water  for  hydraulic  or  irrigation 
purposes. 

Divide.— The  top  of  a ridge,  hill,  or  mountain. 

Dividing  Slate. — A stratum  of  slate  separating  two  benches  of  coal.  See 
Parting. 

Divining,  or  Dowsing,  Rod.— A small  forked  hazel  twig  that,  when  held 
loosely  in  the  hands,  is  supposed  to  dip  downwards  when  passing  over 
water  or  metallic  minerals. 

Dizzue  {Cornish).— See  Dessue. 

Dog.—{l)  An  iron  bar,  spiked  at  the  ends,  with  which  timbers  are  held 
together  or  steadied.  (2)  A short  heavy  iron  bar,  used  as  a drag  behind 
a car  or  trip  of  cars  when  ascending  a slope  to  prevent  their  running 
back  down  the  slope  in  case  of  accident.  See  Drag. 

Dog  Hole.— A little  opening  from  one  place  in  a mine  to  another,  smaller 
than  a breakthrough. 

Dog  Iron.— A short  bar  of  iron  with  both  ends  pointed  and  bent  down  so  as 
to  hold  together  two  pieces  of  wood  into  which  the  points  are  driven. 
Or  one  end  may  be  bent  down  and  pointed,  while  the  other  is  formed 
into  an  eye,  so  that  if  the  point  be  driven  into  a log,  the  other  end  may 
be  used  to  haul  on. 

Doles.— Small  piles  of  assorted  or  concentrated  ore. 

Dolly.— {!)  A machine  for  breaking  up  minerals,  being  a rough  pestle  and 
mortar,  the  former  being  attached  to  a spring  pole  by  a rope.  (2)  A 
tool  used  to  sharpen  drills. 

Dolly  Tub  (Cornish).— A tub  in  which  ore  is  washed,  being  agitated  by  a 
dolly  or  perforated  boards. 

Donk  (North  of  England).— Soft  mineral  found  in  cross-veins. 

Donkey  Engine  (English).— (1)  A small  steam  engine  attached  to  a large  one, 
and  fed  from  the  same  boiler;  used  for  pumping  water  into  the  boiler. 
(2)  A small  steam  engine. 

Door  Piece  (English).— The  portion  of  a lift  of  pumps  in  which  the  clack  or 
valve  is  situated. 

Z>oors.— Wooden  doors  in  underground  roads  or  airways  to  deflect  the  air- 
current. 

Door  Tender.— A boy  whose  duty  it  is  to  open  and  close  a mine  door  before 
and  after  the  passage  of  a train  of  mine  cars. 

Dope.— An  absorbent  for  holding  a thick  liquid.  The  material  that  absorbs 
the  nitroglycerine  in  explosives. 

Double  Shift. — When  there  are  two  sets  of  men  at  work,  one  set  relieving  the 
other. 

Double  Tape  Fuse.— Fuse  of  superior  quality,  or  having  a heavier  and  stronger 
covering. 

Double  Timber.— Tvfo  props  with  a bar  placed  across  the  tops  of  them  to  sup- 
port the  roof  and  sides. 

Downcast.— The  opening  through  which  the  fresh  air  is  drawn  or  forced  into 
the  mine;  the  intake. 

Dradg'e  (Cornish).— (1)  Inferior  ore  separated  from  the  prill.  (2)  Pulverized 
refuse. 

Draftage.—A  deduction  made  from  the  gross  weight  of  ore  when  transported, 
to  allow  for  loss. 

Drag.—{1)  The  frictional  resistance  offered  to  a current  of  air  in  a mine. 
(2)  See  Dog. 

Draw.—{1)  To  “ draw  ” the  pillars;  robbing  the  pillars  after  the  breasts  are 
exhausted.  (2)  An  effect  of  creep  upon  the  pillars  of  a mine. 

Draw  a Charge. — To  take  a charge  from  a furnace. 

Drawlift.—A  pump  that  receives  its  water  by  suction  and  will  not  force  it 
above  its  head. 

Draw-Hole.— An  aperture  in  a battery  through  which  the  coal  is  drawn. 

Drawing  an  Entry.— Removing  the  last  of  the  coal  from  an  entry. 

Drawn.— The  condition  in  which  an  entry  or  room  is  left  after  all  the  coal 
has  been  removed,  ^ee  Robbed. 

Dresser  (Staffordshire).— A large  coal  pick. 


Dre 


GLOSSARY. 


Egg 


585 


Preparing  poor  or  mixed  ores  mechanically  for  metallurgical 
operations. 

Dressing  Floors.— TYiq  floors  or  places  where  ores  are  dressed. 

Drift.— \l)  A horizontal  passage  underground.  A drift  follows  the  vein,  as 
distinguished  from  a crosscut,  which  intersects  it,  or  a level  or  gallery, 
which  may  do  either.  (2)  In  coal  mining,  a gangway  above  water 
level,  driven  from  the  surface  in  the  seam.  (3)  Unstratified  diluvium. 

Drifting.— Yfirming  pay  dirt  from  the  ground  by  means  of  drives. 

Drill.— An  instrument  used  in  boring  holes. 

Drive  {Drift).  A horizontal  passage  in  a lode. 

Drive.— To  cut  an  opening  through  strata. 

Driwwsr.— Excavating  horizontal  passages,  in  contradistinction  to  sinking  or 
raising. 

Di'iving  on  Line.— Keeping  a heading  or  breast  accurately  on  a given  course 
by  means  of  a compass  or  transit. 

Dropper. — (1)  A spur  dropping  into  the  lode.  (2)  A feeder.  (3)  A branch 
leaving  the  vein  on  the  footwall  side.  (4)  Water  dropping  from  the  roof. 

Drop  Shaft. — A monkey  shaft  down  which  earth  and  other  matter  are  lowered 
by  means  of  a drop  (i.  e.,  a kind  of  pulley  with  break  attached);  the 
empty  bucket  is  brought  up  as  the  full  one  is  lowered. 

Druggon  (Stafibrdshire).— A vessel  for  carrying  fresh  water  into  a mine. 

Drum.-TYie  cylinder  or  pulley  on  which  the  winding  ropes  are  coiled  or 
wound. 

Drum  Rings.— Q2i^i-iTon  rings  with  projections  to  which  are  bolted  the 
laggings  forming  the  surface  for  the  ropes  to  lap  on. 

Drummy.— Sounding  loose,  open,  shaky,  or  dangerous  when  tested. 

Druse. — A hollow  cavity  lined  with  small  crystals. 

Dry  Amalgamation.— Treating  ores  with  hot,  dry  mercury. 

Dry  Diggings.— Yiaeers  never  subject  to  overflow. 

Dry  Ore.— Argentiferous  ores  that  do  not  contain  enough  lead  for  smelting 
purposes. 

Duck  Machine.— An  arrangement  of  two  boxes,  one  working  within  the 
other,  for  forcing  air  into  mines. 

Duelas  (Mexican).— Staves  of  a barrel  or  cask,  etc*. 

Dumb'd.— Choked,  of  a sieve  or  grating. 

Dumb  Drift— A short  tunnel  or  passage  connecting  the  main  return  airways 
of  a mine  with  the  upcast  shaft  some  distance  above  the  furnace,  in  order 
to  prevent  the  return  air  laden  with  mine  gases  from  passing  through  or 
over  the  ventilating  furnace. 

Dump.—{\)  A pile  or  heap  of  ore,  coal,  culm,  slate,  or  rock.  (2)  The  tipple 
by  which  the  cars  are  dumped.  (3)  To  unload  a car  by  tipping  it  up. 
(4)  The  pile  of  mullock  as  discharged  from  a mine. 

Dumper.— A car  so  constructed  that  the  body  may  be  revolved  to  dump  the 
material  in  front  or  on  either  side  of  the  track. 

Durn  (Cornish). — A timber  frame. 

Durr  (German).— Barren  ground. 

Dust.— See  Coal  Dust. 

Dust  Gold.—Yieees,  under  2 to  3 dwt. 

Duty.-TYie  unit  of  measure  of  the  work  of  a pumping  engine  expressed  in 
foot-pounds  of  work  obtained  from  a bushel,  or  100  lb.,  or  other  unit  of 
fuel. 

Dyke^  or  Dike.—{1)  A wall  of  igneous  rock  passing  through  strata,  with  or 
without  accompanying  dislocation  of  the  strata.  (2)  A fissure  filled  with 
igneous  matter.  (3)  Barren  rock. 

Dzhu  (Cornish).— See  Dessue. 

Ear.— The  inlet  or  intake  of  a fan. 

Echadero  (Mexican).— A level  place  near  a mine  where  ore  is  cleaned,  piled, 
weighed,  and  loaded  on  mules  or  other  conveyance.  Also  called  patio  of 
the  mine. 

Echado  (Mexican).— The  dip  of  the  vein. 

Edge  Coals  (English).— Highly  inclined  seams  of  coal,  or  those  having  a dip 
greater  than  30°. 

Efflorescence.— An  incrustation  by  a secondary  mineral,  due  to  loss  of  water 
of  crystallization. 

Efydd  (Wales).— Copper. 

Egg  Coo?.— Anthracite  coal  that  will  pass  through  a 2i"  square  mesh  and 
over  a 2"  square  mesh  (see  page  434). 


586 


Elb 


GLOSSARY. 


Pal 


Elbow— A sharp  bend,  as  in  a lode  or  pipe. 

Electric  Instantaneous  blasting  of  rock  by  means  of  electricity. 

Elevator  Pump—Kn  endless  band  with  buckets  attached,  running  over  two 
drums  for  draining  shallow  ground. 

Elvan.—A  Cornish  name  applied  to  most  dike  rocks  of  that  county,  irre- 
spective of  the  mineral  constitution,  but  in  the  present  day  restricted 
to  quartz  porphyries. 

Emborrascarse  (Mexican).— To  go  barren  by  the  vein  terminating  or  pinching 
out,  etc. 

Empties.— Empty  mine  or  railroad  cars. 

Encino  (Mexican). — Live  oak. 

End  Joint  (End  Cleat).— A joint  or  cleat  in  a seam  about  at  right  angles  to 
the  principal  or  race  cleats. 

Endless  Chain. — A system  of  haulage  or  pumping  by  the  moving  of  an 
endless  chain. 

Endless  Rope. — A system  of  haulage  same  as  endless  chain,  except  that  a 
, wire  rope  is  used  instead  of  chain. 

End,  or  End-On.— Working  a seam  of  coal  at  right  angles  to  the  principal 
or  face  cleats. 

Engine  Plane. — An  incline  up  which  loaded  cars  are  drawn  by  a rope 
operated  by  an  engine  located  at  the  top  or  bottom  of  the  incline.  The 
empty  cars  descend  by  gravity,  pulling  the  rope  after  them. 

Engineer. — (1)  One  who  has  charge  of  the  surveying  or  machinery  about  a 
mine.  (2)  One  who  runs  an  engine. 

Ensayes  (Mexican).— Assays. 

Entibar  (Mexican)'.— To  timber  a mine  or  any  part  thereof. 

Entry.— A main  haulage  road,  gangway,  or  airway.  An  underground  passage 
used  for  haulage  or  ventilation,  or  as  a manway. 

Entry  Stumps. — Pillars  of  coal  left  in  the  mouths  of  abandoned  rooms  to 
support  the  road,  entry,  or  gangway  till  the  entry  pillars  are  drawn. 

Erosion.- The  wearing  away  of  rocks  by  rains,  etc. 

Escaleras  (Mexican).— Ladders,  generally  made  of  notched  sticks. 

Escarpment. — A nearly  vertical  natural  face  of  rock  or  soil. 

Escoria  (Mexican). — Slag  or  cinders. 

Escoriai.— Slag  pile. 

Esconficador  (Mexican). — A scorifier,  in  assaying. 

Espejuelo  (Mexican).— A mineral  gangue,  with  a faintly  reflecting  surface. 

Espeton  (Mexican).— The  tapping  bar  of  a smelting  furnace. 

Estano  (Spanish). — Tin. 

Estrujon  (Mexican). — A second  collection  of  amalgam,  generally  verj^  pasty. 

Exploder.— A chemical  employed  for  the  instantaneous  explosion  of  powder. 

Exploitation. — The  working  of  a mine,  and  similar  undertakings;  the  exami- 
nation instituted  for  that  purpose. 

Exploration. — Development. 

Explosion. — Sudden  ignition  of  a body  of  firedamp. 

Eye  (English).— (1)  A circular  hole  in  a bar  for  receiving  a pin  and  for 
other  purposes.  (2).  The  eye  of  a shaft  is  the  very  beginning  of  a pit. 
(3)  The  eye  of  a fan  is  the  central  or  intake  opening. 

Face.— (1)  The  place  at  which  the  material  is  actually  being  worked,  either 
in  a breast  or  heading  or  in  longwall.  (2)  The  end  of  a drift  or  tunnel. 

Face-On. — When  the  face  of  the  breast  or  entry  is  parallel  to  the  face  cleats 
of  the  seam  (see  page  285). 

Face  Wall.— A wall  built  to  sustain  a face  cut  into  the  natural  earth,  in 
distinction  to  a retaining  wall,  which  supports  earth  deposited  behind  it. 

Faenas  (Mexican).— Dead  work,  in  the  way  of  development. 

Fahlband  (German). — A course  impregnated  with  metallic  sulphides. 

Faiscador  (Spanish). — A gold  washer. 

Fall.—{1)  A mass  of  roof  or  side  which  has  fallen  in  any  part  of  a mine. 
(2)  To  blast  or  wedge  down  coal. 

False  Bedding. — Irregular  lamination,  wherein  the  laminae,  though  for 
short  distances  parallel  to  each  other,  are  oblique  to  the  general  strati- 
fication of  the  mass  at  varying  angles  and  directions. 

Fal.se  Bottom.— Ci)  A movable  bottom  in  some  apparatus.  (2)  A stratum  on 
which  pay  dirt  lies,  but  which  has  other  layers  below  it. 

False  Cleavage. — A secondary*  slip  cleavage  superinduced  on  slaty  cleavage. 

False  Set.— A temporary  set  of  timber  used  until  work  is  far  enough  advanced 
to  put  in  a permanent  set. 


Fam 


GLOSS AEY. 


Fla 


587 


Famp  (Northof  England).— Thin  beds  of  soft  tough  shale. 

Fan. — A machine  for  creating  a circulation  of  air  in  a mine. 

Fan  Drift. — A short  tunnel  or  conduit  leading  from  the  top  of  the  air-shaft  to 
the  fan. 

Fanega  (Mexican).— A Spanish  measure  of  about  bushels. 

Fang  (Derbyshire). — An  air-course. 

Fascines  (English).— Bunches  of  twigs  and  small  branches  for  forming 
foundations  on  soft  ground. 

Fast. — (1)  A road  driven  in  a seam  with  the  solid  coal  at  each  side.  “ Fast 
at  an  end,’'  or  “ fast  at  one  side,”  implies  that  one  side  is  solid  coal  and 
the  other  open  to  the  goaf  or  some  previous  excavation.  (2)  Bed  rock. 

Fast  End. — An  end  of  a breast  of  coal  that  requires  cutting. 

Fat  Coals.— Those  containing  volatile  oily  matters. 

Fathom  (English). — 6 ft. 

Fault— K fracture  or  disturbance  of  the  strata  breaking  the  continuity  of 
the  formation. 

Feather. — A slightly  projecting  narrow  rib  lengthwise  on  a shaft,  arranged 
to  catch  into  a corresponding  groove  in  anything  that  surrounds  and 
slides  along  the  shaft. 

Feather  Edge. — (1)  A passage  from  false  to  true  bottom.  (2)  The  thin  end 
of  a wedge-shaped  piece  of  rock  or  coal. 

Feather  Ore.— Sulphide  of  lead  and  antimony. 

Feed. — Forward  motion  imparted  to  the  cutters  or  drills  of  rock-drilling  or 
coal-cutting  machinery,  either  hand  or  automatic. 

Feeder.— {1)  A runner  of  water.  (2)  A small  blower  of  gas. 

Feigh  (North  of  England).— Ore  refuse. 

Fencing.— Fenemg  in  a claim  is  to  make  a drive  round  the  boundaries  of 
an  alluvial  claim,  to  prevent  wash  dirt  from  being  worked  out  by 
adjoining  claim  holders. 

Fend- Of  {English) .—A  sort  of  bell-crank  for  turning  a pump  rod  past  the 
angle  of  a crooked  shaft. 

Fierros  (Mexican).— Iron  matte. 

Fzeri/.— Containing  explosive  gas. 

Fines. — Very  small  material  produced  in  breaking  up  large  lumps. 

Fire.—{1)  A miners’  term  for  firedamp.  (2)  To  blast  with  gunpowder  or 
other  explosive.  (3)  A word  shouted  by  miners  to  warn  one  another 
when  a shot  is  fired. 

Fire-Bars  (English). — ^The  iron  bars  of  a grate  on  which  the  fuel  rests. 

Fireboard.—A  piece  of  board  with  the  word  fire  painted  upon  it  and  sus- 
pended to  a prop,  etc.,  in  the  workings,  to  caution  men  not  to  take  a 
naked  light  beyond  it,  or  to  pass  it  without  the  consent  of  the  foreman 
or  his  assistants. 

Fire  Boss. — An  underground  official  who  examines  the  mine  for  gas  and 
inspects  safety  lamps  taken  into  the  mine. 

Fireclay.— Any  clay  that  will  withstand  a great  heat  without  vitrifying. 

Firedamp. — (1)  A mixture  of  light  carburetted  hydrogen  {CHf)  and  air  in 
explosive  proportions;  often  applied  to  CH^  alone  or  to  any  explosive 
mixture  of  mine  gases. 

Fireman. — See  Fire  Boss. 

Fire-Setting.— The  process  of  exposing  very  hard  rock  to  intense  heat,  ren- 
dering it  thereby  easier  for  breaking  down. 

First  Working. — See  Whole  Working. 

Firsts. — The  best  ore  picked  from  a mine. 

Fish.— To  join  two  beams,  rails,  etc.  together  by  long  pieces  at  their  sides. 

Fissure.— An  extensive  crack. 

Fissure  Vein.— Any  mineralized  crevice  in  the  rock  of  very  great  depth. 

Flags. — Broad  fiat  stones  for  paving. 

Flagstone.— Any  kind  of  a stone  that  separates  naturally  into  thin  tabular 
plates  suitable  for  pavements  and  curbing.  Especially  applicable  to 
sandstone  and  schists. 

Flang  (Cornish). — A double-pointed  pick. 

Flange  (English). — A projecting  ledge  or  rim. 

Flat.—{1)  A district  or  set  of  workings  separated  by  faults,  old  workings,  or 
barriers  of  solid  coal.  (2)  The  siding  or  station  laid  with  two  or  more 
lines  of  railway,  to  which  the  putters  bring  the  full  cars  from  the  work- 
ing face,  and  where  they  get  the  empty  cars  to  take  back.  (3)  The  area 
of  working  places,  from  which  coal  is  brought  to  the  same  station,  is  also 
called  “flat.” 


588 


Fla 


GLOSSARY, 


Fre 


Flat  Rod.— A horizontal  rod  for  conveying  power  to  a distance. 

Flats.— Narrow  decomposed  parts  of  limestones  that  are  mineralized. 

Flat  Sheet.— Qheei-iron  flooring  at  landings  and  in  the  plats,  chambers,  and 
junctions  of  drives,  to  facilitate  the  turning  and  management  of  trucks. 

Flat  Wall  (Cornish).— Foot-wall. 

Flintshire  Furnace. — A kind  of  reverberatory  furnace  used  for  smelting  lead 
ores. 

Broken  and  transported  particles  or  boulders  of  vein  matter. 

Float  Gold. — Gold  in  thin  scales,  which  floats  on  water. 

Float  Ore.— A term  applied  by  miners  to  ore  found  loose  in  the  clay  or  soil. 

Float  Stones.— boulders  from  lodes  lying  on  or  near  the  surface. 

Flood  Gate  (English).— A gate  to  let  off  excess  of  water  in  flood  or  other 
times. 

Floor.— {1)  The  stratum  of  rock  upon  which  a seam  of  coal  immediately 
lies.  (2)  That  part  of  a mine  upon  which  you  walk  or  upon  which  the 
road  bed  is  laid. 

Floram  (Cornish).— Very  flne  tin. 

Flour  Gold.—Tlao  flnest  alluvial  gold. 

Flouring.— Korcnry  reduced  to  flne  globules  that  are  easily  contaminated 
and  will  not  amalgamate. 

Flucan. — A soft,  greasy,  clayey  substance  found  in  the  joints  of  veins. 

Fluke.— A rod  for  cleaning  out  drill  holes. 

Flume. — An  artificial  watercourse. 

F turning— lAiting  a river  out  of  its  bed  with  wooden  launders  or  pipes,  in 
order  to  get  at  the  bed  for  working. 

Flush.— il)  To  clean  out  a line  of  pipes,  gutters,  etc.  by  letting  in  a sudden 
rush  of  water.  (2)  The  splitting  of  the  edges  of  stone  under  pressure. 
(3)  Forming  an  even  continuous  line,  or  surface.  (4)  To  fill  a mine 
with  fine  material. 

Fluthwerk  (German).— River  prospecting. 

Fte.— Iron  ore,  limestone,  and  sand,  which  are  added  in  various  propor- 
tions to  the  charge  in  a furnace  to  make  the  gangue  melt  up  and  flow 
off*  easily. 

Fodder  (North  of  England).— 21  cwt.  of  lead. 

Following  Stone. — Roof  stone  that  falls  on  the  removal  of  the  seam. 

Foot  (Cornish). — 2 gallons,  or  60  lb.,  black  tin. 

Foot-Hole.— FLolos,  cut  in  the  sides  of  shafts  or  winzes  to  enable  miners  to 
ascend  and  descend. 

Foot-Piece.— {!)  A wedge  of  wood  or  part  of  a slab  placed  on  the  foot-wall 
against  which  a stull  piece  is  jammed.  (2)  A piece  of  wood  placed  on 
the  floor  of  a drive  to  support  a leg  or  prop  of  timber. 

Foot-  Wall. — The  lower  boundary  of  a lode. 

Footway.— Ladders  in  mines. 

Force  Fan.—^ee  Blowdown  Fan. 

Force  P^ece.— Diagonal  timbering  to  secure  the  ground. 

Force  Pump.— A pump  that  forces  water  above  its  valves. 

Forebay.— PenstocL.  The  reservoir  from  which  water  passes  directly  to  a 
waterwheel. 

Forepoling. — Driving  the  poles  over  the  timbers  so  that  their  ends  project 
beyond  the  last  set  of  timber,  so  as  to  protect  the  miner  from  roof  falls; 
used  also  in  quicksand  or  other  loose  material. 

Forewinning.— Prie  first  working  of  a seam  in  distinction  from  pillar  drawing. 

PorA:.— (1)  A deep  receptacle  in  the  rock,  to  enable  a pump  to  extract  the 
bottom  water.  A pump  is  said  to  be  “ going  in  fork  ” when  the  water  is 
so  low  that  air  is  sucked  through  the  windbore.  (2)  (Cornish)  Bottom 
of  sump.  (3)  (Derbyshire)  Prop  for  soft  ground. 

Formation.— A series  of  strata  that  belong  to  a single  geological  age. 

Fossickers  (Australian).— Grubbers  for  gold  in  the  beach  sand. 

PosszcA:i7ic/.— Overhauling  old  workings  and  refuse  heaps  for  gold. 

Fossil. — Organic  remains  or  impressions  of  them  found  in  mineral  matter. 

Fother  (North  of  England).— i chaldron. 

Frame.— A table  composed  of  boards,  slightly  inclined,  over  which  water 
runs  to  wash  off  waste  from  sluice  tin. 

Frame  The  legs  and  cap  or  collar  arranged  so  as  to  support  a passage 
mined  out  of  the  rock  or  lode;  also  called  Framing. 

Free. — Coal  is  said  to  be  “ free  ” when  it  is  loose  and  easily  mined,  or  when  it 
will  “run”  without  mining. 

Free  Milling.— Ores  requiring  no  roasting  or  chemical  treatment. 


Fre 


GLOSSARY. 


(tOB 


589 


Free  Jlfiw€r.— Licensed  miner. 

Fresno  (Mexican) .—An  ash  tree. 

Fronton  (Mexican).— Any  working  face. 

FueUe  (Mexican).— A bellows. 

Furnace.— A large  coal  fire  at  or  near  the  bottom  of  an  upcast  shaft,  for  pro- 
ducing a current  of  air  for  ventilating  the  mine. 

Furnace  Shaft.— The  upcast  shaft  in  furnace  ventilation. 

FxLse.—iX)  A hollow  tube  filled  with  an  explosive  mixture  for  igniting  car- 
tridges. (2)  To  melt. 

Gabarro  (Mexican).— Ore  in  large  pieces,  from  egg  size  up. 

Gad.— A small  steel  wedge  used  for  loosening  jointy  ground. 

Gal  (Cornish).— Hard  gossan. 

Galapago  (Mexican).— A turtle-shaped  pig  of  lead. 

Gale.— A grant  of  mining  ground. 

Galemador  (Spanish).— A silver  furnace. 

Galeme  (Mexican).— A reverberatory  furnace.  See  Cendradilla. 

Galera  (Mexican).— A shed;  any  long  or  large  room;  a storehouse. 

G'aKagre.— Royalty. 

Gallery. — A horizontal  passage. 

Gallos  (Mexican).— Rich  specimens  of  silver  or  gold  ore,  particularly  those 
that  show  native  silver  or  gold. 

Gallows  Frame.— frame  supporting  a pulley  over  which  the  hoisting  rope 
passes  to  the  engine. 

Gambucino  (Mexican).— A prospector  for  gold  placers  or  ores. 

Gang.— A set  of  miners,  a “ shift.” 

Waste  material  from  lodes. 

Gangway.— The  main  haulage  road  or  level. 

Ganister.—A  hard,  compact,  extremely  silicious  fireclay. 

Garabata  (Mexican). — A curved  iron  bar  used  in  copper  smelting. 

Oas.— See  Firedamp.  Any  firedamp  mixture  in  a mine  is  called  gas. 

Gas  Coa?.— Bituminous  coal  containing  a large  percentage  of  gas. 

Gash  Vein.— A wedge-shaped  vein. 

Gasket.— A band  or  ring  of  any  material  put  between  the  flanges  of  pipes 
before  bolting,  to  make  them  water-tight  or  steam-tight. 

Gatches  (Cornish).— Final  sludge  from  tin  dressing. 

Gate.— An  underground  road  connecting  a stall  or  breast  with  a main  road. 

Gateway.— {1)  A road  kept  through  goaf  in  longwall  working.  (2)  A gang- 
way having  ventilating  doors. 

Gauge  Door.— A wooden  door  fixed  in  an  airway  for  regulating  the  supply 
of  ventilation  necessary  for  a certain  district  or  number  of  men. 

Gauge  Pressure. — The  pressure  shown  by  an  ordinary  steam  gauge.  It  is 
the  pressure  above  that  of  the  atmosphere. 

Gears y or  Pair  of  Gears.— {1)  Two  props  and- a plank,  the  plank  being  sup- 
ported by  the  props  at  either  end.  (2)  The  teeth  of  a gear-wheel  or 
pinion. 

Geodes.— LaTgQ  nodules  of  stone  with  a hollow  in  the  center. 

Geordie.—A  safety  lamp  invented  by  George  Stephenson. 

Ge^/ser.— Natural  fountain  of  hot  water  and  steam. 

Gib.—{V)  A short  prop  of  timber  by  which  coal  is  supported  while  being 
holed  or  undercut.  (2)  A piece  of  metal  often  used  in  the  same  hole 
with  a wedge-shaped  key  for  holding  pieces  together. 

Ginneys.—^QQ  Billies. 

Gin,  or  Horse  Gin.— A vertical  drum  and  framework  by  which  the  minerals 
and  dirt  are  raised  from  a shallow  pit. 

Giraffe.— A mechanical  appliance  for  receiving  and  tipping  a car  full  of  ore 
or  waste  rock  when  it  arrives  at  the  surface. 

Girdle.— A thin  bed  or  band  of  stone.  A roof  is  described  as  a post  roof 
with  metal  girdles,  or  a metal  roof  with  post  girdles,  according  as  the 
post  or  the  metal  predominates. 

Glist  (Cornish).— Micaceous  iron  ore. 

Goaf,  or  Goave.— That  part  of  a mine  from  which  the  coal  has  been  worked 
away,  and  the  space  more  or  less  filled  up  with  waste. 

Gob.—{l)  Another  word  for  Goaf.  (2)  To  leave  coal  and  other  minerals 
that  are  not  marketable  in  the  mine.  (3)  To  stow  or  pack  any  useless 
underground  roadway  with  rubbish. 

€hb  Spontaneous  combustion  underground  of  fine  coal  and  slack  in 
the  gob. 


590 


Gob 


GLOSSARY. 


Gut 


Gobbing  C^.— Filling  with  waste. 

Gob  Road. — A roadway  in  a mine  carried  through  the  goaf. 

Going  Headways,  or  Going  Bord. — A headway  or  bord  laid  with  rails,  and 
used  for  conveying  the  coal  tubs  to  and  from  the  face. 

Golpeador  (Mexican). — A striker,  in  hand  drilling. 

Gossan. — A spongy  ferruginous  oxide,  left  after  the  soluble  substances  have 
been  dissolved  out  of  a lode. 

Goths  (Staffordshire).— Sudden  burstings  of  coal  from  the  face,  owing  to 
tension  caused  by  unequal  pressure. 

Gouge.— The  layer  of  clay,  or  decomposed  rock,  that  lies  along  the  wall  or 
walls  of  a vein.  It  is  not  always  valueless. 

Grade. — The  amount  of  fall  or  inclination  in  ditches,  flumes,  roads,  etc. 

Grain.— An  obscure  vertical  cleavage  usually  more  or  less  parallel  to  the  end 
or  dip  joints. 

Granza  (Mexican). — Metallic  minerals  from  the  size  of  rice  to  that  of 
hens’  eggs. 

Grasa  (Mexican).— Literally,  grease.  Slags. 

Grass.— The  surface  of  the  ground. 

Grassero  (Spanish).— Slag  heap. 

Grate  Coal. — See  Broken  Coal. 

Grating.— A perforated  iron  sheet  or  wire  gauze  placed  in  front  of  reducing 
machinery. 

Graved.— Water- worn  stones  about  the  size  of  marbles. 

Gray  Metal.— ^hsTe  of  a grayish  color. 

Graywacke.—A  compact  gray  sandstone  frequently  found  in  Paleozoic 
formations. 

(Greenstone.— A general  term  employed  to  designate  green-colored  igneous 
rocks,  as  diorite,  dolerite,  diabase,  gabbro,  etc. 

Grena  (Spanish). — Undressed  ore. 

Greta  (Mexican). — Impure  litharge  formed  in  a reverberatory  furnace. 

Griddle.— A coarse  sieve  used  for  sifting  ores,  clay,  etc. 

Grizzly.— A grating  to  throw  out  large  stones  from  hydraulic  gold 
sluices. 

Ground  Rent. — Rent  paid  for  surface  occupied  by  the  plant,  etc.  of  a 
colliery. 

Groundsill. — A log  laid  on  the  floor  of  a drive  on  which  the  legs  of  a set  of 
timber  rest. 

Ground  Washing  alluvial,  loosened  by  pick  and  shovel,  intrenches 

cut  out  of  the  bed  rock,  using  bars  of  rock  as  natural  riifles.  Used  in 
shallow  placers,  hill  claims,  bank  claims,  and  stream  diggings. 

Grout  (English).— Thin  mortar  poured  into  the  interstices  between  stones 
and  bricks. 

Grove  (Derbyshire).— A mine. 

(Grub  Stake.— The  mining  outfit  or  supplies  furnished  to  a prospector  on  con- 
dition of  sharing  in  his  finds. 

Grueso  (Mexican).— Lump  ore. 

Grundy. — Granulated  pig  iron. 

Guag  ( Cornish ) . — W orked-out  ground . 

Gualdria  (Mexican).— A long  and  stout  beam,  generally  sustaining  other 
beams  or  some  heavy  weight. 

Guano.— A brown,  gray,  or  white,  light  powdery  deposit,  consisting  mainly 
of  the  excrement  of  sea  fowl  in  rainless  tracts,  or  of  bats  in  caves. 

Guarda  Raya  (Mexican). — A landmark;  a monument. 

Guardas  (Mexican).— The  country  seat  immediately  enclosing  any  metal- 
liferous vein  or  deposit. 

Gubbin. — Ironstone. 

Guia  (Mexican).— Indications  where  to  cut  a pay  streak  or  to  find  a vein. 

Guides.—See  Cage  Guides. 

Guija  (Spanish). — Quartz. 

Guijo  (Mexican).— A pointed  pivot,  upon  which  turns  the  upright  center 
piece  of  an  arrastre,  of  a door,  etc. 

Gunboat. — A self-dumping  car,  holding  from  5 to  8 tons  of  coal,  used  upon 
inclined  planes  or  slopes.  They  are  filled  by  emptying  the  mine  cars 
into  them  at  the  foot  of  the  slope. 

Gunnies  (Cornish).— 3 ft. 

Gurt  (Cornish).- Water  runnel  from  dressing  floor. 

Gutter.— {\)  A small  water-draining  channel.  (2)  The  lowest  part  of  a lead 
that  contains  the  most  highly  auriferous  dirt. 


Hac 


GLOSSARY. 


Hea 


591 


Hacienda  de  Beneficio  (Mexican).— In  mining,  a metallurgical  works;  any 
metallurgical  works,  usually  an  amalgamation  works. 

Hacienda  de  Fundicion  (Mexican).— A smelting  works. 

Hacienda  de  Maquila  (Mexican).— A custom  mill. 

Hade. — The  inclination  of  a vein  or  fault,  taking  the  vertical  as  zero. 

Haiarn  (Wales).— Iron. 

Half  Course.— {!)  At  an  angle  of  45°  from  general  or  previous  course.  (2) 
Half  on  the  level  and  half  on  the  dip. 

Half  Set.—OnQ  leg  piece  and  a cap. 

Halvans.—GangMQ  containing  a little  ore. 

Hammer-and-Plate. — A signaling  apparatus. 

Hand  Barrow.— K long  box  with  handles  at  each  end. 

Hand  Dog.— A.  kind  of  spanner  or  wrench  for  screwing  up  and  disconnecting 
the  joints  of  boring  rods  at  the  surface. 

Handspike.— A wooden  lever  for  working  a capstan  or  windlass. 

Handwhip.— An  apparatus  used  in  shallow  alluvial  workings,  consisting  of 
an  upright,  at  the  top  of  which  is  balanced  a long  sapling;  at  the  thick 
end  of  the  sapling,  a bag  of  earth  is  fastened  to  counterbalance  the 
bucket  of  dirt  to  be  raised  at  the  other  end. 

Hanger-On.— The  man  that  runs  the  loaded  cars  on  to  the  cages  and  gives 
the  signal  to  hoist.  See  Cager. 

Hanging  Spear  Rod.— y^oodenpmnp  rods  adjustable  by  screws,  etc.  by  which 
a sinking  set  of  pumps  is  suspended  in  a shaft. 

Hanging  Wall.— In  metalliferous  mining,  the  stratum  lying  geologically 
directly  above  a bed  or  vein. 

Hardhead.— Residne  from  tin  refining;  contains  much  iron  and  arsenic. 

Ha?TOic.— Somewhat  like  an  agricultural  harrow;  it  is  fixed  to  the  pole  of  a 
puddling  machine  and  dragged  around  to  break  up  and  mix  the  aurifer- 
ous clays  with  water. 

Hatajo  (Mexican).— A drove  of  pack  mules. 

Hat  Rollers.— Cast-iron  or  steel  rollers  shaped  like  a hat,  revolving  on  a 
vertical  pin,  for  guiding  inclined  haulage  ropes  around  curves. 

Hatter.— A miner  working  hy  himself  on  his  own  account. 

Haulage  Levers,  jaws,  wedges,  etc.  by  which  cars,  singly  or  in  trains, 

are  connected  to  the  hauling  ropes. 

Hauling. — The  drawing  or  conveying  of  the  product  of  the  mine  from  the 
working  places  to  the  bottom  of  the  hoisting  shaft,  or  slope. 

Haunches.— The  parts  of  an  arch  from  the  keystone  to  the  skew  back. 

Hazle  (North  of  England).— Sandstone  mixed  with  shale. 

Head. — (1)  Pressure  of  water  in  pounds  per  square  inch.  (2)  Any  subter- 
ranean passage  driven  in  solid  coal.  (3)  That  part  of  a face  nearest 
the  roof. 

Head,  or  Sluice  Head  (Australia  and  New  Zealand) . — A supply  of  1 cu.  ft.  of 
water  per  second,  regardless  of  the  head,  pressure,  or  size  of  orifice. 

Head-Block.— {1)  A stop  at  the  head  of  a slope  or  shaft  to  stop  cars  from 
going  down  the  shaft  or  slope.  (2)  A cap  piece. 

Headboard.— A wedge  of  wood  placed  against  the  hanging  wall,  and  against 
which  one  end  of  the  stull  piece  is  jammed. 

Header.— (1)  A rock  that  heads  off  or  delays  progress.  (2)  A blast  hole  at  or 
above  the  head.  (3)  A stone  or  brick  laid  lengthwise  at  right  angles  to 
the  face  of  the  masonry.  (4)  The  Stanley  Header  is  an  entry  boring 
machine  that  bores  the  entire  section  of  the  entry  in  one  operation. 

Head-Gear.— The  pulley  frame  erected  over  a shaft. 

Head-House.— When  the  head-frame  is  housed  in,  the  structure  is  known  by 
this  name. 

Heading.— (1)  A continuous  passage  for  air  or  for  use  as  a manway;  a gang- 
way or  entry.  (2)  A connecting  passage  between  two  rooms,  breasts,  or 
other  working  places. 

Head-Piece. — A cap;  a collar. 

Headrace. — An  aqueduct  for  bringing  a supply  of  water  on  to  the  ground. 

Headstocks.— Gallows  frame;  head-frame. 

Headways.— {!)  A road;  usually  9 ft.  wide,  in  a direction  parallel  to  the 
main-cleavage  planes  of  the  coal  seams,  which  direction  is  called 
“headways  course,”  and  is  generally  about  north  and  south  in  the 
Newcastle  coal  field.  It  is  termed  “on  end”;in  other  districts.  (2) 
Cross-headings. 

Heave.— The  shifting  of  rocks,  seams,  or  lodes  on  the  face  of  a cross-course, 

etc. 


592 


Hea 


GLOSSARY. 


Hyd 


Heaving.— The  rising  of  the  thill  (or  floor)  of  a seam  where  the  coal  has  been 
removed. 

Hechado  (Spanish).— Dip. 

Heel  of  Coal.— A small  body  of  coal  left  under  a larger  body  as  a support. 

Heel  of  a Shot. — In  blasting,  the  front  of  a shot,  or  the  face  of  the  shot  farthest 
from  the  charge. 

Heep  Stead  (English).— The  entire  surface  plant  of  a colliery. 

Helper.— A miner’s  assistant,  who  works  under  the  direction  of  the  miner. 

Helve. — A handle. 

Hewer. — A collier  that  cuts  coal;  a digger. 

High  Reef.— The  bed  rock  or  reef  is  frequently  found  to  rise  more  abruptly 
on  one  side  of  a gutter  than  on  the  other,  and  this  abrupt  reef  is  termed 
a high  reef. 

Hijuelas  (Mexican). — Literally,  little  children.  A small-sized  torta  made  up 
as  a sort  of  assay  on  a large  scale,  with  from  1 to  5 kilograms  of  argentif- 
erous mud. 

Hill  Diggings.— Flacers  on  hills. 

Hilo  (Spanish).— A thin  metalliferous  vein. 

Hitch.— {1)  A fault  or  dislocation  of  less  throw  than  the  thickness  of  the 
seam  in  which  it  occurs.  (2)  Step  cut  in  the  rock  or  lode  for  holding 
stay-beams,  beams,  or  timber,  etc.  for  various  purposes. 

Hoarding.— A temporary  close  fence  of  boards  placed  around  a work  in 
progress. . 

Hogback.— A roll  occurring  in  the  floor  and  not  in  the  roof,  the  coal  being 
cut  out  or  nearly  so,  for  a distance. 

Hoister. — A machine  used  in  hoisting  the  product.  It  may  be  operated  by 
steampower  or  horsepower. 

Hole.—{l)  To  undercut  a seam  of  coal  by  hand  or  machine.  (2)  A bore 
hole.  (3)  To  make  a communication  from  one  part  of  a mine  to 
another. 

Holing.— {1)  The  portion  of  the  seam  or  underclay  removed  from  beneath 
the  coal  before  it  is  broken  down.  (2)  A short  passage  connecting  two 
roads.  (3)  See  Kirving. 

Holing  Through. — Driving  a passage  through  to  make  connection  with 
another  part  of  the  same  workings,  or  with  those  in  an  adjacent  mine. 

Hood.—^ee  Bonnet. 

Hopper.— A coal  pocket;  a funnel-shaped  feeding  trough. 

Horn. — A piece  of  bullock’s  horn  about  8 in.  in  length,  cut  boat-shaped,  for 
concentrating  by  water  on  a small  scale. 

Horn  Coal. — Coal  worked  partly  end-on  and  partly  face-on. 

Horn  Silver. — Chloride  of  silver. 

Horse  Gin.— A gearing  for  winding  by  horsepower. 

Horsepower.— The  power  that  will  raise  33,000  lb.  1 ft.  high  per  minute. 

Horse,  or  Horsebacks.— {1)  Natural  channels  cut  or  washed  away  by  water  in 
a coal  seam,  and  filled  up  with  shale  and  sandstone.  Sometimes  a bank 
or  ridge  of  foreign  matter  in  a coal  seam.  (2)  A mass  of  country  rock 
lying  within  a vein  or  bed.  (3)  Any  irregularity  cutting  out  a portion 
of  the  vein.  See  Dirt  Fault  and  Rock  Fault. 

Horse  Whim.— A vertical  drum  worked  by  a horse,  for  hauling  or  hoisting. 
Called  also  Horse  Gin. 

Hose. — A strong  flexible  pipe  made  of  leather,  canvas,  rubber,  etc.,  and  used 
for  the  conveyance  of  water,  steam,  or  air  under  pressure  to  any  partic- 
ular point. 

H Piece.— The  portion  of  a column  pipe  containing  the  valves  of  the 
pump. 

Hueco  (Mexican). -7-See  Demasia. 

Hulk  (Cornish).— To  pick  out  the  soft  portions  of  a lode. 

Hundido  ( Mexican) . — See  Derrumbe. 

Hungry. —S^orthless  looking. 

Hurdy  Gurdy.—A  waterwheel  that  receives  motion  from  the  force  of 
traveling  water. 

.HwsMngf.— Prospecting  by  laying  ground  bare  by  sudden  discharges  of 
pent-up  water. 

Hutch  (Cornish).— (1)  An  ore-washing  box.  (2)  (English)  A mine  car. 

Hydraulic  Cement. — A mixture  of  lime,  magnesia,  alumina,  and  silica  that 
solidifies  beneath  water. 

Hydraulicking. — Working  auriferous  gravel  beds  by  hydraulic  power. 

//ydrocarbcns.— Compounds  of  hydrogen  and  carbon. 


Ign 


GLOSSARY. 


Jig 


593 


Igneous  Rocks.— Those  that  have  been  in  a more  or  less  fused  state. 

Inbye.— In  a direction  inward  toward  the  face  of  the  workings,  or  away  from 
the  entrance. 

Incline.— haoTt  for  inclined  plane.  Any  inclined  heading  or  slope  road  or 
track  having  a general  inclination  or  grade  in  one  direction. 

Incorporo  (Mexican).— The  act  of  adding  and  mixing  the  mercury  and 
other  ingredients  in  and  to  the  metalliferous  mud  for  the  patio  process 
of  amalgamation.  Incorporadero. — Place  where  the  incorporo  is 
eifected. 

Indicator.— (1)  A mechanical  contrivance  attached  to  winding,  hauling,  or 
other  machinery,  which  shows  the  position  of  the  cages  in  the  shaft  or 
the  cars  on  an  incline  during  its  journey  or  run.  (2)  An  apparatus  for 
showing  the  presence  of  firedamp  in  mines,  the  temperature  of 
goaves,  the  speed  of  a ventilator,  pressure  of  steam,  air,  or  water,  etc. 

Indicator  Card,  or  Diagram.— K diagram  showing  the  variation  of  steam 
pressure  in  the  cylinder  of  an  engine  during  an  entire  stroke  or  revo- 
lution. 

Indoor  Catches.— strong  beams  in  Cornish  pumping-engine  houses  to  catch 
the  beam  in  case  of  a smash,  thus  preventing  damage  to  the  engine 
itself. 

/7i-/orfc.— When  a pump  continues  working  after  water  has  receded  below 
the  holes  of  the  wind  bore. 

Ingot. — A lump  of  cast  metal. 

In  Place.— A vein  or  deposit  in  its  original  position. 

Insalmoro  (Mexican). — The  addition  of  salt  to  the  torta  or  mud  heap. 

Inset. — The  entrance  to  a mine  at  the  bottom,  or  part  way  down  a shaft 
where  the  cages  are  loaded. 

Inside  Slope.— A slope  on  which  coal  is  raised  from  a lower  to  a higher 
gangway. 

Inspector.— A government  official  whose  duties  are  to  enforce  the  laws  regu- 
lating the  working  of  mines. 

Instroke.— Yhe.  right  to  take  coal  from  a royalty  to  the  surface  by  a shaft  in 
an  adjoining  royalty.  A rent  is  usually  charged  for  this  privilege. 

Intake.— {1)  The  passage  through  which  the  fresh  air  is  drawn  or  forced  in 
a mine,  commencing  at  the  bottom  of  a downcast  shaft,  or  the  mouth 
of  a slope.  (2)  The  fresh  air  passing  into  a colliery. 

Inversion. —Such  a change  in  the  dip  of  a vein  or  seam  as  makes  the  foot- 
wall  or  floor  the  upper  and  the  hanging  wall  or  roof  the  lower  of 
the  two. 

Irestone  (Cornish).— Any  hard  tough  stone. 

Iron  Hat. — Decomposed  ferruginous  mineral  capping  a lode. 

Iron  Man.— A coal-cutting  machine. 

Jaboncilio  (Mexican).— Decomposed  talcose  rock  or  hardened  clay,  generally 
found  in  a vein,  and  sometimes  indicating  the  proximity  of  a rich  strike. 

Jacal  (Mexican).— See  Xacal. 

Jack.— A lantern-shaped  case  made  of  tin,  in  which  safety  lamps  are  carried 
in  strong  currents  of  air. 

Jacket. — (1)  An  -extra  surface  covering,  as  a steam  jacket.  (2)  A water- 
jacket  is  a furnace  having  double  iron  walls,  between  which  water 
circulates. 

Jack-Lamp.— A Davy  lamp,  with  the  addition  of  a glass  cylinder  outside 
the  gauze. 

Jacotinga  (Brazilian).— Ferruginous  ores  associated  with  gold. 

Jales  (Spanish).— Tailings. 

Jales-Jalsontles  (Mexican).— Rich  tailings  or  middlings  from  concentration 
or  amalgamation. 

Jars. — In  rope  drilling,  two  long  links  which  take  up  the  shock  of  impact 
when  the  falling  tools  strike  the  bottom  of  the  hole. 

Jenkin.—A  road  cut  in  a pillar  of  coal  in  a bordways  direction,  that  is,  at 
right  angles  to  the  main-cleavage  planes. 

Jig. — (1)  A self-acting  incline.  (2)  A machine  for  separating  ores  or  minerals 
from  worthless  rock  by  means  of  their  difference  in  specific  gravity; 
also  called  Jigger  or  Washer. 

Jigger. — (1)  A kind  of  coupling  hook  for  connecting  cars  on  an  incline. 
(2)  An  allowance  of  liquor  sometimes  issued  to  workmen  (almost 
obsolete).  {^)  See  Jig. 

Jigging.— Sepamtmg  heavy  from  light  particles  by  agitation  in  water. 


594 


Joe 


GLOSSARY. 


Lag 


Jockey.— A self-acting  apparatus  carried  on  the  front  truck  of  a set  for  re- 
leasing it  from  the  hauling  rope. 

Joggle.— A joint  of  trusses  or  sets  of  timber  for  receiving  pressure  at  right 
angles,  or  nearly  so. 

Joints.— {!)  Divisional  planes  that  divide  the  rock  in  a quarry  into  natural 
blocks.  There  are  usually  two  or  three  nearly  parallel  series,  called  by 
quarrymen  end  joints,  back  joints,  and  bottom  joints,  according  to  their 
position.  (2)  In  coal  seams,  the  less  pronounced  cleats  or  vertical 
cleavages  in  the  coal.  The  shorter  cleats,  about  at  right  angles  to  the 
face  cleats  and  the  bedding  plane  of  the  coal. 

Jud.—{1)  A portion  of  the  working  face  loosened  by  “kirving”  underneath, 
and  “nicking”  up  one  side.  The  operation  of  kirving  and  nicking  is 
spoken  of  as  “making  a jud.”  (2)  The  term  jud  is  also  applied  to  a 
working  place,  usually  6 to  8 yd.  wide,  driven  in  a pillar  of  coal.  When 
a jud  has  been  driven  the  distance  required,  the  timber  and  rails  are 
removed,  and  this  is  termed  “ dramng  a jud.” 

Judge  (Derbyshire  and  North  of  England). — A measuring  staff. 

Jugglers,  or  J^itZars.— Timbers  set  obliquely  against  the  rib  in  a breast,  to 
form  a triangular  passage  to  be  used  as  a manway,  airway,  or  chute. 

Jump.— An  upthrow  or  a downthrow  fault. 

Jumper.— A hand  drill  used  in  boring  holes  in  rock  for  blasting. 

Kann  (Cornish).— Fluorspar. 

Kazen  (Cornish).— A sieve. 

Keckle'Meckle.-YooTQst  lead  ore. 

Keeker.— An  official  that  superintends  the  screening  and  cleaning  of  the  coal. 

Ked  Wedge.— A long  iron  wedge  for  driving  over  the  top  of  a pick  hilt. 

Keeps,  or  Aeps.— Wings,  catches,  or  rests  to  hold  the  cage  at  rest  when  it 
reaches  any  landing. 

Keeve.—A  large  wooden  tub  used  for  the  final  concentration  of  tin  oxide. 

Kenner. — Time  for  quitting  work. 

Kerf. — The  undercut  made  to  assist  the  breaking  of  the  coal. 

Kerned  (Cornish).— Pyrites  hardened  by  exposure. 

Kerve  (North  of  England).— In  coal  mining,  to  cut  under. 

Kevil  (Derbyshire).— Calcspar  found  in  lead  veins. 

Key.—{\)  An  iron  bar  of  suitable  size  and  taper  for  filling  the  keywaysof 
shaft  and  pulley  so  as  to  keep  both  together.  (2)  A kind  of  spanner 
used  in  deep  boring  by  hand. 

Kibble.— Bowk.  Often  made  with  a bow  or  handle,  and  carrying  over  a 
ton  of  debris. 

Kickup.— An  apparatus  for  emptying  trucks. 

Kieve.— Tossing  tub. 

Killas  (Cornish).— Clay  slate. 

Kiln.— A chamber  built  of  stone  or  brick,  or  sunk  in  the  ground,  for  burning 
minerals  in. 

Kind.—{1)  Tender,  soft,  easy.  (2)  Likely  looking  stone. 

Kind-Chaudron. — A system  of  sinking  shafts  through  water-bearing  strata. 

Kirving  (North  of  England).— The  cutting  made  beneath  the  coal  seam. 

Kist.— The  wooden  box  or  chest  in  which  the  deputy  keeps  his  tools.  The 
chest  is  always  placed  at  the  flat  or  lamp  station,  and  this  spot  is  often 
referred  to  by  the  expression  “at  the  kist.” 

Kit. — Any  workman’s  necessary  outfit,  as  tools,  etc. 

Kitty. — A squib  made  of  a straw  tube  filled  with  powder. 

Knee  Piece.— A bent  piece  of  piping. 

Knocker.— A lever  that  strikes  on  a plate  of  iron  at  the  mouth  of  a shaft,  by 
means  of  which  miners  below  can  signal  to  those  on  the  top. 

Knocker  Line.— The  signal  line  extending  down  the  shaft  from  the  knocker. 

Koepe  System.— A system  of  hoisting  without  using  drums,  the  rope  being 
endless  and  passing  over  pulleys  instead  of  around  a drum. 

Labor  (Mexican).— Mine  workings  in  general.  Specifically,  a stope  or  any 
other  place  where  ore  is  being  taken  out. 

Ladderway,  Ladder  Road.— The  particular  shaft,  or  compartment  of  a shaft, 
used  for  ladders. 

Lagging.— {1)  Small  round  timbers,  slabs,  or  plank,  driven  in  behind  the 
legs  and  over  the  collar,  to  prevent  pieces  of  the  sides  or  roof  from  falling 
through.  (2)  Long  pieces  of  timber  closely  fitted  together  and  fastened 
to  the  drum  rings  to  form  a surface  for  the  rope  to  wind  on. 


Lam 


GLOSSARY. 


Ltd 


595 


Lamas  (Spanish).— (1)  Slimes.  (2)  Argentiferous  mud  treated  by  amalga- 
mation. 

Lamero  (Mexican). — Place  of  deposit  for  lamas. 

Laminse.— Sheets  not  naturally  separated,  but  which  may  be  forced  apart. 

Lampazo  (Mexican).— A sort  of  broom  formed  of  green  branches  on  the  end 
of  a long  stick,  to  dampen  the  flame  in  a reverberatory  furnace. 

Lamp  ifew.— Cleaners,  repairers,  and  those  having  charge  of  the  safety  lamps 
at  a colliery. 

Lamp  Stations. — Certain  fixed  stations  in  a mine  at  which  safety  lamps 
are  allowed  to  be  opened  and  relighted  by  men  appointed  for  that 
purpose,  or  beyond  which,  on  no  pretense,  is  a naked  light  allowed 
to  be  taken. 

Lander.— The  man  that  receives  a load  of  ore  at  the  mouth  of  a shaft. 

Lander* s Crook.— A hook  or  tongs  for  upsetting  the  bucket  of  hoisted  rock. 

Landing.— {1)  A level  stage  for  loading  or  unloading  a cage  or  skip. 
(2)  The  top  or  bottom  of  a slope,  shaft,  or  inclined  plane. 

Land  The  sale  of  coal  loaded  into  carts  or  wagons  for  local  consump- 
tion. 

Land-Sale  Collieries.— Those  selling  the  entire  product  for  local  consumption, 
and  shipping  none  by  rail  or  water. 

Xap.— One  coil  of  rope  on  a drum  or  pulley. 

Lappior  (Cornish).— An  ore  dresser. 

Large.— The  largest  lumps  of  coal  sent  to  the  surface,  or  all  coal  that  is  hand 
picked  or  does  not  pass  over  screens;  also,  the  large  coal  that  passes 
over  screens. 

Larry.— {V)  A car  to  which  an  endless  rope  is  attached,  fixed  at  the  inside 
end  of  the  road,  forming  part  of  the  appliance  for  taking  up  slack  rope. 
See  Balance  Car.  (2)  See  Barney.  (3)  A car  with  a hopper  bottom  and 
adjustable  chutes  for  feeding  coke  ovens.  (4)  A hopper-shaped  car  for 
charging  coke  ovens. 

Latches.— A synonym  of  switch.  Applied  to  the  split  rail  and  hinged 
switches.  (2)  Hinged  switch  points,  or  short  pieces  of  rail  that  form 
rail  crossings. 

Lateral.— Yrom  the  side. 

Lath.— A.  plank  laid  over  a framed  center  or  used  in  poling. 

Launder.— Water  trough. 

Laundry  Xox.— The  box  at  the  surface  receiving  the  w^ater  pumped  up  from 
below. 

Lava.— A common  term  for  all  rock  matter  that  has  flowed  from  a volcano  or 
fissure. 

Lavadero  (Mexican).— A washer.  A tank  with  a stirring  arrangement  to 
loosen  up  the  argentiferous  mud  from  the  patio,  and  dilute  the  same 
with  water,  so  that  the  silver  amalgam  may' have  a chance  to  precipitate. 
An  agitator. 

Lazadores  (Mexican).— Men  formerly  employed  in  recruiting  Indians  for 
work  in  the  mines  by  the  gentle  persuasion  of  a lasso. 

Lazy  Back  (Statfordshire). — A coal  stack,  or  pile  of  coal. 

Leaching.— To  dissolve  out  by  some  liquid. 

Lead  (pronounced  leed).—{l)  Ledge  (America);  reef  (Australia);  lode  or 
vein  (England).  A more  or  less  vertical  deposit  of  ore  formed  after  the 
rock  in  which  it  occurs.  (2)  A bed  of  alluvial  pay  dirt  or  an  auriferous 
gutter.  (3)  The  distance  to  which  earth  is  hauled  or  wheeled. 

Leader.— A seam  of  coal  too  small  to  be  worked  profitably,  but  often  being  a 
guide  to  larger  seams  lying  in  known  proximity  to  it. 

Leat.—A  small  water  ditch. 

Leavings  (Cornish).— Hal  vans. 

Ledge.— See  Lead. 

Leg.— A wooden  prop  supporting  one  end  of  a collar. 

Leg  Piece.— An  upright  log  placed  against  the  side  of  a drive  to  support  the 
cap  piece. 

Lenador  (Mexican).— One  that  cuts,  carries,  or  furnishes  wood  for  com- 
bustible. 

Level.— A road  or  gangway  running  parallel  or  nearly  so  with  the  strike 
of  the  seam. 

Ley  (^Mexican) . — Law.  As  applied  in  mining  matters,  it  means  the  propor- 
tion of  precious  or  other  metals  contained  in  any  mineral  substance  or 
metallic  alloy. 

Lid.— A cap  piece  used  in  timbering. 


596 


Lip 


GLOSSAHr. 


Lum 


The  vertical  height  traveled  by  a cage  in  a shaft.  (2)  The  lift  of  a 
pump  is  theoretical  height  from  the  level  of  the  water  in  the  sump  to  the 
point  of  discharge.  (3)  The  distance  between  the  first  level  and  the 
surface,  or  between  two  levels.  (4)  The  levels  of  a shaft  or  slope. 

Lifting  Guards.—FevLcing  placed  around  the  mouth  of  a shaft,  which  is 
lifted  out  of  the  way  by  the  ascending  cage. 

Lignite— K coal  of  a woody  character  containing  about  66^  carbon  and 
having  a brown  streak. 

Limadura  (Mexican).— Filings.  The  mercurial  globules  seen  when  a piece 
of  argentiferous  mud  from  a patio  is  washed  in  a spoon  or  saucer  for 
an  assay. 

Lime  Cartridge. — A charge  or  measured  quantity  of  compressed  dry  caustic 
lime  made  up  into  a cartridge  and  used  instead  of  gunpowder  for 
breaking  down  coal.  Water  is  applied  to  the  cartridge,  and  the  expan- 
sion breaks  down  the  coal  without  producing  a flame. 

Lime  Coa^.— Small  coal  suitable  for  lime  burning. 

Lines. — Plumb-lines,  not  less  than  two  in  number,  hung  from  hooks  driven 
in  wooden  plugs.  A line  drawn  through  the  centers  of  the  two  strings 
or  wires,  as  the  case  may  be,  represents  the  bearing  or  course  to  be 
driven  on. 

Lining.— planks  arranged  against  frame-sets. 

Linnets  (Derbyshire). — Oxidized  lead  ores. 

Linternilla  (Mexican). — The  drum  of  a Horse  Whim. 

Lip  Screen. — A small  screen  or  screen  bars,  placed  at  the  draw  hole  of  a coal 
pocket  to  take  out  the  fine  coal. 

Lis  (Mexican).— The  flouring  of  mercury. 

Little  Giant.— name  given  to  a special  sort  of  hydraulic  nozzle  used  for 
sluicing  purposes. 

Live  Quartz.— K variety  of  quartz  usually  associated  with  mineral. 

Lixiviating. — See  Leaching. 

Llaves  (Mexican).— Horizontal  cross-beams  in  a shaft;  or  the  upright  pieces 
that  sustain  the  roof  beams  in  a drift  or  tunnel. 

Loaded  TracA:.— Track  used  for  loaded  cars. 

Loader.— OiiQ  that  fills  the  mine  cars  at  the  working  places. 

Loam.— Any  natural  mixture  of  sand  and  clay  that  is  neither  distinctly  sandy 
nor  clayey. 

Location. — The  first  approximate  staking  out  or  survey  of  a mining  claim,  in 
distinction  from  a Patent  Survey^  or  a Patented  Claim. 

Location  Survey. — See  Location. 

Lode  (Cornish).— Strictly  a fissure  in  the  country  rock  filled  with  mineral; 
usually  applied  to  metalliferous  lodes.  In  general  miners’  usage,  a lode, 
vein,  or  ledge  is  a tabular  deposit  of  valuable  minerals  between  definite 
boundaries.  Whether  it  be  a fissure  formation  or  not  is  not  alwaj’^s 
known,  and  does  not  affect  the  legal  title  under  the  United  States  federal 
and  local  statutes  and  customs  relative  to  lodes.  But  it  must  not  be  a 
placer,  i.  e.,  it  must  consist  of  quartz  or  other  rock  in  place,  and  bearing 
valuable  mineral. 

Lodestone,  or  Lode.—{l)  Magnetic  iron  ore.  (2)  Stone  found  in  veins  or  lodes. 

Logs. — Portions  of  trunks  of  trees  cut  to  lengths  and  built  up  so  as  to  raise 
the  mouth  or  collar  of  a shaft  from  the  surface,  in  order  to  give  the 
requisite  space  for  the  dumping  of  mullock  and  ore. 

Long-Pillar  Work.— A system  of  working  coal  seams  in  three  separate  oper- 
tions:  (1)  large  pillars  are  left;  (2)  a number  of  parallel  headings  are 
driven  through  the  block;  and  (3)  the  ribs  or  narrow  pillars  are  worked 
away  in  both  directions. 

Long  Tom.— A wooden  sluice  about  24  ft.  long,  2 ft.  wide,  and  1 ft.  high,  for 
washing  auriferous  gravel. 

Long  Ton. — 2,240  lb. 

Longwall.—A  system  of  working  a seam  of  coal  in  which  the  whole  seam  is 
taken  out  and  no  pillars  left,  excepting  the  shaft  pillars,  and  sometimes 
the  main-road  pillars. 

Loot)  (Cornish).— Sludge  from  tin  dressing. 

Loose  End.—{1)  A portion  of  a seam  worked  on  two  sides.  (2)  A portion 
that  projects  in  the  shape  of  a wedge  between  previous  workings. 

Low  Grade.— rich  in  mineral. 

Lumber.— Timber  cut  to  the  various  sizes  and  shapes  for  carpenters’  purposes. 

Lumbreras  (Mexican).— Ventilating  shafts  in  a mine  or  other  underground 
work. 


Lum 


GLOSSARY. 


Mer 


597 


Lump  Coa?.— (1)  All  coal  (anthracite  only)  larger  than  broken  coal,  or,  when 
steamboat  coal  is  made,  lumps  larger  than  this  size.  (2)  In  soft  coal,  all 
coal  passing  over  the  nut-coal  screen. 

Lute.—A.n  adhesive  clay  used  either  to  protect  any  iron  vessel  from  too 
strong  a heat  or  for  securing  air-  and  gas-tight  joints. 

Lye  (English).— A siding  or  turnout. 

Machote  (Mexican).— A stake  or  permanent  bench  mark  fixed  in  an  under- 
ground working,  from  which  the  length  and  progress  thereof  is 
measured. 

Macizo  (Spanish).— Unworked  lode. 

Magistral  (Spanish).— Roasted  copper  pyrites,  copper  sulphate,  etc.,  used  to 
"reduce  silver  ores. 

Magnetic  AeedZe.- Needle  used  in  surveying. 

Magnetic  North.— direction  indicated  by  the  north  end  of  the  magnetic 
needle. 

Magnetic  Meridian.— line  or  great  circle  in  which  the  magnetic  needle 
sets  at  any  given  place. 

Main  i^oad.— The  principal  haulage  road  of  a mine  from  which  the  several 
crossroads  lead  to  the  working  face. 

Main  Rod  (English).— See  Pump  Rod. 

Main  Rope.— In  tail-rope  haulage,  the  rope  that  draws  the  loaded  cars 
out. 

Makings  (North  of  England).— Small  coal  produced  in  kirving.  Fines. 

Malacate  (Mexican).— A Horse  Whim;  now  extended  to  any  hoisting  machine 
used  in  mines. 

Mamposteria  (Mexican).— Mason  work. 

Manager. — An  official  who  has  the  control  and  supervision  of  a mine,  both 
under  and  above  ground. 

Man  Engine.— A.n  apparatus  consisting  of  one  or  two  reciprocating  rods,  to 
which  suitable  stages  are  attached,  used  for  lowering  and  raising  men 
in  shafts. 

Manga  (Spanish).— Canvas  bag  for  straining  amalgam. 

Manhole. — (1)  A refuge  hole  constructed  in  the  side  of  a gangway,  tunnel, 
or  slope.  (2)  A hole  in  cylindrical  boilers  through  which  a man  can 
get  into  the  boiler  to  examine  and  repair  it. 

Mano  (Mexican). — A grinding  stone  of  an  arrastre,  etc. 

Mantas  (Mexican).— Jute  or  henequen,  etc.,  sacks  in  which  ore  or  waste 
is  carried. 

Manteo  (Mexican).— The  act  of  hoisting  ore  or  waste  from  a mine. 

Manto  (Mexican).— A blanket  vein. 

Manway.— A.  small  passage  used  as  a traveling  way  for  the  miner,  and  also 
often  used  as  an  airway  or  chute,  or  both. 

Maquilla  (Spanish).— A custom  mill. 

Maquilar  (Mexican).— To  work  ore  for  its  owner  on  shares  or  for  a money 
payment. 

Marco  (Mexican).— A weight  of  8 oz. 

Marl.—Q\ay  containing  calcareous  matter. 

Marlinespike.—A  sharp  pointed  and  gradually  tapered  round  iron,  used  in 
splicing  ropes. 

Marmajas  (Spanish).— Concentrated  sulphides. 

Marrow. — A partner. 

Marsaut  Lamp.— A type  of  safety  lamp  whose  chief  characteristic  is  the 
multiple-gauze  chimneys. 

Marsh  Gas.—CH^,  often  used  synonymously  with  Firedamp  (see  page  348). 

Match.— {1)  A charge  of  gunpowder  put  into  a paper  several  inches  long,  and 
used  for  igniting  explosives.  (2)  The  touch  end  of  a squib. 

Matte. — A compound  of  iron  and  other  metals,  chiefly  copper,  with  sulphur, 
formed  during  smelting. 

Mattock.— A kind  of  pick  with  broad  ends  for  digging. 

Maul.— A driver’s  hammer. 

Maundril.—A  pick  with  two  shanks  and  points,  used  for  getting  coal,  etc. 

Mazo  (Mexican).— A stamp. 

Mear  (Derbyshire).— 32  yd.  along  the  vein. 

Measures. — Strata . 

Mecha  (Mexican). — A wick  for  a lamp  or  candle;  a torch. 

Merced  (Mexican).— A gift,  grant,  or  concession. 

Meridian.— A north  and  south  line,  either  true  or  approximate. 


598 


Met 


GLOSSARY. 


Mou 


Metal.^il)  In  coal  mining,  induratea  clay  or  slate.  (2)  An  element  that 
forms  a base  by  combining  with  oxygen  that  is  solid  at  ordinary  tem- 
perature (with  exception  of  quicksilver),  opaque  (except  in  the  thinnest 
possible  films),  has  a metallic  luster,  and  is  a good  conductor  of  heat 
and  electricity,  and,  as  a rule,  of  a higher  specific  gravity  than  the  non- 
metals.  (3)  (Mexican)  All  kinds  of  metalliferous  minerals  are  called 
“metal”  in  Mexico.  Metal  de  Ayuda— Fluxing  ore  of  any  kind.  Metal 
de  Cebo—Yeiy  rich  ore,  usually  treated  in  small  reverberatory  furnaces. 
Metal  Ordinario.— Common  ore.  Melal  Pepena.— The  best  class  of  selected 
ore. 

Metlapil  (Mexican).— See  Mano. 

MW.— Works  for  crushing  and  amalgamating  gold  and  silver  ores. 

Mill  Cinder.— The  slag  from  the  puddling  furnace  of  a rolling  mill. 

Mill  Hole.—A.n  auxiliary  shaft  connecting  a stope  or  other  excavation  with 
the  level  below. 

Mill  The  test  of  a given  quantity  of  ore  by  actual  treatment  in  a mill. 

Mine.— Any  excavation  made  for  the  extraction  of  minerals. 

Miner.— One  who  mines. 

Mineral.— Any  constituent  of  the  earth’s  crust  that  has  a definite  com- 
position. 

Mineral  Oz7.— Petroleum  obtained  from  the  earth,  and  its  distillates. 

Minero  (Mexican).— A mine  owner;  a mining  captain;  an  underground  boss. 

Mine  Road.— Any  mine  track  used  for  general  haulage. 

Mine  Run.— The  entire  unscreened  output  of  a mine. 

Minero  Mayor  (Mexican).— The  head  mining  captain.  A mining  workman 
is  called  Operario. 

Miners'  Dial.— An  instrument  used  in  surveying  underground  workings. 

Miners'  Inch.— A measure  of  water  varying  in  different  districts,  being  the 
quantity  of  water  that  passes  through  a slit  1 in.  high,  of  a certain  width 
under  a given  head  (see  page  136). 

Miner's  Right.— An  annual  permit  from  the  Government  to  occupy  and  work 
mineral  land. 

Mining.— In  its  broad  sense,  it  embraces  all  that  is  concerned  with  the 
extraction  of  minerals  and  their  complete  utilization. 

Mining  Engineer.— A man  having  knowledge  and  experience  in  the  many 
departments  of  mining. 

Mining  Retreating.— A process  of  mining  by  which  the  vein  is  untouched 
until  after  all  the  gangways,  etc.  are  driven,  when  the  mineral  extraction 
begins  at  the  boundary  and  progresses  toward  the  shaft. 

Mistress  (North  of  England).— A miner’s  lamp. 

Mock  Lead  (Cornish).— Zinc  blende. 

Mogrollo  (Mexican).— Same  as  Metal  de  Cebo. 

Moil.— A short  length  of  steel  rod  tapered  to  a point,  used  for  cutting 
hitches  etc. 

Molonque  (Mexican).— A rich  specimen  of  which  one-half  or  more  is  native 
silver. 

Monitor.— See  Gunboat. 

Monkey.— The  hammer  or  ram  of  a pile  driver. 

Monkey  Drift.— A small  drift  driven  in  for  prospecting  purposes,  or  a crosscut 
driven  to  an  airway  above  the  gangway. 

Monkey  Gangway.— A small  gangway  parallel  with  the  main  gangway. 

Monkey  Rolls.— the  smaller  rolls  in  an  anthracite  breaker. 

Monkey  Shaft.— A shaft  rising  from  a lower  to  a higher  level. 

Monoclinal.— Applied  to  an  area  in  which  the  rocks  all  dip  in  the  same 
direction. 

Mp.— Some  material  surrounding  a drill  in  the  form  of  a disk,  to  prevent 
water  from  splashing  up. 

Mortar.— The  vessel  in  which  ore  is  placed  to  be  pulverized  by  a pestle. 

Mortise.— A hole  cut  in  one  piece  of  timber,  etc.  to  receive  the  tenon  that 
projects  from  another  piece. 

Mote  {Moat).— A straw  filled  with  gunpowder,  for  igniting  a shot. 

Mother  Gate.— The  main  road  of  a district  in  longwall  working. 

Mother  Lode  {Main  Lode).— The  principal  vein  of  any  district. 

Motive  Column.— The  length  of  a column  of  air  whose  weight  is  equal  to  the 
difference  in  weight  of  like  columns  of  air  in  downcast  and  upcast  shafts. 
The  ventilating  pressure  in  furnace  ventilation  is  measured  by  the  differ- 
ence of  the  weights  of  the  air  columns  in  the  two  shafts. 

Mouth.— The  top  of  a shaft  or  slope,  or  the  entrance  to  a drift  or  tunnel. 


Moy 


GLOSSARY. 


Ope 


599 


Moyle— An  iron  with  a sharp  steel  point,  for  driving  into  clefts  when 
levering  off  rock. 

Muckle. — Soft  clay  overlying  or  underlying  coal. 

Mucks  (Staffordshire).— Bad  earthy  coal. 

Muescas  (Mexican).— Notches  in  a stick;  mortises;  notches  cut  in  a round 
or  square  beam,  for  the  purpose  of  using  it  as  a ladder. 

Mueseler  Lamp. — A type  of  safety  lamp  invented  and  used  in  the  collieries 
of  Belgium.  Its  chief  characteristic  is  the  inner  sheet-iron  chimney  for 
increasing  the  draft  of  the  lamp. 

Muffle.— A thin  clay  oven  heated  from  the  outside. 

Muller.— YhQ  upper  grinding  iron  or  rubbing  shoe  of  amalgamating 
pans,  etc. 

Mullock.— CoxmiTy  rock  and  worthless  minerals  taken  from  a mine. 

Mundic.—lion  pyrites. 

Naked  Light.— A candle  or  any  form  cf  lamp  that  is  not  a safety  lamp. 

Narrow  Work.—{l)  All  work  for  which  a price  per  yard  of  length  driven  is 
paid,  and  which,  therefore,  must  be  measured.  (2)  Headings,  chutes, 
crosscuts,  gangways,  etc. 

Natas  (Mexican).— Same  as  Escoria  or  Grasa. 

Native  Metal.— A metal  found  naturally  in  that  state. 

Natural  Ventilation.— NentilaXion  of  a mine  without  either  furnace  or  other 
artificial  means;  the  heat  imparted  to  the  air  by  the  strata,  men, 
animals,  and  lights  in  the  mine,  causing  it  to  flow  in  one  direction,  or 
to  ascend. 

Neck.— A cylindrical  body  of  rock  differing  from  the  country  around  it. 

Needle.— {1)  A sharp-pointed  metal  rod  with  which  a small  hole  is  made 
through  the  stemming  to  the  cartridge  in  blasting  operations.  (2)  A 
hitch  cut  in  the  side  roc.k  to  receive  the  end  of  a timber. 

Negrillo  (Mexican).— Black  sulphide  of  silver. 

Nick. — To  cut  or  shear  coal  after  holing. 

Nicking.— {!)  A vertical  cutting  or  shearing  up  one  side  of  a face  of  coal.  (2) 
The  chipping  of  the  coal  along  the  rib  of  an  entry  or  room  which  is 
usually  the  first  indications  of  a squeeze. 

Night  Shift.— Yho,  set  of  men  that  work  during  the  night. 

Nip. — When  the  roof  and  floor  of  a coal  seam  come  close  together,  pinching 
the  coal  between  them. 

Nip  Owf.— The  disappearance  of  a coal  seam  by  the  thickening  of  the  adjoin- 
ing strata,  which  takes  its  place. 

Nitro. — A corrupted  abbreviation  for  nitroglycerine  or  dynamite. 

Nittings.—RQfns,e  of  good  ore. 

Nodular.— Blistered  or  kidney-shaped  ore. 

iVbdwZes.— Concretions  that  are  frequently  found  to  enclose  organic  remains. 

Nogs.— Logs  of  wood  piled  one  on  another  to  support  the  roof.  See  Chock. 

Nook. — The  corner  of  a working  place  made  by  the  face  with  one  side. 

Noria  (Spanish).— An  endless  chain  of  buckets. 

Nozzle.— The  front  nose  piece  of  bellows  of  a blast  pipe  for  a furnace,  or  of  a 
water  pipe. 

Nugget. — A natural  lump  of  gold  or  other  metal,  applied  to  any  size  above  2 
to  3 dwt. 

Nut  Coal.— A contraction  of  the  term  chestnut  coal. 

Nuts.— Smsdl  lumps  of  coal  that  will  pass  through  a screen  or  bars,  the  spaces 
between  which  vary  in  width  from  i to  2k  in. 

Ocote  (Mexican).— Pitch  pine. 

Odd  Work. — Work  other  than  that  done  by  contract,  such  as  repairing 
roads,  constructing  stoppings,  dams,  etc. 

Offtake.— The  raised  portion  of  an  upcast  shaft  above  the  surface,  for  carrying 
off  smoke  and  steam,  etc.,  produced  by  the  furnaces  and  engines  under- 
ground. 

Oil  Shale.— ShAle  containing  such  a proportion  of  hydrocarbons  as  to  be 
capable  of  yielding  mineral  oil  on  slow  distillation. 

Oil  Sm,eUers.—M.en  that  profess  to  be  able  to  indicate  where  petroleum  oil  is 
to  be  found. 

Old  Man.— Old  workings  in  a mine. 

Oolitic.— A structure  peculiar  to  certain  rocks,  resembling  the  roe  of 
a fish. 

Open  Casf.— Workings  having  no  roof. 


600 


Ope 


GLOSSARY, 


Pan 


Open  Cutting.^{l)  An  excavation  made  on  the  surface  for  the  purpose  of  get* 
ting  a face  wherein  a tunnel  can  be  driven.  (2)  Any  surface  excavation, 

Openings,  An  Opening —Any  excavation  on  a coal  or  ore  bed,  or  to  reach  the 
same;  a mine. 

Openwork.— An  open  cut. 

Operario  (Mexican). — A working  miner. 

Operator.— The  individual  or  company  actually  working  a colliery. 

Ore.— A mineral  of  sufficient  value  (as  to  quality  and  quantity),  to  be  mined 
with  profit. 

Ores.— Minerals  or  mineral  masses  from  which  metals  or  metallic  combina- 
tions can  be  extracted  on  a large  scale  in  an  economic  manner. 

Ore  Shoot. — A large  and  usually  rich  aggregation  of  mineral  in  a vein. 
Distinguished  from  pay  streak  in  that  it  is  a more  or  less  vertical  zone 
or  chimney  of  rich  vein  matter  extending  from  wall  to  wall,  and  having 
a definite  width  laterally. 

Oro  (Spanish).— Gold. 

Oroc/ie  (Spanish).— (1)  Retorted  bullion.  (2)  (Mexican)  Bullion  containing 
gold  and  silver. 

Outburst. — A blower.  A sudden  emission  of  large  quantities  of  occluded  gas. 

Outbye. — In  the  direction  of  the  shaft  or  slope  bottom,  or  toward  the  outside. 

Outcrop. — ^The  portion  of  a vein  or  bed,  or  any  stratum  appearing  at  the  sur- 
face, or  occurring  immediately  below  the  soil  or  diluvial  drift. 

Outcropping. — See  Cropping  Out. 

Outlet— A passage  furnishing  an  outlet  for  air,  for  the  miners,  for  water,  or 
for  the  mineral  mined. 

Output. — The  product  of  a mine  sent  to  market,  or  the  total  producj:  of  a mine. 

Outset. — The  walling  of  shafts  built  up  above  the  original  level  of  the  ground. 

Outstroke  Rent. — The  rent  that  the  owner  of  a royalty  receives  on  coal  brought 
into  his  royalty  from  adjacent  properties. 

Outtake.— The  passage  by  which  the  ventilating  current  is  taken  out  of  the 
mine;  the  upcast. 

Overburden.— The  covering  of  rock,  earth,  etc.  overlying  a mineral  deposit 
that  must  be  removed  before  effective  work  can  be  performed. 

Overcast. — A passage  through  which  the  ventilating  current  is  conveyed  over 
a gangway  or  airway. 

Overhand  Stoping. — The  ordinary  method  of  stoping  upwards. 

Overlap  Fault.— A fault  in  which  the  shifted  strata  double  back  over  them- 
selves. 

Overman.— One  who  has  charge  of  the  workings  while  the  men  are  in  the 
mine.  He  takes  his  orders  from  the  Underviewer. 

Overwind.— To  hoist  the  cage  into  or  over  the  top  of  the  head-frame. 

Oyamel  (Mexican).— White  pine. 

Pack.— A rough  wall  or  block  of  coal  or  stone  built  up  to  support  the  roof. 

Packing. — The  material  placed  in  stuffingboxes,  etc.  to  prevent  leaks. 

Pack  Wall. — A wall  of  stone  or  rubbish  built  on  either  side  of  a mine  road,  to 
carry  the  roof  and  keep  the  sides  up. 

Pacos  (Spanish). — Ferruginous  silver  ores. 

Paddock.— {!)  An  excavation  made  for  procuring  wash  dirt  in  shallow 
ground.  (2)  A place  built  near  the  mouth  of  a shaft  where  ore  is  stored. 

Paint  Qold.—The  very  finest  films  of  gold  coating  other  minerals. 

Paleozoic.— The  oldest  series  of  rocks  in  which  fossils  of  animals  occur. 

Palero  (Mexican).— A mine  carpenter. 

Palm.— A piece  of  stout  leather  fitting  the  palm  of  the  hand,  and  secured  by 
a loop  to  the  thumb;  this  has  a flat  indented  plate  for  forcing  the  needle. 

Palm  Needle.— A straight  triangular-sectioned  needle,  used  for  sewing  canvas. 

Palo  (Mexican).— A stick;  a piece  of  timber. 

Pan. — A thin  sheet-iron  dish  16  in.  across  the  top,  and  10  in.  at  the  bottom, 
used  for  panning  gold. 

Panel.— {1)  A large  rectangular  block  or  pillar  of  coal  measuring,  say, 
130  by  100  yd.  (2)  A group  of  breasts  or  rooms  separated  from  the  other 
workings  by  large  pillars. 

Panel  Working. — A system  of  working  coal  seams  in  which  the  colliery  is 
divided  up  into  large  squares  or  panels,  isolated  or  surrounded  by  solid 
ribs  of  coal,  in  each  of  which  a separate  set  of  breasts  and  pillars  is 
worked,  and  the  ventilation  is  kept  distinct,  that  is,  every  panel  has  its 
own  circulation,  the  air  of  one  not  passing  into  the  adjoining  one,  but 
being  carried  direct  to  the  main  return  airway. 


Pan 


OLOISSAR  Y 


Pic 


601 


Panino  f Mexican). —The  peculiar  appearance,  form,  or  manner  in  which 
the  metallife^us  minerals  present  themselves  m any  given  district 

PanMntoTPanning  0#.-Separating  .gold  or  tin  from  its  accompanying 
minerals  by  washing  off  the  latter  in  a pan. 

^S^?;ra.K?nS>o7to«rsVi“'?;^  a chattering  noise 

nart  of  the  ores  in  place  of  wages.  Usually,  the  mine  provides 

Sndles  nowdir,  and  steel,  and  keeps  the  drills  sharpened,  and  receives, 
in  navnient  of  royalty  and  supplies,  two-thirds  or  more  of  the  ore  taken 
ouU  ^his  contract  is  renewed  weekly  or  monthly,  etc., 
tion  of  ore  retained  by  the  miners  is  more  or  less,  according  to  the  richness 
of^the  stones  where  they  work.  This  is  a cheap  way  of  getting  ore  as  far 
S^labor  is  concern^^^^^^^  But  the  miners  must  be  constantly  watched; 
Sherwie  they  will  leave  the  mine  in  bad  state.  The  proportion  of  pre 
assigned  to  the  miners  is  generally  bought  from  them  by  the  mine 

owner  himself,  for  various  reasons.  ^ i /o\  a 

Parting —{1)  Any  thin  interstratified  bed  of  earthy  material.  (2)  A side 
track  or  turnout  in  a haulage  road. 

down  ore  to  a lower  level  (2)  A 
pasLge  left  in  old  workings  for  men  to  travel  in  from  one  level  to 

Pas^^v^.— A siding  in  which  cars  pass  one  another  underground.  A turnout. 

Pass-into.— When  one  mineral  gradually  passes  into  another  without  any 

coal  mixed  with  8 to  10^  of  pitch  or  tar,  and  compressed 

to  which  a patent  right  has  been  secured  from  the 
government  by  compliance  with  the  laws  relating  to  such  claims. 

Patent  Survey— An  accurate  survey  of  a claim  by  a deputized  surveyor  as 
required  by  law  in  order  to  secure  a patent  right  to  the  claim. 

PaHiTSeidcanl^-Any  paved  enclosure  more  or  less  surrounded  by  build- 
hig“  In  OTe-s^r?higyard.  A floor  or  yard  where  argentiferous  mud  is 
treated  by  amalgamation. 

Paf  Pir^.— That  portion  of  an  alluvial  deposit  that  contains  gold  in  payable 
quantities. 

Pay  Out— To  slacken  or  let  out  rope. 

Pay  PocA:— Mineralized  rock. 

Pay  Mineralized  part  of  rock. 

Peac/i /Stone  (Cornish).— Chlorite  schist. 

Pea  Coal— A small  size  of  anthracite  coal  (see  page  434). 

Pm?  — T^edecomposed^ partly  carbonized  organic  matter 

Pebble  Jack.— Zino  blende  in  small  crystals  or 

attached  to  rock,  but  is  found  in  clay  openings  in  the  rock. 

Pee  (Derbyshire).— A fragment  of  lead  ore. 

Pdla,  or  Plata  Pella  (Mexican).— Silver  amalgam. 

PerdHous^—J^wooden  covering  for  the  protection  of  sinkers  working  in  a 

Pc»(to-Af^  pieces  of  timber  laid  as  a roof  over  men’s  heads,  to  screen 
them  when  working  in  dangerous  piaces,  e.  g.,  at  the  bottom  of  shafts. 

Pepenado  (Spanish).— Dressed  ore. 

pS^i^Tabk^-USn^oh^oW^^  table  used  in  separating  very  fine  ores 
from  slimes.  . .14^ 

Petlanque  (Mexican).— Ruby  silver. 

^et?rU^K"eu7trnfa»^^^^^^  or  face 

of  an  excavation  with  a pick. 


602 


Pic 


GLOSSARY. 


Pla 


Picker.— {1)  A small  tool  used  to  pull  up  the  wick  of  a miner’s  lamp. 
(2)  A person  who  picks  the  slate  from  the  coal  in  an  anthracite-coal 
breaker. 

Picking  Chute. — A chute  in  an  anthracite  breaker  along  which  boys  are 
stationed  to  pick  the  slate  from  coal. 

Picking  Table.— {1)  A flat  or  slightly  inclined  platform  on  which  anthracite 
coal  is  run  to  be  picked  free  from  slate.  (2)  A sorting  table. 

Pico  (Mexican).— A striking  or  sledge  hammer. 

Picture.— K screen  to  keep  off  falling  water  from  men  at  work. 

Piedras  de  Mano  (Mexican).— Hand  specimens. 

Pig.— A piece  of  lead  or  iron  cast  into  a long  iron  mold. 

Pigsty  Timhering.—^oWovf  pillows  built  up  of  logs  of  wood  laid  crosswise 
for  supporting  heavy  weights. 

Pike. — A pick. 

Pilar  (Mexican).— A pillar  of  rock  or  ore  left  to  sustain  some  portion  of  the 
mine. 

Pileta  (Mexican).— (1)  A sump.  (2)  The  basin  or  pot  where  melted  metal 
is  collected. 

Piling.— Long  pieces  of  timber  driven  into  soft  ground  for  the  purpose  of 
securing  a solid  base  on  which  to  build  any  superstructure. 

Pillar.— {!)  A solid  block  of  coal,  etc.  varying  in  area  from  a few  square 
yards  to  several  acres.  (2)  Sometimes  applied  to  a single  timber 
support. 

Pillar-and-Room.—A  system  of  working  coal  by  which  solid  blocks  of  coal 
are  left  on  either  side  of  the  rooms,  entries,  etc.  to  support  the  roof  until 
the  rooms  are  driven  up,  after  which  they  are  drawn  out. 

Pillar -and-Stall.— See  Breast-and-Pillar. 

Pillar  Roads. — Working  roads  or  inclines  in  pillars  having  a range  of  long- 
wall  faces  on  either  side. 

Pillion  (Cornish).— Metal  remaining  in  slag. 

Pina  (Mexican).— Same  as  Pella. 

Pinch.— A contraction  in  the  vein. 

Pinch  Owi.— When  a lode  runs  out  to  nothing. 

Pinta  (Mexican).— The  color,  weight,  grain,  etc.  of  ores,  whereby  it  is  pos- 
sible to  form  some  idea  of  their  richness  in  the  various  metals. 

Pipe.— An  elongated  body  of  mineral.  Also  the  name  given  to  the  fossil 
trunks  of  trees  found  in  coal  veins. 

Pipe  Clay. — A soft  white  clay. 

Piped  Air.— Air  carried  into  the  working  place  by  pipes  or  brattices. 

Undercutting  and  washing  away  gravel  before  the  water  nozzle. 

P^^.— (1)  A shaft.  (2)  The  underground  portion  of  a colliery,  including  all 
workings.  (3)  A gravel  pit. 

Pit  Bank. — The  raised  ground  or  platform  where  the  coal  is  sorted  and 
screened  at  the  surface. 

Pit  Bottom.— Y\ie  portion  of  a mine  immediately  around  the  bottom  of  a shaft 
or  slope.  See  Shaft  Bottom. 

Pitch.— {1)  Rise  of  a seam.  (2)  Grade  of  an  incline.  (3)  Inclination.  (Cor- 
nish) A part  of  a lode  let  out  to  be  worked  on  shares,  or  by  the  piece. 

Pit  Coa?.— Generally  signifies  the  bituminous  varieties  of  coal. 

Pit  Frame.— See  Head-Frame. 

Pit  Headman. — The  man  who  has  charge  at  the  top  of  the  shaft  or  slope. 

Pitman. — A miner;  also,  one  who  looks  after  the  pumps,  etc. 

Pit  Prop.— A piece  of  timber  used  as  a temporary  support  for  the  roof. 

Pit  Rails. — Mine  rails  for  underground  roads. 

Pit  Poom.— The  extent  of  underground  workings  in  use  or  available  for  use. 

Pit’s  Eye. — Pit  bottom  or  entrance  into  a shaft. 

Pit  Top.- The  mouth  of  a shaft  or  slope. 

Place. — The  portion  of  coal  face  allotted  to  a hewer  is  spoken  of  as  his 
“working  place,”  or  simply  “place.” 

Placer. — A surface  accumulation  of  mineral  in  the  wash  of  streams. 

Placer  Mmnp.— Surface  mining  for  gold  where  there  is  but  little  depth  of 
alluvial. 

Plan.—{1)  The  system  on  which  a colliery  is  worked  as  Longwall,  Pillar- 
and-Breast,  etc.  (2)  A map  or  plan  of  the  colliery  showing  outside 
improvements  and  underground  workings.  (3)  (Mexican)  The  very 
lowest  working  in  a mine.  Trabajar  de  Plan.— To  work  to  gain  depth. 

Plancha  (Mexican).— A pig  of  lead,  etc.  A plate,  thick  sheet,  or  mass  of  any 
metal. 


Pla 


OLOSSARY. 


Pop 


603 


Planchera  (Mexican).— A mold  of  sand,  earth,  or  iron, . to  form  pigs 
of  lead. 

Plane— K main  road,  either  level  or  inclined,  along  which  coal  is  conveyed 
by  engine  power  or  gravity. 

Plane  Table— K simple  surveying  instrument  by  means  of  which  one  can 
plot  on  the  field. 

Planilla  (Mexican). — An  inclined  plane  of  mason  work,  wood,  etc.,  on  which 
tailings  are  spread  out,  to  be  concentrated  by  jets  of  water,  skilfully 
applied. 

Planillero  (Mexican).— A workman  who  devotes  himself  to  concentrating 
tailings,  etc.  on  the  Planillas;  always  paid  by  weight,  measure,  or  con- 
centrates produced. 

Plank  Pam.— A water-tight  stopping  fixed  in  a heading  constructed  of 
timber  placed  across  the  passage,  one  upon  another,  sidewise,  and 
tightly  wedged. 

Plank  Tubbing. — Shaft  lining  of  planks  driven  down  vertically  behind 
wooden  cribs  all  around  the  shaft,  all  joints  being  tightly  wedged,  to 
keep  back  the  water. 

Plant.— ThQ  shafts  or  slope,  tunnels,  engine  houses,  railways,  machinery, 
workshops,  etc.  of  a colliery  or  other  mine. 

Plat,  or  Map. — A map  of  the  surface  and  underground  workings,  or  of 
either,  to  draw  such  a map  from  survey. 

Plata  (Spanish).— Silver. 

Plata  Blanca  (Mexican).— Native  silver. 

Plata  Cornea  Amarillia  (Spanish).— lodyrite. 

Plata  Cornea  Blanca  (Spanish).— Cerargy rite. 

Plata  Cornea  Verde  (Spanish). — Embolite. 

Plata  Mixta  (Spanish).— Gold  and  silver  alloy. 

Plata  Negra  (Spanish).— Argentite. 

Plata  Pasta  (Spanish).— Spongy  silver  bars  after  retorting. 

Plata  Piha  (Spanish). — Silver  after  retorting. 

Plata  Verde  (Spanish).— Bromyrite. 

PZa^e  (North  of  England).— Scaly  shale  in  limestone  beds. 

Plates.— Metal  rails  4 ft.  long. 

Plenum. — A mode  of  ventilating  a mine  or  a heading  by  forcing  fresh  air 
into  it. 

Plomada  (Mexican).— A plumb-line  or  plumb-bob. 

Plomb  Oeuvre  (French).— Dressed  galena. 

Plomillos  (Mexican).— Shots  of  lead  found  in  slags. 

Plomo  (Spanish).— Lead,  galena. 

Plugging. — When  drift  water  forces  its  way  through  the  puddle  clay  into 
the  shaft,  holes  are  bored  through  the  slabs  near  the  leakage  point,  and 
plugs  of  clay  forced  into  them  until  the  leakage  is  stopped. 

Plumb.— V ertical . 

Plummet. — (1)  A heavy  weig;ht  attached  to  a string  or  fine  copper  wire  used 
for  determining  the  verticality  of  shaft  timbering.  (2)  A plumb-bob  for 
setting  a surveying  instrument  over  a point. 

Plunger.— Th.e  solid  ram  of  a force  pump  working  in  the  plunger  case. 

Plunger  Case.— The  pump  cylinder  or  barrel  in  which  the  plunger  works. 

Plush  Popper.- Chalcotrichite. 

Plwm  (Welsh).— Lead. 

Poblar  (Mexican). — To  set  men  at  work  in  a mine. 

Pocket.— il)  A thickening  out  of  a seam  of  coal  or  other  mineral  over  a small 
area.  (2)  A hopper-shaped  receptacle  from  which  coal  or  ore  is  loaded 
into  cars  or  boats. 

Podar  (Cornish). — Copper  pyrites. 

Pole  TooZs.— Drilling  tools  used  in  drilling  in  the  old  fashiop  with  rods,  now 
superseded  by  the  rope-drilling  method. 

Polroz  (Cornish). — Waterwheel  pit. 

Poling.— Behning  metal,  when  in  a molten  condition,  by  stirring  it  up  with  a 
green  pole  of  wood. 

Poll  Pick.— A pick  having  the  longer  end  pointed  and  the  shorter  em.  uam- 
mer-shaped. 

Polvillos  (Spanish).— Rich  ores  or  concentrates. 

Polvoulla  (Spanish).— Black  silver. 

Poppet  Heads.— The  pulley  frame  or  hoisting  gear  over  a shaft. 

Poppet  {Puppet).— {1)  A pulley  frame  or  the  head -gear  over  a shaft.  (2)  A 
valve  that  lifts  bodily  from  its  seat  instead  of  being  hinged. 


604 


Pos 


GLOSSARY. 


Pun 


Post.—{l)  Any  upright  timber;  applied  particularly  to  the  timbers  used  for 
propping.  See  Prop.  (2)  Local  term  for  sandstone.  Post  stone  may  be 
“strong,”  “framey,”  “short,”  or  “broken.” 

Post-and-Stall.—A  system  of  working  coal  much  the  same  as  Pillar-and-Stall. 

Post  Tertiary.— StTatSi  younger  than  the  Tertiary  formation. 

Pot  Bottom.— A large  boulder  in  the  roof  slate,  having  the  appearance  of  the 
rounded  bottom  of  a pot,  and  which  easily  becomes  detached. 

Pot  Growan  (Cornish).— Decomposed  granite. 

Pot  Hole.— A circular  hole  in  the  rock  caused  by  the  action  of  stones  whirled 
around  by  the  water  when  the  strata  was  covered  by  water.  They  are 
generally  filled  with  sand  and  drift. 

Power  Drill.— A rock  drill  employing  steam,  air,  or  electricity  as  a motor. 

Prian  (Cornish).— Soft  white  clay. 

Pricker.— {1)  A thin  brass  rod  for  making  a hole  in  the  stemming  when 
blasting,  for  the  insertion  of  a fuse.  (2)  A piece  of  bent  wire  by  which 
the  size  of  the  flame  in  a safety  lamp  is  regulated  without  removiug  the 
top  of  the  lamp. 

Prill.— {!)  An  extra-rich  stone  of  ore.  (2)  A bead  of  metal. 

Prong  (English).— The  forked  end  of  the  bucket-pump  rods  for  attachment  to 
the  traveling  valve  and  seat. 

Prop.— A wooden  or  cast-iron  temporary  support  for  the  roof. 

Propping.— timbering  of  a mine. 

Prospect— name  given  to  underground  workings  whose  value  has  not 
yet  been  made  manifest.  A prospect  is  to  a mine  what  mineral  is 
to  ore. 

Prospect  Hole.— Any  shaft  or  drift  hole  put  down  for  the  purpose  of  prospect- 
ing the  ground. 

Prospect  Tunnel  or  Entry.— A tunnel  or  entry  driven  through  barren  measures 
or  a fault  to  ascertain  the  character  of  strata  beyond. 

Prospecting. — Examining  a tract  of  country  in  search  of  minerals. 

Prospector. — One  engaged  in  searching  for  minerals. 

Protector  Lamp. — A safety  lamp  whose  flame  cannot  be  exposed  to  the  out- 
ward atmosphere,  as  the  action  of  opening  the  lamp  extinguishes  the 
light. 

Prove. — (1)  To  ascertain,  by  boring,  driving,  etc.,  the  position  and  character 
of  a coal  seam,  a fault,  etc.  (2)  To  examine  a mine  in  search  of  fire- 
damp, etc.,  known  as  “ proving  the  pit.” 

Proving  Hole.—{l)  A bore  hole  driven  for  prospecting  purposes.  (2)  A 
small  heading  driven  in  to  find  a bed  or  vein  lost  by  a dislocation  ol 
the  strata,  or  to  prove  the  quality  of  the  mineral  in  advance  of  the 
other  workings. 

Pudding  Machine.— A circular  machine  for  washing  pa^y  dirt. 

Pudding  i^ocfc.— Conglomerate. 

Puddle. — (1)  Earth  well  rammed  into  a trench,  etc.,  to  prevent  leaking. 
(2)  A process  for  converting  cast  iron  into  wrought  iron. 

(Mexican). — The  actual  wmking  of  a mine;  the  aggregation  of 
persons  employed  therein. 

Puertas  ( Mexican )‘.— Massive  barren  rocks,  or  “ horses,”  occurring  in  a vein. 

Pug  Mill.— A mill  for  preparing  clay  for  bricks,  pottery,  etc. 

PuUey.—{\)  The  wheel  over  which  a winding  rope  passes  at  the  top  of  the 
head-gear.  (2)  Small  wooden  cylinders  over  which  a winding  rope  is 
carried  on  the  floor  or  sides  of  a plane. 

Overwinding  or  drawing  up  a cage  into  the  pulley  frame. 

Pi^Zp.— Crushed  ore,  wet  or  dry. 

Pump. — Any  mechanism  for  raising  water. 

Pump  Po?).— See  Boh. 

Pump  Ring.— A flat  iron  ring  that,  when  lapped  with  tarred  baize  or  engine 
shag,  secures  the  joints  of  water  columns. 

Pump  Pods.— Heavy  timbers  by  which  the  motion  of  the  engine  is  trans- 
mitted to  the  pump.  In  Cornish  and  bull  pumps,  the  weight  of  the  rods 
makes  the  effective  (pumping)  stroke,  the  engine  merely  lifting  the  rods 
on  the  up  stroke. 

Pump  Slope. — A slope  used  for  pumping  machinery. 

Pump  Station.— An  enlargement  made  in  the  shaft,  slope,  or  gangway,  to 
receive  the  pump. 

Pump  Tree.- -Cast-iron  pipes,  generally  9 ft.  long,  of  which  the  column  or  set 
is  formed. 

Punch-and‘Thirl.—A  kind  of  pillar-and-stall  system  of  working. 


Pun 


GLOSSARY. 


Ree 


605 


Punch  Prop.— A.  short  timber  prop  set  on  the  top  of  a crown  tree,  or  used  in 
holding,  as  a sprag. 

Putty  Stones.— pieces  of  decomposed  rock  found  in  placer  deposits. 

Pyran  (Cornish).— See  Prian. 

Pi/n^es.— Sulphide  of  iron. 

Pyrometer.— An  instrument  for  measuring  high  degrees  of  heat. 

Quajado  (Spanish).— Dull  lead  ore. 

0uarry.—{l)  An  open  surface  excavation  for  working  valuable  rocks  or 
minerals.  (2)  An  underground  excavation  for  obtaining  stone  for 
stowage  or  pack  walls. 

Quartz  Bucket— K bucket  for  hoisting  quartz. 

Quaternary.— Post-tQrtmry  period. 

Quemadero  (Mexican).— A burning  place;  a retorting  furnace  for  silver  or 
gold  amalgam. 

Quemados  (Mexican). — Burnt  stuff.  Any  dark  cinder-like  mineral  encoun- 
tered in  a vein  or  mineral  deposit,  generally  manganiferous. 

Qtteme  (Mexican). — A roast  of  ore;  the  process  of  roasting  ore. 

Quick  (Adjective).— Soft,  running  ground;  an  ore  or  pay  streak  is  said  to  be 
quickening  when  the  associated  minerals  indicate  richer  mineral 
ahead.  Quick  (Noun).— (1)  Productive.  (2)  Mercury. 

Quicksand.— Soft  watery  strata  easily  moved,  or  readily  yielding  to  pressure.  • 

Quicksilver.— Mercury. 

Quillato  (Spanish).— Carat. 

Quitapepena  (Mexican).— A watchman  that  searches  the  miners  as  they 
come  out  at  the  mouth  of  a mine. 

Rabban  (Cornish).— Yellow  dry  gossan. 

Rabbling.— Stirring  up  a charge  of  ore  in  a reverberatory  furnace  with 
specially  designed  iron  rods. 

Race.— A channel  for  conducting  water  to  or  from  the  place  where  it  per- 
forms work.  The  former  is  termed  the  headrace,  and  the  latter  the 
tailrace. 

Rack  (Cornish).— A stationary  huddle. 

Raff.—TYie  coarse  ore  after  crushing  by  Cornish  rolls. 

Raffain  (Cornish).— Poor  ore. 

Raff  Wheel.— A revolving  wheel  with  side  buckets  for  elevating  the  raff. 

Rdjter  Timbenng.— That  in  which  the  timbers  appear  like  roof  rafters. 

Rag  Burning  (Cornish).— The  first  roasting  of  tin-witts. 

Ragging  (Cornish).  Rough  cobbing. 

Rag  BTied.— Sprocket  wheel.  A wheel  with  teeth  or  pins  that  catch  into  the 
links  of  chains. 

Rails.— The  iron  or  steel  portion  of  the  tramway  or  railroad. 

Rake  (Cornish).— (1)  A vein.  (2)  (Derbyshire)  Fissure  vein  crossing  strata. 

Pam.— (1)  The  plunger  of  a pump.  (2)  A device  for  raising  water. 

Ramal  (Mexican).— A branch  vein. 

Ramalear  (Mexican)  .— To  branch  off  into  various  divisions. 

PambZe.— Stone  of  little  coherence  above  a seam  that  falls  readily  on  the 
removal  of  the  coal.  See  Following  Stone. 

Ranee. — A pillar  of  coal. 

Rapper.— A lever  with  a hammer  attached  at  one  end,  which  signals  by 
striking  a plate  of  metal,  when  the  signaling  wire  to  which  it  is  attached 
is  pulled. 

Rash.— A term  used  to  designate  the  bottom  of  a mine  when  soft  and  slaty. 

Rastrillo  (Mexican).— A rake;  a stirrer  for  moving  ore  in  a furnace. 

Rastron  (Mexican).— A Chilian  mill. 

Raw  Ore.— Not  roasted  or  calcined. 

Reacher.—A  slim  prop  reaching  from  one  wall  to  the  other. 

Reamer. — An  enlarging  tool. 

Peamtng.— Enlarging  the  diameter  of  a bore  hole. 

Receiving  Pit.— A shallow  pit  for  containing  material  run  into  it. 

Red-Ash  Coal.— Coal  that  produces  a reddish  ash,  when  burnt. 

Red  Rab  (Cornish).— Red  slaty  rock. 

Reduced.—S^hen  a metal  is  freed  from  its  chemical  associate  it  is  said  to  be 
reduced  to  the  metallic  state. 

Reduction  Works. — Works  for  reducing  metals  from  their  ores. 

Pee/.— (1)  A vein  of  quartz.  (2)  Bed  rock  of  alluvial  claims. 

JieeJ  Drive.— In  alluvial  mines,  drives  made  in  the  country  rock  or  reef. 


606 


Ref 


GLOSSARY, 


Riv 


Refining. —Yhe  freeing  of  metals  from  impurities. 

i2e/racibry.— Rebellious  ore,  not  easily  treated  by  ordinary  processes. 

Refuge  Hole— A place  formed  in  the  side  of  an  underground  plane  in  which 
a man  can  take  refuge  during  the  passing  of  a train,  or  when  shots  are 
fired. 

Regulator.— A door  in  a mine,  the  opening  or  shutting  of  which  regulates  the 
supply  of  ventilation  to  a district  of  the  mine. 

Regulus. — See  Matte. 

Relampago,  or  Relampaguear  (Mexican).— The  brightening  of  the  silver 
button  during  cupellation. 

Reliz  (Spanish). — Wall  of  lode. 

Rendif  (Mexican).— Is  when  all  the  silver  has  been  amalgamated  in  a heap 
of  argentiferous  mud  on  a patio. 

Rendrock.—A  variety  of  dynamite. 

Repairman.— A workman  whose  duty  it  is  to  repair  tracks,  doors,  brattices, 
or  to  reset  timbers,  etc.,  under  the  direction  of  the  foreman. 

Repaso-Repasar  (Mexican).— The  art  of  mixing  up  the  mud  heaps  in  the 
patio  process  of  amalgamation  by  treading  them  over  with  horses  or 
mules. 

Repos  Adero  (Mexican).— The  bottom  of  a crucible  or  pot  in  an  upright 
smelting  furnace. 

Rescatadores  (Mexican).— Ore  buyers. 

Reserve.— MmevaX  already  opened  up  by  shafts,  winzes,  levels,  etc.,  which 
may  be  broken  at  short  notice  for  any  emergency. 

Reservoir.— An  artificially  built,  dammed,  or  excavated  place  for  holding  a 
reserve  of  water, 

Respaldos  (Mexican).— The  walls  enclosing  a vein.  Respaldo  AHo.-TIoq 
hanging  wall.  Respaldo  Bajo.— The  foot-wall. 

Rests,  Keeps,  M'w.— Supports  on  which  a cage  rests  when  the  loaded  car 
is  being  taken  off  and  the  empty  one  put  on. 

Resue —See  Stripping. 

Retort— {!)  A vessel  with  a long  neck,  used  for  distilling  the  quicksilver 
from  amalgam.  (2)  The  vessel  used  in  distilling  zinc. 

Return.— The  air-course  along  which  the  vitiated  air  of  a mine  is  returned 
or  conducted  back  to  the  upcast  shaft. 

Return  Air.— The  air  that  has  been  passed  through  the  workings. 

Reverberatory.- A class  of  furnaces  in  which  the  flame  from  the  fire-grate  is 
made  to  beat  down  on  the  charge  in  the  body  of  the  furnace. 

Reversed  Fault.— See  Overlap  Fault. 

Rib.— The  side  of  a pillar. 

Rib-and-Pillar.—A  system  of  working  similar  to  Pillar-and-Stall. 

Ribbon.— A line  of  bedding  or  a thin  bed  appearing  on  the  cleavage  surface 
and  sometimes  of  a different  color. 

RfcA:.— Open  heap  in  which  coal  is  coked. 

Ridding.— Clearing  away  fallen  stone  and  debris. 

Riddle.— An  oblong  frame  holding  iron  bars  parallel  to  each  other,  used  for 
sifting  material  that  is  thrown  against  it. 

Ride,  Riding.— To  be  conveyed  on  a cage  or  mine  car. 

Rider.— iX)  A guide  frame  for  steadying  a sinking  bucket.  (2)  Boys  that 
ride  on  trips  on  mechanical  haulage  roads.  (3)  A thin  seam  of  coal 
overlying  a thicker  one. 

Riffle,  or  Crosspieces  placed  on  the  bottom  of  a sluice  to  save  gold; 

or  grooves  cut  across  inclined  tables. 

Right  Shore.— The  right  shore  of  a river  is  on  the  right  hand  when  descend- 
ing the  river. 

Rill.— The  coarse  ore  at  the  periphery  of  a pile. 

Rim  Rock.— Bed  rock  forming  a boundary  to  gravel  deposit. 

Ring.—{1)  A complete  circle  of  tubbing  plates  placed  round  a circular  shaft. 
(2)  Troughs  placed  in  shafts  to  catch  the  falling  water,  and  so  arranged 
as  to  convey  it  to  a certain  point. 

J^zppm.gr.— Removing  stone  from  its  natural  position  above  the  seam. 

Riscos  (Mexican).— Sharp  and  precipitous  rocks;  amorphous  quartz  found 
in  veins  or  outcrops. 

The  inclination  of  the  strata,  when  looking  up  the  pitch. 

Rise  Workings. — Underground  workings  carried  on  to  the  rise  or  high  side 
of  the  shaft. 

River  Mining. — Working  beds  of  existing  rivers  by  deflecting  their  course 
or  by  dredging. 


Roa 


GLOSSARY. 


Sap 


607 


Road.—{l)  Any  underground  passageway  or  gallery.  (2)  The  iron  rails, 
etc.  of  underground  roads. 

Roasting.— Ueating  ores  at  a temperature  sufficient  to  cause  a chemical 
change,  but  not  enough  to  smelt  them. 

Rob.— To  cut  away  or  reduce  the  size  of  pillars  of  coal. 

Robbing.— The  taking  of  mineral  from  pillars. 

Robbing  an  Entry.— ^ee  Drawing  an  Entry. 

Eock.—A  mixture  of  different  minerals  in  varying  proportions. 

Rock  Breaker.— K machine  for  reducing  ore  in  size  by  crunching  it  between 
powerful  jaws. 

Rock  Chute. — See  Slate  Chute. 

Rock  Drill.— K rock-boring  machine  worked  by  hand,  compressed  air,  steam, 
or  electrical  power. 

Rocker See  Cradle. 

Rock  Fault.— A replacement  of  a coal  seam  over  greater  or  less  area,  by  some 
other  rock,  usually  sandstone. 

Rodding.— The  operation  of  fixing  or  repairing  wooden  eye  guides  in 

An  inequality  in  the  roof  or  floor  of  a mine. 

Roller.— A small  steel,  iron,  or  wooden  wheel  or  cylinder  upon  which  the 
hauling  rope  is  carried  just  above  the  floor. 

Rolleyway.—A  main  haulage  road. 

Rolling  Ground.— ^hen  the  surface  is  much  varied  by  many  small  hills  and 
valleys. 

Cast-iron  cylinders,  either  plain  or  fitted  with  steel  teeth,  used  to 
break  coal  and  other  materials  into  various  sizes. 

Roof.— The  top  of  any  subterranean  passage. 

Room. — Synonymous  with  Breast. 

Room-and-Rance.—A  system  of  working  coal  similar  to  Pillar-and-Stall. 

Rope  Roll.— The  drum  of  a winding  engine. 

Rosiclara  (Spanish).— Ruby  silver  ore. 

Roughs  (Cornish).— Second  quality  tin  sands. 

Round  Coal. — Coal  in  large  lumps,  either  hand-picked,  or,  after  passing  over 
screens,  to  take  out  the  small. 

Royalty.— The  price  paid  per  ton  to  the  owner  of  mineral  land  by  the  lessee. 

Rubbing  Surface.— The  total  area  of  a given  length  of  airway;  that  is,  the 
area  of  top,  bottom,  and  sides  added  together,  or  the  perimeter  multi- 
plied by  the  length. 

jRwbbZe.— Coarse  pieces  of  rock. 

Rumbo  (Mexican).— The  course  or  direction  of  a vein. 

Run.—{1)  The  sliding  and  crushing  of  pillars  of  coal.  (2)  The  length  of  a 
lease  or  tract  on  the  strike  of  the  seam. 

Run  Coa?.- Soft  bituminous  coal. 

Rung,  Rundle,  or  Round.— A step  or  cross-bar  of  a ladder.  ^ 

Runner.— A man  or  boy  whose  duty  it  is  to  run  mine  cars  by  gravity  from 
working  places  to  the  gangway. 

Running  Lift.— A sinking  .^et  of  pumps  constructed  to  lengthen  or  shorten 
at  will,  by  means  of  a sliding  or  telescoping  wind  bore. 

Rush.— An  old-fashioned  way  of  exploding  blasts  by  filling  a hollow  stalk 
with  slow  powder  and  then  igniting  it. 

Rush  Gold.— Gold  coated  with  oxide  of  iron  or  manganese. 

Rush  Together. — See  Caved  In. 

Rusty.— stained  by  iron  oxide. 

Saca  (Mexican).— A bagful  of  ore.  A mine  is  said  to  be  de  buena  saca  when 
it  has  large  quantities  of  ore  easy  to  get  out. 

Saddle.— An  anticlinal,  a hogback. 

Saddleback.— A depression  in  the  strata.  See  Roll. 

Saddle  Reef.— A reef  having  the  form  of  an  inverted  V. 

Safety  Cage.— A cage  fitted  with  an  apparatus  for  arresting  its  motion  in  the 
shaft  in  case  the  rope  breaks. 

Safety  Car.— See  Barney. 

Safety  Catches.— Applmnces  fitted  to  cages,  to  make  them  safety  cages. 

Safety  Door. — A strongly  constructed  door,  hinged  to  the  roof,  and  always 
kept  open  and  hung  near  to  the  main  door,  for  immediate  use  when 
main  door  is  damaged  by  an  explosion  or  otherwise. 

Safety  Fuse.— A cord  with  slow-burning  powder  in  the  center  for  exploding 
charged  blast  holes. 


608 


' Saf 


GLOSSARY. 


Seg 


Safety  Lamp.— A miner’s  lamp  in  which  the  flame  is  protected  in  such  a 
manner  that  an  explosive  mixture  of  air  and  firedamp  can  he  detected 
by  the  mixture  burning  inside  the  gauze. 

Sag.— A depression,  e.  g.,  in  ropes,  ranges  of  mountains,  etc. 

Sagre,  or  Seggar.—A  local  term  for  fireclay,  often  forming  the  floor  (or  thill) 
of  coal  seams. 

Salting. — (1)  Changing  the  value  of  the  ore  in  a mine  or  of  ore  samples 
before  they  have  been  assayed,  so  that  the  assay  will  show  much  higher 
values  than  it  should.  (2)  Sprinkling  salt  on  the  floors  of  underground 
passages  in  very  dry  mines,  in  order  to  lay  the  dust. 

Sampler.— {!)  An  instrument  or  apparatus  for  taking  samples.  (2)  One  whose 
duty  it  is  to  select  the  samples  for  an  assay,  or  to  prepare  the  mineral 
to  be  assayed,  by  grinding  and  sampling. 

Sampling  TFbrArs.— Works  for  sampling  and  determining  the  values  obtained 
in  ores;  where  ores  are  bought  and  sold. 

Samson  Post.— An  upright  supporting  the  working  beam  that  communicates 
oscillatory  motion  to  pump  or  drill  rod. 

Sand  Bag.— A bag  filled  with  sand  for  preventing  a washout  by  obstructing 
the  flow. 

Sand  Pump.— A sludger;  a cylinder  provided  with  a stem  (or  other)  valve, 
lowered  into  a drill  hole  to  remove  the  pulverized  rock. 

Scaffolding.— IncTustations  on  the  inside  of  a blast  furnace. 

Scale.— (1)  A small  portion  of  the  ventilating  current  in  a mine  passing 
through  a certain  size  of  aperture.  (2)  The  rate  of  wages  to  be  paid, 
which  varies  under  certain  contingencies. 

Scale  Door. — See  Regulator. 

Scallop. — ^To  hew  coal  without  kirving  or  nicking  or  shot  firing. 

Schist. — Crystalline  or  metamorphic  rocks  having  a slaty  structure. 

Schute.—See  Chute. 

Scissors  Fault.— A fault  of  dislocation,  in  which  two  beds  are  thrown  so  as  to 
cross  each  other. 

Scoop.— A large-sized  shovel  with  a scoop-shaped  blade. 

Scoria. — Ashes. 

Scarifier. —A  small  dish  used  in  assaying. 

Scovan  (Cornish).— A tin  lode  showing  no  gossan  at  surface. 

Score  (Cornish).— Purest  tin  ore. 

Scramming.— Cleaning  up  small  bodies  or  patches  of  ore  left  in  the  ordinary 
process  of  mining. 

Scraper.— {1)  A tool  for  cleaning  the  dust  out  of  the  bore  hole.  (2)  A 
mechanical  contrivance  used  at  colleries  to  scrape  the  culm  or  slack 
along  a trough  to  the  place  of  deposit. 

Scrapper.— A local  name  given  to  parties  that  pick  up  the  ore  left  on  dumps. 

Screen.— il)  A mechanical  apparatus  for  sizing  materials.  (2)  A cloth  brat- 
tice or  curtain  hung  across  a road  in  a mine,  to  direct  the  ventilation. 

Serin  (Derbyshire;.— A small  vein. 

Scrowl  (Cornish).— Loose  ore  where  a vein  is  crossed. 

Fracturing  the  slate  aloflg  the  grain,  i.  e.,  across  the  cleavage. 

Scupper  Nails. — Nails  with  broad  heads,  for  nailing  down  canvas,  etc. 

Sea  Coal. — That  which  is  transported  by  sea. 

SeaZmgr.— Shutting  off  all  air  from  a mine  or  a part  of  a mine  by  stoppings. 

Seam.—{1)  Synonymous  with  Bed,  Vein,  etc.  (2)  (Cornish)  A horse  load 
of  ore. 

Seam-Out.— A term'applied  to  a shot  or  blast  that  has  simply  blown  out  a softer 
stratum  of  the  deposit  in  which  it  was  placed,  without  dislodging  the 
other  strata  or  layers  of  the  seam. 

Second  Outlet  {Second  Opening).— A passageway  out  of  a mine,  for  use  in  case 
of  accident  to  the  main  outlet. 

/Seconds.- The  second-class  ore  of  a mine  that  requires  dressing. 

Second  Working.— The  operation  of  getting  or  working  out  the  pillars  formed 
by  the  first  working. 

Section.— {1)  A vertical  or  horizontal  exposure  of  strata.  (2)  A drawing  or 
sketch  representing  the  rock  strata  as  cut  by  a vertical  or  a horizontal 
plane. 

Sedimentary  Rocks.— Blocks  formed  from  deposits  of  sediment  by  wind  or 
water. 

Seedbag. — A water-tight  packing  of  flaxseed  around  the  tube  of  a drill  hole, 
to  prevent  the  influx  into  the  hole  of  water  from  above. 

Segregations.— Detaehed  porTions  of  veins  in  place. 


Sel 


GLOSSARY. 


Sho 


609 


Self-Acting  Plane.— An  inclined  plane  upon  which  the  weight  or  force  of 
gravity  acting  on  the  full  cars  is  sufficient  to  overcome  the  resistance  of 
the  empties;  in  other  words,  the  full  car,  running  down,  pulls  the  other 
car  up. 

Self- Detaching  Hook.— A self-acting  hook  for  setting  free  a hoisting  rope  in 
case  of  overwinding. 

Self-Feeders.— AnXomatio,  appliances  for  feeding  ore-dressing  machines. 

Selvage. — The  clay  seam  on  the  walls  of  veins;  gouge. 

Separation  Doors.— The.  main  doors  at  or  near  the  shaft  or  slope  bottom, 
which  separate  the  intake  from  the  return  airways. 

Separation  Valve.— A massive  cast-iron  plate  suspended  from  the  roof  of  a 
return  airway  through  which  all  the  return  air  of  a separate  district 
flows,  allowing  the  air  to  always  flow  past  or  underneath  it;  but  in 
the  event  of  an  explosion  of  gas,  the  force  of  the  blast  closes  it  against 
its  frame  or  seating,  and  prevents  a communication  with  other  districts. 
The  blast  being  over,  the  weight  of  the  valve  allows  it  to  return  to  its 
normal  position. 

Set.— To  flx  in  place  a prop  or  sprag. 

Set  Hammer.— The  flat-faced  hammer  held  on  hot  iron  by  a blacksmith  when 
shaping  or  smoothing  a surface  by  aid  of  his  striker’s  sledge. 

Set  of  Timber. — The  timbers  which  compose  any  framing,  whether  used  in 
a shaft,  slope,  level,  or  gangway.  Thus,  the  four  pieces  forming  a single 
course  in  the  curbing  of  a shaft,  or  the  three  or  four  pieces  forming 
the  legs  and  collar,  and  sometimes  the  sill  of  an  entry  framing  are 
together  called  a set  of  timber,  or  timber  set. 

Shackle. — A U-shaped  link  in  a chain  closed  by  a pin;  when  the  latter  is  with- 
drawn the  chain  is  severed  at  that  point. 

Shadd  (Cornish). — Rounded  fragments  of  ore  overlying  a vein. 

Shaft— A vertical  or  highly  inclined  pit  or  hole  made  through  strata,  through 
which  the  product  of  the  mine  is  hoisted,  and  through  which  the  ventila- 
tion is  passed  either  into  or  out  of  the  mine.  A shaft  sunk  from  one 
seam  to  another  is  called  a “blind  shaft.” 

Shaft  Pillar.— Solid  material  left  unworked  beneath  buildings  and  around 
the  shaft,  to  support  them  against  subsidence. 

Shaking  Table.— An  inclined  table  for  concentrating  fine  grains  of  ore,  which 
is  rapidly  shaken  by  a short  motion 

Shale.— {!)  Strictly  speaking,  all  argillaceous  strata  that  split  up  or  peel  off 
in  thin  laminae.  (2)  A laminated  and  stratified  sedimentary  deposit  of 
clay,  often  impregnated  with  bituminous  matter. 

Shank.— The  body  portion  of  any  tool,  up  from  its  cutting  edge  or  bit. 

Shearing. — Cutting  a vertical  groove  in  a coal  face  or  breast.  The  cutting  of 
a “ fast  end  ” of  coal. 

Shear  Legs.— A high  wooden  frame  placed  over  an  engine  or  pumping  shaft 
fitted  with  small  pulleys  and  rope  for  lifting  heavy  w.Mghts. 

Shears,  or  Sheers  (English). — Two  tall  poles,  with  their  leet  some  distance 
apart  and  their  tops  fastened  together,  for  supporting  hoisting  tackle. 

Shear  Zone.— Hogback. 

Sheave.— A wheel  with  a grooved  circumference  over  which  a rope  is  turned 
either  for  the  transmission  of  power  or  for  winding  or  hauling. 

Sheel  Pump. — See  Sludgen 

Sheets.— Coarse  cloth  curtains  or  screens  for  directing  the  ventilating  current 
underground. 

Shelly.— A name  applied  to  coal  that  has  been  so  crushed  and  fractured  that 
it  easily  breaks  up  into  small  pieces.  The  term  is  also  applied  to  a lami- 
nated roof  that  sounds  hollow  and  breaks  into  thin  layers  of  slate  or 
shale. 

Shet  (Staffordshire). — Fallen  roof  of  coal  mine. 

Sheth. — An  old  term  denoting  a district  of  about  eight  or  nine  adjacent  bords. 
Thus,  a “ sheth  of  bords,”  or  a “ sheth  of  pillars.” 

Shift. — (1)  The  number  of  hours  worked  without  change.  (2)  A gang  or 
force  of  workmen  employed  at  one  time  upon  any  work,  as  the  day  shift, 
or  the  night  shift. 

Shoad  (Cornish).— See  Shadd. 

Sheading  ( Cornish)  .—Prospecting. 

Shoe.—{l)  A steel  or  iron  guide  piece  fixed  to  the  ends  or  sides  of  cages,  to 
fit  or  run  on  the  conductors.  (2)  The  upper  working  face  of  a stamp  or 
grinding  pan.  (3)  The  lower  capping  of  any  post  or  pile,  to  protect  its 
end  while  driving.  (4)  A wooden  or  sheet-iron  frame  or  muff  arranged 


610  Sho  glossary.  Sin 


at  the  bottom  of  a shaft  while  sinking  through  quicksand,  to  prevent  the 
inflow  of  sand  while  inserting  the  shaft  lining. 

Shoot,  Chute,  Shute—{1)  A run  of  rich  material  in  a vein.  (2)  An  inclined 
or  vertical  trough  or  pipe  for  conveying  materials  from  a higher  to  a 
lower  level. 

Shoot~Yo  break  rock  or  coal  by  means  of  explosives. 

Shooting. — Blasting  in  a mine. 

Shore  (English). — A studdle  or  thrusting  stay. 

Shore  Up.— To  stay,  prop  up,  or  support  by  braces. 

Shot.—{l)  A charge  or  blast.  (2)  The  firing  of  a blast.  (3)  Injured  by  a 
blast. 

Shot-Firer.— See  Shot  Lighter. 

Shot  Hole.—Tloe  bore  hole  in  which  an  explosive  substance  is  placed  for 
blasting. 

Shot  Lighter,  or  Shot  Firer. — A man  specially  appointed  by  the  manager  of 
the  mine  to  fire  off  every  shot  in  a certain  district,  if,  after  he  has 
examined  the  immediate  neighborhood  of  the  shot,  he  finds  it  free  from 
gas,  and  otherwise  safe. 

Shotty  Granular  pieces  like  shot. 

Show.—S^hen  the  flame  of  a safety  lamp  becomes  elongated  or  unsteady, 
owing  to  the  presence  of  firedamp  in  the  air,  it  is  said  to  show. 

Showing. — The  first  appearance  of  float,  indicating  the  approach  to  an  out- 
cropping vein  or  seam.  Blossom. 

Shroud.— A housing  or  jacket. 

Shute. — See  Chute,  Shoot,  and  Schute. 

Shutter.— {1)  A movable  sliding  door,  fitted  within  the  outer  casing  of  a 
Guibal  or  other  closed  fan,  for  regulating  the  size  of  the  opening  from 
the  fan,  to  suit  the  ventilation  and  economical  working  of  the  machine. 
(2)  A slide  covering  the  opening  in  a door  or  brattice,  and  forming  a 
regulator  for  the  proportionate  division  of  the  air-current  between  two 
or  more  districts  of  a mine. 

Sickening. — A coating  of  impurities  on  quicksilver  that  retards  amalgama- 
tion or  the  coalescence  of  the  globules  of  quicksilver. 

Inclination. 

Side.—{1)  The  more  or  less  vertical  face  or  wall  of  coal  or  goaf  forming  one 
side  of  an  underground  working  place.  (2)  Rib.  (3)  A district. 

Side  Chain.— A chain  hooked  on  to  the  sides  of  cars  running  on  an  incline  or 
along  a gangway,  to  keep  the  cars  together  in  case  the  coupling 
breaks. 

Sidelong  Reef.— An  overhanging  wall  of  bed  rock  in  alluvial  formations 
running  parallel  with  the  course  of  the  gutter;  generally  only  on  one 
side  of  it. 

Siding.— A short  piece  of  track  parallel  to  the  main  track,  to  serve,  as  a 
passing  place. 

Siding  Over.— A short  road  driven  in  a pillar  in  a head  wise  direction. 

Sight.— {\)  A bearing  or  angle  taken  with  a compass  or  transit  when  making 
a survey.  (2)  Any  established  point  of  a survey. 

Sights— '^oh^  or  weighted  strings  hung  from  two  or  more  established  points 
in  the  roof  of  a room  or  entry,  to  give  direction  to  the  men  driving  the 
entry  or  room. 

SiU.—{\)  Q'he  fioor  piece  of  a timber  set,  or  that  on  which  the  track  rests; 
the  base  of  any  framing  or  structure.  (2)  The  floor  of  a seam. 

Silver.— {1)  A certain  white  ductile  and  valuable  metal.  (2)  Short  for  quick- 
silver. 

Sing. — The  noise  made  by  a feeder  of  gas  issuing  from  the  coal. 

Singing  Coal.— Cool  from  which  gas  is  issuing  with  a hissing  sound. 

Singing  Lamp.— A safety  lamp,  which,  when  placed  in  an  atmosphere  of 
explosive  gas,  gives  out  a peculiar  sound  or  note,  the  strength  of  the 
note  varying  in  proportion  to  the  percentage  of  firedamp  present. 

Single-Entry  System. — A system  of  opening  a mine  by  driving  a single  entry 
only,  in  place  of  a pair  of  entries.  The  air-current  returns  along  the 
face  of  the  rooms,  which  must  be  kept  open. 

Single-Intake  Fan.— A ventilating  fan  that  takes  or  receives  its  air  upon  one 
side  only. 

Single-Rope  Haulage. — A system  of  underground  haulage  in  which  a single 
rope  is  used,  the  empty  trip  running  in  by  gravity.  This  is  engine-plane 
haulage. 

Sink.— To  excavate  a shaft  or  slope;  to  bore  or  put  down  a bore  hole. 


Sin 


GLOSSARY. 


Sli 


611 


Sinker. —A  man  who  works  at  the  bottom  of  a shaft  or  face  of  a slope  during 
the  course  of  sinking. 

Sinker  Bar.— In  rope  drilling,  a heavy  bar  attached  above  the  jars,  to  give 
force  to  the  up  stroke,  so  as  to  dislodge  the  bit  in  the  hole. 

Sinking.— TYiq  process  of  excavating  a shaft  or  slope  or  boring  a hole. 

Siphon.— A simple,  effective,  and  economical  mode  of  conveying  water  over 
a hill  whose  height  is  not  greater  than  what  the  atmospheric  pressure 
will  raise  the  water.  Its  mrm  is  that  of  an  iron  pipe,  bent  like  an 
inverted  U;  the  vertical  height  between  the  surface  of  the  water  in  the 
upper  basin  and  the  top  of  the  hill  is  called  the  lift  of  the  siphon;  while 
the  vertical  height  between  the  surfaces  of  the  water  in  the  upper  and 
lower  basins  is  called  the  fall  of  the  siphon. 

Sizing. — To  sort  minerals  into  sizes. 

Skew  Back.-YYiQ  beveled  stone  from  which  an  arch  springs,  and  upon  which 
it  rests. 

Skids.— Slides  upon  which  heavy  bodies  are  slid  from  place  to  place. 

Skimpings  (Cornish).— The  poorest  ore  skimmed  off  the  jigger. 

Skip.—{1)  A mine  car.  (2)  A car  for  hoisting  out  of  a slope.  (3)  A thin 
slice  taken  off  from  a breast  or  pillar  or  rib  along  its  entire  length  or 
part  of  its  length. 

Skirting.— Road  opened  up  or  driven  next  a fall  of  stone,  or  an  old  fallen  place. 

Skit  (Cornish).— A pump. 

Slab.— Split  pieces  of  timber  from  2 in.  to  3 in.  thick,  4 ft.  to  6 ft.  long,  and 
7 in.  to  14  in.  wide,  placed  behind  sets  or  frames  of  timber  in  shafts  or 
levels. 

Slack.— (1)  Fine  coal  that  will  pass  through  the  smallest  sized  screen.  The 
fine  coal  and  dust  resulting  from  the  handling  of  coal,  and  the  disinte- 
gration of  soft  coal.  (2)  The  process  by  which  soft  coal  disintegrates 
when  exposed  to  the  air  and  weather. 

Slag.— The  liquid  refuse  from  a smelting  operation,  which  floats  on  top  of 
the  metal. 

Slant.— {1)  An  underground  roadway  driven  at  an  angle  between  the  full 
rise  or  dip  of  the  seam  and  the  strike  or  level.  (2)  Any  inclined  road 
in  a seam. 

Slant  Chutes.— Chutes  driven  diagonally  across  a pillar,  to  connect  a breast 
manway  with  a manway  chute. 

Slate.— (1)  A hardened  clay  having  a peculiar  cleavage.  (2)  About  coal 
mines,  slate  is  any  shale  accompanying  the  coal,  also  sometimes  applied 
to  bony  coal. 

Slate  Ricker.— (1)  A man  or  boy  that  picks  the  slate  or  bony  coal  from 
anthracite  coal.  (2)  A mechanical  contrivance  for  separating  slate  and 
coal. 

Slate  Chute.— {1)  A chute  for  conveying  slate  or  bony  coal  to  a pocket  from  • 
which  it  is  loaded  into  “ dumpers.”  (2)  A chute  driven  through  slate. 

Sleek  (Derbyshire).— Mud  in  a mine. 

Sled. — A drag  used  to  convey  coal  along  the  face  to  the  road  head  where  it  is 
loaded,  or  to  the  chute. 

Sledge.— A heavy  double-handed  hammer. 

Sleeper  (English).— The  foundation  pieces  or  cross-ties  on  which  rails  rest. 

Sleeping  Tab'e  (Cornish). — A buddle. 

Sleeve.— A ho  How  cylinder  fitting  over  two  pieces,  to  hold  them  together. 

Polished  surfaces  of  vein  walls. 

Slide.— Loose  deposit  covering  the  outcrop  of  a seam. 

Slides.— See  Guides. 

Sliding  Scale.— A mode  of  regulating  the  wages  paid  workingmen  by  taking 
as  a basis  for  calculation  the  market  price  of  coal,  the  wages  rising  and 
falling  with  the  state  of  trade. 

Sliding  Wind  Bore  (English). — The  bottom  pipe  or  suction  piece  of  a sinking 
set  of  pumps  having  a lining  made  to  slide  like  a telescope  within  it,  to 
give  length  without  altering  the  adjustment  of  the  whole  column 
of  pipes.  / 

Slime,  Sludge. — (1)  The  pulp  or  fine  mud  from  a mill  or  from  a drill  hole. 
(2)  Silt  containing  a very  fine  ore,  which  passes  oflF  in  the  water  from 
the  jigs. 

Slings.— Rieees  of  ropes  or  chains  to  be  put  around  stones,  etc.  for  raising 
them. 

Slip.—{1)  A fault.  (2)  A smooth  joint  or  crack  where  the  strata  have 
moved  upon  each  other. 


612 


Sli 


GLOSSARY. 


Spi 


Slip  Cleavage.— Microscopic  folding  and  fracture  accompanied  by  slippage; 
quarrymen’s  “false  cleavage.” 

Slit— A short  heading  put  through  to  connect  two  other  headings. 

Slitter.— See  Pick. 

Slope.— A plane  or  inclined  roadway,  usually  driven  in  the  seam  from  the 
surface.  A rock  slope  is  a slope  driven  across  the  strata,  to  connect  two 
seams;  or  a slope  opening  driven  from  the  surface,  to  reach  a seam  below 
that  does  not  outcrop  at  an  accessible  point. 

Sludge.— See  Slime. 

Sludger,  Sludge  Pump. — A cylinder  having  an  upward  opening  valve  at  the 
bottom,  which  is  lowered  into  a bore  hole,  to  pump  out  the  sludge  or  fine 
rock  resulting  from  drillings. 

Sluice.— {!)  A long  channel  in  rock  or  built  of  timber,  with  checks  to  catch 
gold.  (2)  Any  overflow  channel. 

Sluice  Box.— A trough  with  ripples  or  false  bottom  for  catching  gold. 

Sluice  Head,  or  Head  (Australia  and  New  Zealand).— A supply  of  1 cu.  ft.  of 
water  per  second,  regardless  of  the  head,  pressure,  or  size  of  orifice. 

Ground  sluicing  is  working  gravel  by  excavating  with  pick  and 
shovel,  and  washing  the  debris  in  trenches  with  water  not  under 
pressure. 

Slurry  (North  of  Wales).— Half-smelted  ore. 

Small.— See  Slack. 

Smeddum. -Leadi-ore  dust. 

Smelting. — Method  of  extracting  a precious  metal  from  its  ores. 

Smift,  Snift. — A bit  of  touch  paper,  touch  wood,  etc.  attached  by  a bit  of 
clay  or  grease  to  the  outside  end  of  the  train  of  gunpowder  when 
blasting. 

Smittem.— Fine  gravel-like  ore,  occurring  free  in  mud  openings,  or  derived 
from  the  breaking  of  the  ore  in  blasting. 

Smut  (Staffordshire).— Soft,  bad  coal.  ^ 

Snore,  Snore  Piece. — The  hole  in  the  lower  part  of  a sinking  or  Cornish  pump, 
through  which  water  enters. 

Soapstone. — A term  incorrectly  applied  by  the  miner  to  any  soft,  unctuous 
rock. 

Socabon  (Mexican). — A mining  tunnel;  an  adit.  Socavon  d hilo  de  veta. — A 
drift  tunnel.  Socavon  crucero.—A  crosscut  tunnel  or  adit. 

Socket. — (1)  The  innermost  end  of  a shot  hole,  not  blown  away  after  firing. 
(2)  A wrought-iron  contrivance  by  means  of  which  a wire  rope  is 
securely  attached  to  a chain  or  block. 

Sole,  Sole  Plate.— A piece  of  timber  set  underneath  a prop. 

Sollar. — A wooden  platform  fixed  in  a shaft,  for  the  ladders  to  rest  on. 

Sondear  (Mexican).— To  bore  for  prospecting  purposes. 

Sondeo  (Mexican).— A boring  for  prospecting  purposes. 

Soplete  (Mexican).— A blowpipe.  Ensaye  at  Soplete.—A  blowpipe  assay. 

Sorting. — Separating  valuable  from  worthless  material. 

Sounding.— {!)  Knocking  on  a roof  to  see  whether  it  is  sound  or  safe  to  wwk 
under.  (2)  Rapping  on  a pillar  so  that  a person  on  the  other  side  of  it 
may  be  signaled  to,  or  to  enable  him  to  estimate  its  width. 

Sow.—{l)  A tool  used  for  sharpening  drills.  (2)  Iron  deposits  at  the  bottom 
of  furnaces. 

Spall. — To  break  up  rocks  with  a large  hammer,  for  hand  sorting. 

Spalls.— Five  chips' and  other  waste  material  cut  from  a block  of  stone  in 
process  of  dressing. 

Spar.— A name  given  to  certain  white  quartz-like  minerals,  e.  g.,  calcspar, 
feldspar,  fluorspar. 

Spears. — Pump-rods. 

Specimen.— A picke,d  piece  of  mineral. 

Speiss. — A basic  arsenide  or  antimonide  of  iron,  often  containing  nickel, 
cobalt,  lead,  bismuth,  copper,  etc.,  having  a metallic  luster  of  high 
specific  gravity  and  a strong  tendency  toward  crystallization. 

Spelter.— The  commercial  name  for  zinc. 

Spent  Shot.— A blast  hole  that  has  been  fired,  but  has  not  done  its  work. 

Spew.— The  extension  of  mineral  matter  on  the  surface,  past  the  ordinary 
limits  of  the  lode. 

Spiders. — See  Drum  Rings. 

Spiegeleisen.—MaingSLnifeTous  white  cast  iron. 

Sjpiking  Curbs.— A light  ring  of  wood  to  which  planks  are  spiked  when 
plank  tubbing  is  used. 


Spi 


GLOSSARY. 


Sta 


613 


Spiles  (Cornish).— A temporary  lagging  driven  ahead  on  levels  in  loose 
ground.  Short  pieces  of  planking  sharpened  flatways,  and  used  for 
driving  into  watery  strata  as  sheath  piling,  to  assist  in  checking  the 
flow;  used  much  in  sinking  through  quicksands. 

Spiling.— A process  of  timbering  through  soft  ground. 

Spiral  Brum.— See  Conical  Drum. 

Splint,  or  Splent.—A  laminated,  coarse,  inferior,  dull-looking,  hard  coal,  pro- 
ducing much  white  ash,  intermediate  between  cannel  and  bituminous 
coal. 

Split. — (1)  To  divide  an  air-current  into  two  or  more  separate  currents.  (2) 
Any  division  or  branch  of  the  ventilating  current.  (3)  The  workings 
ventilated  by  that  branch.  (4)  Any  member  of  a coal  bed  split  by  thick 
partings  into  two  or  more  seams.  (5)  A bench  separated  by  a consider- 
able interval  from  the  other  benches  of  a coal  bed. 

Spoil. — Debris  from  a coal  mine. 

Spoon.— A slender  iron  rod  with  a cup-shaped  projection  at  right  angles  to 
the  rod,  used  for  scraping  drillings  out  of  a bore  hole. 

Spout. — A short  underground  passage  connecting  a main  road  with  an  air- 
course. 

Sprag.—{1)  A short  wooden  prop  set  in  a slanting  position  for  keeping  up 
the  coal  during  the  operation  of  holing.  (2)  A short  round  piece  of  hard 
wood,  pointed  at  both  ends,  to  act  as  a brake  when  placed  between  the 
spokes  of  mine-car  wheels.  (3)  The  horizontal  member  of  a square  set 
of  timber  running  longitudinally  with  the  deposit. 

Spragger. — One  who  attends  to  the  spragging  of  cars. 

Sprag  Road.— A mine  road  having  such  a sharp  grade  that  sprags  are  needed 
to  control  the  speed  of  the  car. 

Spreader.— A timber  stretched  across  a shaft  or  stope. 

Spring  Beams. — Two  short  parallel  timber  beams,  built  with  a Cornish  pump- 
ing engine  house,  nearly  on  a level  with  the  engine  beam,  for  catching 
the  beam,  etc.,  and  preventing  a smash  in  case  of  a breakdown. 

Spring  Latch.— Y]ie  latch  or  tongue  of  an  automatic  switch,  operated  by  a 
spring  pole  at  the  side  of  the  track. 

Spring  Pole.— An  elastic  wooden  pole  from  which  boring  rods  are  suspended. 
Used  also  to  operate  a spring  latch. 

Sprocket  Wheel  (English). — Rag  wheel.  A wheel  with  teeth  or  pins  which 
catch  in  the  links  of  a chain. 

Spud,  Spad.—A  horseshoe  nail  with  a hole  in  the  head,  for  driving  into  the 
mine  timbers,  or  into  a wooden  plug  fitted  into  the  roof,  to  mark  a sur- 
veying station. 

Spur.—{1)  A short  ridge  or  offsetting  pointed  branch  from  a main  ridge  or 
mountain.  (2)  A short  branch  or  feeder  from  the  main  lode  of  a vein. 

Square  Set. — A variety  of  timbering  for  large  excavations. 

Squat  (Cornish).— Tin  ore  mixed  with  spar. 

Squeeze. — See  Creep. 

Squib.— A straw,  rush,  paper,  or  quill  tube  filled  with  a priming  of  gun- 
powder, with  a slow  match  on  one  end. 

Stage. — A platform  on  which  mine  cars  stand. 

Staging. — A temporary  flooring  or  scaffold,  or  platform. 

Stage  Pumping. — Draining  a mine  by  means  of  two  or  more  pumps  placed  at 
different  levels,  each  of  which  raises  the  water  to  the  next  pump  above, 
or  to  the  surface. 

Stage  Working. — A system  of  working  minerals  by  removing  the  strata  above 
the  beds,  after  which  the  various  beds  are  removed  in  steps  or  stages. 

Icicle-shaped  formations  of  mineral  matter  depending  from  roof 

strata. 

Stalagmites. — Accumulations  of  mineral  matter  that  form  on  the  floor,  caused 
by  the  continual  dripping  of  water  impregnated  with  mineral  matter. 

Stall. — A narrow  breast,  or  chamber. 

Stall  Gate. — A road  along  which  the  mineral  worked  in  a stall  is  conveyed  to 
the  main  road. 

Stamp  Mill,  Stamps. — Machine  for  crushing  ore. 

Stanchion.— A vertical  prop  or  strut. 

Standage. — Pump  reservoir. 

Standing. — Not  at  work,  not  going  forwards,  idle. 

Standing  Gas.— A body  of  firedamp  known  to  exist  in  a mine,  but  not  in  cir- 
culation; sometimes  fenced  off. 

Standing  Sett  (English). — A fixed  lift  of  pumps  in  a sinking  set. 


614 


GLOSSARY. 


Sto 


Sta 


Stannary.— Tin  works. 

Staple.— {1)  A shallow  pit  within  a mine.  (2)  An  underground  shaft. 

Starter.— A man  who  ascends  a chute  to  the  battery  and  starts  the  coal  to 
running. 

Starved  (English).— When  a pump  is  choked  at  the  brass  holes. 

Station.— A plat  or  convenient  resting  place  in  a shaft  or  level. 

Stave.— A ladder  step. 

Stay  (English).— Props,  struts,  or  ties  for  keeping  anything  in  its  place. 

Steamboat  Coal. — In  anthracite  only,  coal  small  enough  to  pass  through  bars 
set  6 to  8 in.  apart,  but  too  large  to  pass  through  bars  from  3i  to  5 in. 
Comparatively  few  collieries  make  steamboat  coal  except  to  fill  special 
contracts  or  orders. 

Steam  Coal.— A hard,  free-burning,  non-caking  coal. 

Steam  Jet.— A system  of  ventilating  a mine  by  means  of  a number  of  jets  of 
steam,  at  high  pressure,  kept  constantly  blowing  off  from  a series  of  pipes 
in  the  bottom  of  the  upcast  shaft. 

Steel  Mill.— An  apparatus  for  obtaining  light  in  a fiery  mine.  It  consisted  of 
a revolving  steel  wheel,  to  which  a piece  of  flint  was  held,  to  produce 
sparking. 

Steel  Needle.— An  instrument  used  in  preparing  blasting  holes,  before  the 
safety  fuse  was  invented. 

Steening,  or  Steining.— The  brick  or  stone  lining  of  a shaft. 

Stemmer.—A  copper  or  wooden  bar  used  for  stemming. 

Stemming.— {i)  Fine  shale  or  dirt  put  into  a shot  hole  after  the  powder,  and 
rammed  hard.  (2)  Tami)ing  a shot. 

Step  (English).— (1)  The  cavity  in  a piece  for  receiving  the  pivot  of  an 
upright  shaft,  or  the  end  of  an  upright  piece.  (2)  The  shearing  in  a 
coal  face. 

Stint.— The  amount  of  work  to  be  done  by  a man  in  a specified  time. 

Stobb.—A  long  steel  wedge  used  in  bringing  down  coal  after  it  has  been 
holed. 

Stockwork. — A rock  run  through  with  a number  of  small  veins  close 
together,  the  whole  of  which  has  to  be  worked  when  mining  such 
deposits. 

Stomp.— A short  wooden  plug  fixed  in  the  roof  of  a level,  to  serve  as  a bench 
mark  for  surveys. 

Stone  CoaL— Anthracite;  also  other  hard  varieties  of  coal. 

Stone  Head.— A heading  or  gangway  driven  in  stone.  A tunnel. 

Stone  Tubbing.— WsiteT-tight  stone  walling  of  a shaft  cemented  at  the 
back. 

Stook.—A  f)illar  of  coal  about  4 yd.  square,  being  the  last  portion  of  a full- 
sized  pillar  to  be  worked  away  in  bord-and-pillar  workings. 

Stook-and- Feather. —A  wedge  for  breaking  down  coal,  worked  by  hydraulic 
power,  the  pressure  being  applied  at  the  extreme  inner  end  of  the 
drilled  hole. 

Stoop.— A pillar  of  coal. 

Stoop-and-Room.—A  system  of  working  coal  very  similar  to  pillar-and-stall. 

Stop.— Any  cleat  or  beam  to  check  the  descent  of  a cage,  car,  pump  rods,  etc. 

Stope.—{l)  To  excavate  mineral  in  a series  of  steps.  (2)  A place  in  a mine 
that  is  worked  by  sloping. 

(Stopingf.- Working  out  ore  between  two  levels  or  on  the  surface,  by  slopes  or 
steps.  Stoping  Overhand. — Mining  a slope  upwards,  the  flight  of  steps 
being  inverted.  Stoping  Vnder hand. —Mining  a slope  downwards  in 
such  a series  that  it  presents  the  appearance  of  a flight  of  steps. 

Stopping.— An  air-tight  wall  built  across  any  passageway  in  a mine. 

Stove  Coal.— In  anthracite  only;  two  sizes  of  stove  coal  are  made,  large  and 
small:  large  stove,  known  as  No.  3,  passes  through  a 21"  to  2"  mesh 
and  over  a 1^"  to  li"  mesh;  small  stove,  known  as  No.  4,  passes  through 
a Ij"  to  1|"  mesh  and  over  a Ij"  to  1"  mesh.  Only  one  size  of  stove  coal 
is  now  usually  made.  It  passes  through  a 2"  square  mesh  and  over  1|" 
square  mesh. 

Stove  Up.  or  Stoved.— Upset.  When  a rod  of  iron  heated  at  one  end  is  ham- 
mered endwise  the  diameter  of  that  end  is  enlarged,  and  it  is  said  to  be 
upset. 

Stow.— To  pack  away  rubbish  into  goaves  or  old  workings. 

Stowce.—{l)  Windlass.  (2)  Landmarks. 

Stowing.— The  debris  of  a vein  thrown  back  of  a miner  and  which  supports 
the  roof  or  hanging  wall  of  the  excavation. 


Str 


GLOSSARY. 


Swi 


615 


Straight  Ends  and  Walls.— X system  of  working  coal  somewhat  similar  to 
bord-and-pillar.  Straight  ends  are  headings  from  4 ft.  6 in.  to  6 ft.  in 
width.  Walls  are  pillars  30  ft.  wide. 

Straight  Work.—X  system  of  getting  coal  by  headings  or  narrow  work. 

Strake.—A  slightly  inclined  table  for  separating  heavier  minerals  from 
lighter  ones. 

Stratification.— ATT&ngement  in  layers. 

Stratum  (plural,  strata).— A layer  or  bed  of  rocks,  or  other  deposit. 

Streak.— The  color  of  the  mark  made  when  a mineral  is  scratched  against  a 
white  surface. 

Strett.— The  system  of  getting  coal  by  headings  or  narrow  work.  See 
Bor  d-and- Pillar. 

Strike  (of  a seam  or  vein).— The  intersection  of  an  inclined  seam  or  a vein 
with  a horizontal  plane.  A level  course  in  the  seam.  The  direction  of 
strike  is  always  at  right  angles  to  the  direction  of  the  dip  of  the  seam. 

Strike  Joints.— ZoiniB  or  cleavages  that  are  parallel  to  the  strike  of  the  seam. 

Striking  i)eaZ.— Planks  fixed  in  a sloping  direction  just  within  the  mouth  of 
a shaft,  to  guide  the  tub  to  the  surface. 

Stringer  (English).— Any  longitudinal  timber  or  beam. 

Stringpump.—A  system  of  pumping  whereby  the  motion  of  the  engine  is 
transmitted  to  the  pump  by  timbers  or  stringers  bolted  together. 

String  Rods. — A line  of  surface  rods  connected  rigidly  for  the  transmission 
of  power;  used  for  operating  small  pumps  in  adjoining  shafts  from  a 
central  station. 

5fr2p.— (1)  To  remove  the  overlying  strata  of  a bed  or  vein.  (2)  Mining  a 
deposit  by  first  taking  off  the  overlying  material. 

Strut  (English).— A prop  to  sustain  compression,  whether  vertical  or  inclined. 

Struve  Ventilator.— A pneumatic  ventilating  apparatus  consisting  of  two 
vessel-like  gas  holders,  which  are  moved  up  and  down  in  a tank  of 
water.  By  this  means,  the  air  is  sucked  out  of  the  mine  as  required. 

Studdle.—A  piece  of  squared  timber  placed  vertically  between  two  sets  of 
timber  in  a shaft. 

Stull. — A post  for  supporting  the  wall  or  roof  in  a mine;  a prop  timber. 

Stump.— The  pillar  between  the  gangway  and  each  room  turned  off  the  gang- 
way. Sometimes  the  entry  pillars  are  called  stumps. 

Stumping. — A kind  of  pillar-and-stall  plan  of  getting  coal. 

Stup. — Powdered  coke  or  coal  mixed  with  clay. 

Sturt.— A tribute  bargain  profitable  to  the  miner. 

Stuttle,  or  /Spra^/f.- The  horizontal  member  of  a square  set  of  timber  running 
longitudinally  with  the  deposit. 

Carbonic-acid  gas  (blackdamp). 

Sucker  Rod.— The  pump  rod  of  an  oil  or  artesian  well. 

Suction  Pump  (English).— A pump  wherein,  by  the  movement  of  the  piston, 
water  is  drawn  up  into  the  vacuum  caused. 

Sulphur. — (1)  One  of  the  elements.  (2)  Iron  pyrites. 

Sulphuret. — See  Sulphide. 

Sulphide. — A combination  of  sulphur  and  a base. 

Sump,  or  Sumpt.—A  catch  basin  into  which  the  drainage  of  a mine  flows  and 
from  which  it  is  pumped  to  the  surface. 

Surface  Deposits.— Tho^e  that  are  exposed  and  can  be  mined  from  the  surface. 

Swab  Stick.— A short  wooden  rod,  bruised  into  a kind  of  stumpy  brush  at  one 
end,  for  cleaning  out  a drill  hole. 

Swally,  or  Swelly.—A  trough,  or  syncline,  in  a coal  seam. 

Swamp.— A depression  or  natural  hollow  in  a seam.  A basin. 

Sweeping  Table.— A stationary  buddle. 

Sweet.— Yxee  from  deleterious  gases. 

Sweet  Roast.— To  roast  dead  or  completely. 

The  arc  or  curve  described  by  the  point  of  an  instrument,  such  as  a 
pick  or  hammer,  when  being  used. 

Swinging  P^a^e.— Amalgamated  copper  plates  hung  in  sluices,  to  catch  float 
gold. 

Switch.— {1)  The  movable  tongue  or  rail  by  which  a train  is  diverted  from 
one  track  to  another.  (2)  The  junction  of  two  tracks.  (3)  A movable 
arm  for  changing  the  course  of  an  electrical  current. 

Switchboard.— A board  where  several  electrical  wires  terminate,  and  where, 
by  means  of  switches,  connection  may  be  established  between  any  of 
these  wires  and  the  main  wire. 

Swither,—A  crevice  branching  from  a main-lead  lode. 


616 


Syn 


GLOSSARY, 


Tep 


Synclinal  The  line  or  course  of  a syncline. 

Syncline.— The,  point  or  axis  of  a basin  toward  which  the  strata  upon  either 
side  dip.  An  inverted  anticline.  A basin. 

Tackle  (English).— (1)  Ropes,  chain,  detaching  hooks,  cages,  and  all  other 
apparatus  for  raising  coal  or  ore  in  shafts.  (2)  Any  rope  for  hoisting,  as 
a tackle  rope,  block  and  tackle,  etc. 

Tahona  (Mexican).— An  arrastre  moved  by  water-power.  Tahonero.— The 
man  in  charge  of  the  tahona. 

Tail-Back. — When  the  firedamp  ignites  and  the  flame  is  elongated  or  creeps 
backwards  against  the  current  of  air,  it  is  said  to  tail-back. 

Tailing.— The  blossom;  the  outcrop  or  smut. 

Tailings. — The  detritus  from  reduction  or  gold-washing  machinery. 

Tail- Pipe. —The  suction  pipe  of  a pump. 

Tailrace.— The  channel  along  which  water  flows  after  it  has  done  its  work. 

Tail-Rope.— [1)  In  a tail-rope  system  of  haulage,  the  rope  that  is  used  to 
draw  the  empties  back  into  the  mine.  (2)  A wire  rope  attached  beneath 
cages,  as  a balance. 

Tail-Rope  System  of  Haulage.— A.  haulage  system  in  which  the  full  trip  is 
drawn  out  by  the  main  rope,  and  the  empty  trip  is  drawn  in  by  the  tail- 
rope,  these  ropes  being  attached  to  the  opposite  ends  of  the  trip  (see 
page  400). 

Tail-Sheave.— The  sheave  at  the  inbye  end  of  any  haulage  system.  See  Turn 
Pulley. 

Take  the  Air.—{1)  To  measure  the  ventilating  current.  (2)  Applied  to  a 
ventilating  fan  as  working  well,  or  working  poorly. 

Taladro  ( Mexican)  .—A  drill  for  mechanical  or  mining  purposes.  Taladfar.— 
To  bore  or  drill. 

Tally'.— {1)  A mark  or  number  placed  by  the  miner  on  every  car  of  coal  sent 
out  of  his  place,  usually  a tin  ticket.  By  counting  these,  a tally  is  made 
of  all  the  cars  of  coal  he  sends  out.  (2)  Any  numbering,  or  counting,  or 
memorandum,  as  a tally  sheet. 

Tamp.— To  fill  a bore  hole,  after  inserting  the  charge,  with  some  substance 
which  is  rammed  hard  as  it  is  put  into  the  hole.  Vertical  holes  are  often 
tamped  with  water,  when  blasting  with  dynamite. 

Tamping. — The  process  of  stemming  or  filling  a bore  hole. 

Tamping  Bar. — A copper-tipped  bar,  for  ramming  the  tamping  or  stem- 
ming. 

Tanates  (Mexican).— Leather,  hide,  or  jute  bags,  to  carry  ore  or  waste  rock 
within  or  out  of  a mine.  Tanatero.—A  laborer  or  bag  carrier. 

Tap.—{1)  To  cut  or  bore  into  old  workings,  for  the  purpose  of  liberating  accu- 
mulations of  gas  or  water.  (2)  To  pierce  or  open  any  gas  or  water 
feeder.  (3)  To  win  coal  in  a new  district. 

Tapextle  (Mexican).— A working  platform  or  stage  built  up  in  a stope  or  any- 
where in  a mine;  a landing  place  between  two  flights  of  ladders. 

Teem.— To  pour  or  tip. 

Teeming  Trough. — A trough  into  which  the  water  from  a mine  is  pumped. 

Telegraph.— A sheet-iron  trough-shaped  chute,  for  conveying  coal  or  slate 
from  the  screens  to  the  pockets,  or  boilers. 

Tellurides.—Ores,  of  the  precious  metals  (chiefly  gold)  containing  tellurium. 

Temesquitale  (Mexican).— The  earthy  part  of  ground-up  ore. 

Temper.— (1)  To  change  the  hardness  of  metals  by  first  heating  and  then 
plunging  them  into  water,  oil,  etc.  (2)  To  mix  mortar,  or  to  prepare 
clay  for  bricks,  etc. 

Tempering.— The  act  of  reheating  and  properly  cooling  a bar  of  metal  to  any 
desired  degree  of  hardness. 

Temper  Screw.— In  rope  drilling,  a screw  for  gradually  lowering  the  clamped 
(upper)  end  of  the  rope  as  the  hole  is  deepened. 

Tenon. — A projecting  tongue  fitting  into  a corresponding  cavity  called  a 
mortise. 

Tentadura  (Mexican).— An  assay  made  in  a horn  spoon,  an  earthen  saucer, 
or  in  a wide  and  shallow  vessel  of  any  kind,  to  ascertain  the  amount  of 
amalgam  present  in  a sample  of  argentiferous  mud  from  an  amalgama- 
ting patio.  Any  assay  made  by  washing  so  as  to  concentrate  the 
metallic  portions  of  any  mineral,  and  to  cause  the  earthy  portions  to  be 
floated  off. 

Tepetate  (Mexican).— Any  rock  or  earth  found  in  a mine,  which  does  not 
contain  the  metal  sought  for, 


Teq 


GLOSSARY. 


Tra 


617 


Tequio  (Mexican).— A task  set  for  a drillman  or  for  any  laborer  in  a mine,  to 
be  regarded  as  a day’s  work. 

Terrace.— A raised  level  bank,  such  as  river  terraces,  lake  terraces,  etc. 

Terrero  (Mexican).— The  dump  of  a mine. 

Test. — (1)  A trial  of  an  engine,  fan,  or  other  appliance  or  substance.  (2)  An 
iron  framework  that  is  filled  with  bone  ash  for  cupeling  on  a large  scale. 

Theodolite.— An  instrument  used  in  surveying,  for  taking  both  vertical  and 
horizontal  angular  measurements.  An  engineer’s  large  transit,  with 
attachments. 

TMW.- See  Floor. 

Thimble.— {1)  A short  piece  of  tube  slid  over  another  piece,  to  strengthen  a 
joint,  etc.  (2)  An  iron  ring  with  a groove  around  it  on  the  outside,  used 
as  an  eye  when  a rope  is  doubled  about  it. 

Thirl.— See  Crosscut. 

Through-and- Through. — A system  of  getting  bituminous  coal,  without  regard 
to  the  size  of  the  lump. 

Throw.— {1)  A fault  of  dislocation.  (2)  The  vertical  distance  between  the 
two  ends  of  a faulted  bed  of  coal. 

Thrown.— Fanlted;  broken  by  a fault. 

Thrust.— Cree^  or  squeeze  due  to  excessive  weight,  hard  floor,  and  too 
small  pillars. 

Thurl  (Staffordshire).— To  cut  through  from  one  working  into  another. 

Ticketing. — English  periodical  markets  for  the  sale  of  ores. 

Tie-Back.— (1)  A beam  serving  a purpose  similar  to  a fend-off  beam,  but 
fixed  at  the  opposite  side  of  the  shaft  or  inclined  road.  (2)  The  wire 
ropes  or  stayrods  which  are  sometimes  used  on  the  side  of  the  tower 
opposite  the  hoisting  engine,  in  place  of  or  to  reenforce  the  engine 
braces. 

Therms  (Spanish).— Earth  impregnated  with  mercury  ore. 

Tierras  de  Labor  (Mexican). — Dirt  from  a stope,  mixed  with  particles  of  ore. 

Tierras  de  Llunque  (Mexican).— Chips  made  in  breaking  and  sorting  ore. 

Calcite  or  carbonate  of  lime. 

Timber.— (1)  Props,  bars,  collars,  legs,  laggings,  etc.  (2)  To  set  or  place 
timber  in  a mine  or  shaft. 

Timberer,  Timberman.—A  man  who  sets  timber. 

Time. — (1)  Hours  of  work  performed  by  workmen.  (2)  To  count  the 
strokes  of  a pump  or  revolutions  of  an  engine  or  fan. 

Tin-Can  Safety  Lamp.— A Davy  lamp  placed  inside  a tin  can  or  cylinder 
having  a glass  in  front,  air  holes  near  the  bottom,  and  open-topped, 
making  the  lamp  safer  in  a rapid  current  of  air. 

Tin- Witts  (Cornish).— Product  of  first  dressing  of  tin  ores,  containing,  also, 
wolfram  and  sulphides. 

Tip. — A dump.  See  Tipper,  or  Tipple. 

Tipper,  or  Tipple.— An  apparatus  for  emptying  cars  of  coal  or  ore,  by  turning 
them  upside  down,  and  then  bringing  them  back  to  original  position, 
with  a minimum  of  manual  labor. 

Tipple.— T]ie  dump  trestle  and  tracks  at  the  mouth  of  a shaft  or  slope,  where 
the  output  of  a mine  is  dumped,  screened,  and  loaded. 

Tiro  (Mexican).— A mining  shaft.  Tiro  Vertical.— A vertical  shaft. 

Token.— {!)  A mutually  understood  mark  placed  upon  a bucket  of  ore  when 
it  is  hoisted  or  lowered  into  a shaft,  to  acquaint  the  lander  or  filler  of 
some  important  matter.  (2)  A piece  of  leather  or  metal  stamped  with 
the  hewer’s  or  putter’s  number  or  distinctive  mark,  and  fastened  to  the 
tub  he  is  filling  or  putting. 

Ton.— A measure  of  weight.  Long  ton  is  2,240  lb.;  short  ton  is  2,000  lb.; 
metric  ton  is  1,000  kilograms  = 2,204.6  lb. 

Top.—{\)  See  Roof.  (2)  Top  of  a shaft;  surface  over  a mine. 

Topit.—A  kind  of  brace  head  screwed  to  the  top  of  boring  rods,  when  with- 
drawing them  from  the  hole. 

Torf a (Mexican).— A pie  or  cake;  the  heaps  of  argentiferous  mud  that  are 
treated  in  the  patio  process  of  amalgamation. 

Tossingt.- Shaking  powdered  ore  in  water,  to  effect  separation  of  heavy  and 
light  particles. 

Tovera  (Mexican).— The  tuyere  of  a smelting  furnace. 

Tmcfc.  — Railways  or  tramways. 

Tracking.— Wooden  rails. 

Train  Boy.— A boy  that  rides  on  a trip,  to  attend  to  rope  attachments,  signal 
in  case  of  derailment  of  cars,  etc.  Trip  rider. 


C18 


Tra 


GLOSSARY. 


Tum 


Train,  or  Tnp.— The  cars  taken  at  one  time  by  mules,  or  by  any  motor,  ox 
run  at  one  time  on  a slope,  plane,  or  sprag  road,  always  together. 

Tram.— A mine  car,  or  the  track  on  which  it  runs. 

Trammer.— One  who  pushes  cars  along  the  track. 

Tramroad.—A  mine  track  or  railroad. 

Tram  Rope.— A hauling  rope,  to  which  the  cars  are  attached  by  a clip  or 
chain,  either  singly  or  in  trips. 

Tramway.— A small,  roughly  constructed  iron  track  for  running  wagons  or 
trucks  on. 

Transfer  Carriage.— MoYsible  platform  or  truck  used  to  transfer  mine  cars 
from  one  track  to  another. 

Transome  (English).— A heavy  wooden  bed  or  supporting  piece. 

Trap.— (1)  A steep  heading  along  which  men  travel.  (2)  A fault  of  dislo- 
cation. (3)  An  eruptive  rock.  (4)  A dangerous  place. 

Trap  Door.— A small  door,  kept  locked,  fixed  in  a stoping,  for  giving  access 
to  firemen  and  certain  others  to  the  return  airways,  dams,  or  other 
unused  portions  of  the  mine. 

Trap  Dike.— A fault  (not  necessarily  accompanied  by  displacement  of  strata) 
in  which  the  spaces  between  the  fractured  edges  of  the  beds  are  filled  up 
by  a thick  wall  of  igneous  rock. 

Trapiche  (Spanish).— A primitive  grinding  mill. 

Trapper.— A boy  employed  underground  to  tend  doors. 

Traveling  Road.— An  underground  passage  or  way  used  expressly,  though 
not  always  exclusively,  for  men  to  travel  along  to  and  from  their  work- 
ing places. 

Treenail.— A long  wooden  pin  for  securing  planks  or  beams  together. 

Treloobing  (Cornish).— Stirring  tin  slimes  in  water. 

Trend.— The  course  of  a vein,  fault,  or  other  feature. 

Tribute.— A method  of  working  mines  by  contract,  whereby  the  miners 
receive  a certain  share  of  the  products  won.  Tributers.— Miners  paid 
by  results. 

Trig.— A sprag  used  to  block  or  stop  a wheel  or  any  machinery. 

Trilla  (Mexican). — The  same  as  Torta. 

Trip. — The  mine  cars  in  one  train  or  set.  See  Train. 

Triple-Entry  System. — A system  of  opening  a mine  by  driving  three  parallel 
entries  for  the  main  entries. 

Triturate.  To  grind  or  pulverize. 

Trolley.— {\)  A small  four-wheeled  truck,  used  for  carrying  the  ore  bucket 
underground.  (2)  An  electric  motor.  (3)  The  arm  of  a motor  that  con- 
ducts the  electric  current  from  the  wire  above  the  track  to  the  machine. 

Trommel.— A drum,  consisting  of  a cylinder-  or  cone-shaped  sheet-iron 
mantle  (generally  punched  with  holes)  that  revolves;  used  for  washing 
or  sorting  ores. 

Trompa  (Mexican).— A funnel-shaped  mouthpiece  of  cooled  slag  that  forms 
within  a smelting  furnace  over  the  tuyere  opening. 

Trompe. — An  apparatus  for  producing  ventilation  by  the  fall  of  water  down 
a shaft. 

Trouble.— A dislocation  or  fault;  any  irregularity  in  the  bed. 

Trough  Fault— A wedge-shaped  fault,  or,  more  correctly,  a mass  of  rock, 
coal,  etc.  let  down  in  between  two  faults,  which  faults,  however,  are 
not  necessarily  of  equal  throw. 

Troughs,  or  Thirling.— A passage  cut  through  a pillar  to  connect  two  rooms. 

Truck. — Used  synonymously  with  Barney. 

Truck  System. — Paying  miners  in  food  instead  of  money. 

Cylindrical  projections  or  journals,  attached  to  the  sides  of 
a vessel,  so  that  it  can  rotate  in  a vertical  plane. 

Trying  the  Lamp.— The  examination  of  the  flame  of  a safety  lamp  for  the 
purpose  of  forming  a judgment  as  to  the  quantity  of  firedamp  mixed 
with  the  air. 

Tub.—{1)  A mine  car.  (2)  An  iron  or  w^ooden  barrel  used  in  a shaft,  for 
hoisting  material. 

Tubbing.— Oast  iron,  and  sometimes  timber,  lining  or  walling  of  a circular 
shaft. 

Tubbing  TTed^rd’s.— Small  wooden  wedges  hammered  between  the  joints  of 
tubbing  plates. 

Tubing.— Iron  pipes  or  tubes  used  for  lining  bore  holes,  to  prevent  caving. 

Tumbar  (Mexican).— To  knock  down  ore,  etc. 

Tambe  (Mexican).— The  act  of  knocking  down  and  taking  out  ore. 


Tun 


GLOSSARY. 


Ven 


619 


Tunnel.— K horizontal  passage  driven  across  the  measures  and  open  to  day  at 
both  ends;  applied  also  to  such  passages  open  to  day  at  only  one  end,  or 
not  open  to  day  at  either  end. 

Turbary.— A peat  bog. 

Turbine.— A rapidly  revolving  waterwheel,  impelled  by  the  pressure  of  water 
upon  blades. 

Turn.—{1)  The  hours  during  which  coal,  etc.  is  being  raised  from  the  mine. 
(2)  See  Shift.  (3)  To  open  rooms,  headings,  or  chutes  off  from  an  entry 
or  gangway.  (4)  The  number  of  cars  allowed  each  miner. 

Turnout.— A siding  or  passing  on  any  tram  or  haulage  road. 

Turn  Pulley.— A sheave  fixed  at  the  inside  end  of  an  endless-  or  tail-rope 
hauling  plane,  around  which  the  rope  returns.  See  Tail-Sheave. 

Turntable.— A revolving  platform  on  which  cars  or  locomotives  are  turned 
around. 

Tut  ITorA:.— Breaking  ground  at  so  much  per  foot  or  fathom. 

Tuyere.— TYiq  tubes  through  which  air  is  forced  into  a furnace. 

Two-Throw.— WYiQTi,  in  sinking,  a depth  of  about  12  ft.  has  been  reached,  and 
the  debris  has  to  be  raised  to  the  surface  by  two  lifts  or  throws  with  the 
shovel,  one  man  working  on  staging  above  another. 

Tye.—An  inclined  table  used  for  dressing  ores. 

Unconformability.— When  one  layer  of  rock,  resting  on  another  layer,  does  not 
correspond  in  its  angle  of  bedding. 

Tinder  cast. —An  air-course  carried  under  another  air-course  or  roadway. 

Underclay.— A bed  of  fireclay  or  other  less  clayey  stratum,  lying  immediately 
beneath  a seam  of  coal. 

Undercut.— To  remove  a small  portion  of  the  bottom  of  the  bed  or  the  under- 
clay, so  that  the  mass  of  coal  or  mineral  can  be  wedged  or  blasted  down. 

Underhand  Stoping. — See  Stoping  Underhand. 

Underhand  Work. — Picking  or  drilling  downwards. 

Underholing,  Undermining.— To  mine  out  a portion  of  the  bottom  of  a seam 
or  the  underclay,  by  pick  or  powder,  thus  leaving  the  top  unsupported 
and  ready  to  be  blown  down  by  shots,  broken  down  by  wedges,  or  mined 
with  a pick  or  bar. 

Underlie,  or  Underlay. — The  inclination  of  a lode  at  right  angles  to  its  course, 
or  strike;  the  true  dip. 

Underviewer,  or  Underlooker.— An  inside  foreman. 

Unit.—{1)  The  unit  of  metals  is  1^  of  whatever  ton  is  used.  Generally,  the 
20-cwt.  ton,  equal  to  2,240  lb.,  is  employed,  but,  when  dealing  with 
copper  ores,  the  21-cwt.  ton  of  2,352  lb.  is  taken;  therefore,  the  respective 
units  are  22.4  lb.  and  23.52  lb.  (F.  Danvers  Powers).  (2)  Ores  are  quoted 
at  a certain  price  per  unit  or  per  cent,  of  valuable  material  in  the  ore. 
If  an  iron  ore  contains  40^  of  metallic  iron  that  is  worth  5 cents  per  unit, 
the  value  of  the  ore  is  ^2  per  ton. 

Unwater.— To  drain  or  pump  the  water  from  a mine,  or  shaft. 

Upcast. — The  shaft  through  which  the  return  air  ascends. 

Upraise.— An  auxiliary  shaft,  a mill  hole,  or  heading  carried  from  one  level 
up  toward  another. 

Upthrow.^A  fault  in  which  the  displacement  has  been  upward. 

Vapor  (Mexican).— Steam;  heated  and  stinking  gas  sometimes  found  in 
mines,  which  causes  candles  to  burn  dimly  and  go  out. 

Vaso  (Mexican).— A reverberatory  furnace  used  for  smelting  rich  ore,  or  for 
cupeling  silver. 

Fa^.— Large  wooden  tub  used  for  leaching  or  precipitation. 

Vein.— See  Lode.  Often  applied,  incorrectly  to  a seam  or  bed  of  coal  or  other 
mineral. 

Veinstone.— The  non-metallic  portion  of  a vein  associated  with  the  ore. 

Vena  (Mexican).— A thin  vein,  not  over  3 in.  thick— a knife-blade  vein. 

Vend  (North  of  England).— Total  sales  of  coal  from  a mine. 

Vent,  or  Vent  Hole.—{l)  A small  passage  made  with  a needle  through  the 
tamping,  which  is  used  for  admitting  a squib,  to  enable  the  charge  to  be 
lighted.  (2)  Any  opening  made  into  a confined  space. 

Ventilating  Column. — See  Motive  Column. 

Ventilating  Pressure.— The  total  pressure  or  force  required  to  overcome  the 
friction  of  the  air  in  mines;  the  unit  of  ventilating  pressure  or  pressure 
per  sq.  ft.  of  area  multiplied  by  the  area  of  the  airway. 

Ventilation.— CiienldAion.  The  atmospheric  air  circulating  in  a mine. 


620 


Ven 


GLOSSARY, 


Wat 


Ventilator.^ Any  means  or  apparatus  for  producing  a current  of  air  in  mine 
or  other  airways. 

Vestry  (North  of  England).— A refuse. 

Veta  (Mexican).— A metalliferous  vein  of  rock;  a true  fissure  vein.  Loosely, 
any  mineral  deposit.  Veta  Clavada.—A  vertical  vein.  Veta  Echada.—An 
inclined  vein.  Veta  Serpenteada.—A  vein  with  frequent  changes  of 
direction  or  course.  Veta  Soda. — A vein  that  joins  another.  Veta  Ramal. 
— A branch  vein.  Veta  Recostada.—An  inclined  vein. 

Viewer.— general  manager  or  mining  engineer  of  one  or  more  collieries, 
who  has  control  of  the  whole  of  the  underground  works,  and  also  gen- 
erally of  those  on  the  surface. 

Vinney.— Copper  ore  with  green  efflorescence. 

Vuelta  ( Mexican) . — In  refining  silver,  the  moment  when  all  impurities  have 
been  removed  from  the  silver  under  treatment. 

Vug,  or  Vugh  (Cornish).— A cavity  in  the  rock. 

)IVagon.— A mine  car. 

Wagon  Breast.— A breast  in  which  the  mine  cars  are  taken  up  to  the 
working  face. 

Tra27m^/.— Picking  stones  and  dirt  from  among  coals. 

Wale  (North  of  England).— Hand-dressing  coal. 

Walking  Beam.—^ee  Working  Beam. 

Wall.—{1)  The  face  of  a long  wall  working  or  breast.  (2)  A rib  of  solid  coal 
between  two  breasts. 

Walling.— ^ee  Steening. 

Walling  Cribs.— OAk  cribs  or  curbs  upon  which  walling  is  built. 

Walling  Stage.— A movable  wooden  scaffold  suspended  from  a crab  on  the 
surface,  upon  which  the  workmen  stand  when  walling  or  lining  a shaft. 

Wall  Plates.— T\ve  two  longest  pieces  of  timber  in  a set  used  in  a rectan- 
gular shaft. 

Warners. — Apparatus  consisting  of  a variety  of  delicately  constructed 
machines,  actuated  by  chemical,  physical,  electrical,  and  mechanical 
properties,  for  indicating  the  presence  of  small  quantities  of  firedamp  in 
the  mines.  At  present,  most  of  these  ingenious  contrivances  are  more 
suited  to  the  laboratory  than  for  practical  application  underground. 

Warning  Lamp.— A safety  lamp  fitted  with  certain  delicate  apparatus,  for 
indicating  very  small  proportions  of  firedamp  in  the  atmosphere  of  a 
mine.  As  small  a quantity  as  3^  can  be  determined  by  this  means. 

TFas/i.— Drift,  clay,  stones,  etc.  overlying  the  strata. 

Washer.— A jig. 

Wash  Dirt.—ThaX  portion  of  alluvial  working  in  which  most  of  the  gold  is 
found. 

Wash  Fault.— A portion  of  a seam  of  coal  replaced  by  shale  or  sandstone. 

Washing  Apparatus,  or  Washery.—{1)  Machinery  and  appliances  erected  on 
the  surface  at  a colliery,  generally  in  connection  with  coke  ovens,  for 
extracting,  by  washing  with  water,  the  impurities  mixed  with  the  coal 
dust  or  small  slack.  (2)  Machinery  for  removing  impurities  from  small 
sizes  of  anthracite  coal.  . 

Washout.— Ttie  erosion  of  an  appreciable  extent  of  a coal  seam  by  aqueous 
agency. 

Wash  Place.— A place  where  the  ores  are  washed  and  separated  from  the 
waste,  usually  applied  to  places  where  the  hand  jigs  are  used. 

Waste.— {1)  See  Goaf.  (2)  Very  small  coal  or  slack.  (3)  The  portion  of  a 
mine  occupied  by  the  return  airways.  (4)  Also  used  to  denote  the 
spaces  between  the  pack  walls  in  the  gob  of  longwall  working.  (5)  Refuse 
material. 

Waste  Gate  (English).— A door  for  regulating  discharge  of  surplus  water. 

Water  Blast.— The  sudden  escape  of  air  pent  up  in  rise  workings,  under  con- 
siderable pressure  from  a head  of  water  that  has  accumulated  in  a 
connecting  shaft. 

Water  Cartridge. — A waterproof  cartridge  surrounded  by  an  outer  case. 
The  space  between  being  filled  with  water,  which  is  employed  to 
destroy  the  flame  produced  when  the  shot  is  fired,  thereby  lessens  the 
chance  of  an  explosion  should  gas  be  present  in  the  place. 

Water  Gauge.— An  instrument  for  measuring  the  pressure  per  square  foot 
producing  ventilation  in  a mine. 

Water  Hammer.— The  hammering  noise  caused  by  the  intermittent  escape 
of  gas  through  water  in  pipes. 


Wat 


GLOSSARY. 


Won 


621 


Water-Jacket— K jacket  filled  with  water,  to  keep  cool  a cylinder  or  furnace. 

Water  Level.— Kn  underground  passage  or  heading  driven  very  nearly  dead 
level  or  with  suflacient  grade  only  to  drain  off  the  water. 

Water  Right— privilege  of  taking  a certain  quantity  of  water  from  a 
watercourse. 

Watershed.— elevated  land  or  ridge  that  divides  drainage  areas. 

Waterwheel  (English).— Overshot,  undershot,  breast  wheels.  A wheel  pro- 
vided with  buckets,  which  is  set  in  motion  by  the  weight  or  impact  of  a 
stream  of  water. 

Weather.— To  crumble  by  exposure  to  the  atmosphere. 

Weather  Boor.— See  Trap  Door. 

Web.—Tlae  face  of  a longwall  stall  in  course  of  being  holed  and  broken  down 
for  removal.  The  length  of  breast  or  face  brought  down  by  one  mining. 

Wedging.— The  material,  moss  or  wood,  used  to  render  the  shaft  .lining 
tight. 

Wedging  Crib.— A curb  or  crib  of  wood  or  cast  iron  wedged  tightly  in  place 
and  packed,  in  order  to  form  a water-tight  joint  and  upon  which  tubbing 
is  built. 

Wedging  Down.— Breaking  down  the  coal  at  the  face  with  hammers  and 
wedges  instead  of  by  blasting. 

Weeldon.— Old  ironstone  workings. 

Weigh  Bridge  (English).— A platform  large  enough  to  carry  a wagon,  resting 
on  a series  of  levers,  by  means  of  which  heavy  bodies  are  weighed. 

Weize.—A  band  or  ring  of  spun  yarn,  rope,  rubber,  lead,  etc.  put  in  between 
the  flanges  of  pipes  before  bolting  them  together,  in  order  to  make  a 
water-tight  joint. 

Welt—{1)  The  well  of  a furnace  is  the  deepest  lying  portion  or  hollow  in 
which  the  metal  collects.  (2)  A sump,  or  a branch  from  the  sump. 

Whim.— A winding  drum  worked  by  a horse. 

Whim  Shaft— A shaft  through  which  coal,  ore,  water,  etc.  are  raised  from  a 
mine  by  means  of  a whim. 

Whin. — A hard,  compact  rock. 

Whin  Dike.— A fault  or  Assure  filled  with  whin  and  the  debris  of  other 
rocks,  sometimes  accompanied  by  a dislocation  of  the  strata. 

Whip.— A hoisting  appliance  consisting  of  a pulley  supporting  the  hoisting 
rope  to  which  the  horse  is  directly  attached. 

IE Medamp.— Carbonic  oxide  {CO).  A gas  found  in  coal  mines,  generally 
where  ventilation  is  slack.  A product  of  slow  combustion  in  a limited 
supply  of  air.  It  burns  and  will  support  combustion.  It  is  extremely 
poisonous. 

White  Tin.— The  commercial  name  for  metallic  tin. 

TEMs.— See  Tin- Witts. 

Whole  Working.— The  first  working  of  a seam,  which  divides  it  into  pillars. 

Wild  Zmd.— Zinc-blende. 

Wild  Rock.— Any  rock  not  fit  for  commercial  slate. 

Win.— To  sink  a shaft  or  slope,  or  drive  a drift  to  a workable  seam  of  mineral 
in  such  a manner  as  to  permit  its  being  successfully  worked. 

Winch,  or  Windlass.— A hoisting  machine  consisting  of  a horizonal  drum 
operated  by  crank-arm  and  manual  labor. 

Wind  Bore  (England).— The  bottom  or  suction  pipe  of  a lift  of  pumps,  which 
has  suitable  brass  holes  or  perforations  for  suction  of  water  or  air. 

Wind  Gauge.- An  anemometer,  for  testing  the  velocity  of  air  in  mines. 

Winding. — The  operation  of  raising  or  hauling  by  means  of  a steam  engine 
and  ropes,  the  product  of  a mine. 

Winding  Engines. — Hoisting  or  haulage  engines. 

Wind  Method.— A system  of  separating  coal  into  various  sizes,  and  extracting 
the  dirt  from  it,  which  in  principle  depends  on  the  specific  gravity  or 
size  of  the  coal  and  the  strength  of  the  current  of  air. 

Wind  Sait— The  top  part  of  canvas  piping,  which  is  used  for  conveying  air 
down  shallow  shafts. 

Wing  Bore.— A side  or  flank  bore  hole. 

TEin^'s.— See  Rests  and  Keeps. 

Winning. — A sinking  shaft,  a new  coal,  ironstone,  clay,  shale,  or  other  mine 
of  stratified  material.  A working  place  in  a mine. 

Winnowing  Gold. — Air-blowing.  Tossing  up  dry  powdered  auriferous  mate- 
rial in  the  air,  and  catching  the  heavier  particles  not  blown  away. 

TEmse.— Interior  shaft  connecting  levels,  sometimes  used  as  an  ore  chute. 

lEon.— Proved,  sunk  to,  and  tested. 


622 


WOR 


GLOSSARY. 


ZON 


Work.^{l)  To  mine.  (2)  Applied  to  mine  working  when  affected  by  squeeze 
or  creep. 

Workable.— Kny  seam  that  can  be  profitably  mined. 

Worked  Owt.— When  all  available  mineral  has  been  extracted  from  a mine,  it 
is  worked  out. 

Working. — Applied  to  mine  workings  when  squeezing. 

Working  Barrel.— water  cylinder  of  a pump. 

Working  Beam  (English).— A beam  having  a vertical  motion  on  a rock  shaft 
at  its  center,  one  end  being  connected  with  the  piston  rod  and  the  other 
with  a crank  or  pump  rod,  etc. 

Working  Cbsi.— The  total  cost  of  producing  the  mineral. 

Working  Face. — See  Face. 

Working  Home.— Getting  or  working  out  a seam  of  coal,  etc.,  from  the 
boundary  or  far  end  of  the  mine  toward  the  shaft  bottom. 

Working  on  Air. — A pump  works  on  air  when  air  is  sucked  up  with  the 
water. 

Working  Working  outwards  or  in  the  direction  of  the  boundaries  ol 
the  collieries. 

Working  Place.— Yhe  actual  place  in  a mine  at  which  the  coal  is  being  mined. 

Workings.— Y\ie  openings  of  a colliery,  including  all  roads,  ways,  levels, 
dips,  airways,  etc. 

Work  Lead. — Base  bullion,  silver  lead. 

Wrought  Iron.— Iron  in  its  minimum  state  of  carburization. 

Wythern  (Wales).— Lode. 

Xacal  (Mexican).— A miner’s  cabin;  a storehouse  for  mining  goods;  a shaft 
house. 

Yardage,  Yard  Work  .—Price  paid  per  yard  for  cutting  coal. 

Yard  Pnce.— Various  prices,  per  yard  driven  (in  addition  to  the  tonnage 
prices),  paid  for  roads  of  certain  widths,  and  driven  in  certain  directions. 

Yellow  Ore  (Cornish).— Chalcopyrite. 

Yield.— The  proportion  of  a seam  sent  to  market. 

Zone.— In  coal-mining  phraseology,  this  word  means  a certain  series  of  coal 
seams  with  their  accompanying  shales,  etc.,  which  contain,  for  example, 
much  firedamp,  called  a fiery  zone,  or,  if  m«ch  water,  a watery  zone. 


INDEX, 


Absolute  Pressure,  195,  345. 

temperature  and  pressure,  344, 345. 
Abuse  of  instruments,  80. 

Abutments  (dams),  154. 

Acceleration  in  jigging,  440. 

on  inclined  planes,  399. 

Acid  waters.  Pumps  for,  165. 

Acres  to  square  feet,  4. 

Adiabatic  compression,  195,  198. 
Adjustable  bars,  432. 

Adjustment  of  Burt’s  solar  attach- 
ment, 48. 
of  compass,  38. 
of  level,  53. 
of  transit,  41. 

Afterdamp,  351. 

Agonic  line  chart,  40. 

Air  and  mercury  columns,  347. 
brattice,  394. 
bridges,  393. 

columns  in  furnace  ventilation, 
384. 

Compressed,  194. 
compression.  Theory  of,  194. 
compression.  Horsepower  neces- 
sary for,  406. 

Air  compressors,  194. 

Classification  of,  194. 
Compound,  194. 

Construction  of,  194. 

Cooling,  195. 

Dry,  196. 

Duplex,  194. 

Horizontal,  cross-compound, 
194. 

Rating  of,  195. 

Simple,  194. 

Stage,  194. 

Straight-line,  194. 

Vertical,  194. 

Wet,  196. 

Air  currents,  Conducting,  393. 
currents.  Splitting  of,  373,  378. 
leaks,  186. 
lift  pumps,  164. 
required  for  ventilation,  362. 
transmission,  196. 

Airways,  Similar,  372. 

Alabama  method  of  mining,  297. 
Alternating  current,  217. 
current  dynamos,  224. 
current  motors,  226. 

Alternators,  225. 

Multiphase,  225,  226. 

Single-phase,  225. 

Three-phase,  226. 

Two-phase,  226. 

Altitude,  Effect  of,  on  air  compres- 
sion, 195. 

Aluminum,  Electric  properties  of, 

209. 


American  coals,  168. 
gauge  wire,  208. 
measures  of  area,  4. 
measures  of  length,  2. 
measures  of  volume,  5. 

Amount  crushed  by  rolls,  424. 
of  charge,  blasting,  331. 
of  gas  liberated  per  ton  of  coal, 352. 
Analyses  of  American  coals,  168. 
Analysis  of  coal,  173. 

Andre’s  formula  for  shaft  pillars,  285. 
Aneroid  barometer,  339. 

Angle  of  inertia,  398. 

of  rolling  friction,  398. 
reading,  45. 

Annunciator  system,  232. 

Anthracite  coal,  169. 

Cubic  feet  in  ton  of,  449. 
Handling,  443. 

Sizes,  of  434. 

Specific  gravity  of,  109. 
mining.  Costs  of,  323. 
mining  methods,  305. 

Percentages  of  different  sizes  of, 
323,  326. 

Preparation  of,  442. 
screens.  Duty  of,  434. 

Tests  of  compressive  strength  of, 
290. 

Apothecaries’  weight,  1. 

Appliances  in  mine  ventilation,  381. 
Arc,  Error  in,  76. 

lamps,  214. 

Area,  Measures  of,  4. 
of  circle,  31. 
of  ellipse,  32. 

of  largest  square  inscribed  in  a 
circle,  28. 

of  parallelogram,  28. 

of  polygons,  30. 

of  tract  of  land.  To  find,  52. 

of  trapezium,  30. 

of  trapezoid,  30. 

of  triangle,  28. 

Areas,  Calculation  of,  77. 

of  circles,  1 to  1,000,  Table  of,  545, 
of  circles,  to  100,  Table  of,  561. 
Arithmetic,  15. 

Arithmetical  progression,  20. 
Armature,  216. 

‘Arrangement  of  drill  holes,  244,  335. 
of  mine  plan,  381. 
of  slope  tracks,  413. 

Ascensional  ventilation,  381. 

Ash  (coal),  171. 

Ashworth  - Hepplewhite  - Gray  lamp, 
358. 

Asphyxiation,  451. 

Atmosphere,  Composition  of,  337. 

Weight  of.  337. 

Atmospheric  pressure,  339. 


623 


624 


INDEX. 


Atom,  341. 

Atomic  volume,  341. 
weight,  344. 

Austrian  measures  of  length,  3. 
Avoirdupois  weight,  2. 


Back  of  Ore,  Caving  a,  320. 

Balancing  a conical  drum,  396. 

Ball  mills,  427. 

Barometer,  339. 

Barometric  elevations,  340. 
variations,  339. 

Barrel!,  J.,  62. 

Barrier  pillars,  287. 

Bar  signals,  235. 

Base  lines,  46. 

Batteries,  Electric,  229. 

Battery  cells.  Composition  of,  231. 
water,  430. 
working,  307. 

Beams,  102, 105. 

Bearing  in,  283. 

value  of  masonry,  107. 

Bedded  deposits,  279. 

materials.  Prospecting  for,  238. 

Bell  wiring,  230. 

Belting  and  velocity  of  pulleys,  193. 

Bending  rails,  412. 

Bends  in  pipes,  153. 

Bent  plumb-line  method  of  slope  sur- 
veying, 73. 

Biram’s  ventilator,  387. 

Bitumen,  Prospecting  for,  249. 

Bituminous  coal,  169. 

Cubic  feet  in  ton  of,,449. 

Handling,  443. 

Blackdamp,  350. 

Blacksmith  coal,  173. 

Blake  crushers,  419. 

Blasting  by  electricity,  332. 

Bleeding  from  scalp  wounds,  451. 

Blossburg  method  of  mining,  298. 

Blower  fans,  386. 

Board  measure,  13. 

Boiler,  176. 

Care  of,  185. 
capacity,  181. 

Choice  of,  179, 180. 

cleaning,  186. 

coverings,  183. 

feed-pumps,  161. 

iron,  thickness  required,  187. 

scale,  181. 

tests,  188. 

Boltheads,Weight  of,  116. 

Bolts  per  mile  of  track,  117. 

Bolts,  Weight  of,  116. 

Bonnett,  268. 

Bord-and-pillar,  280. 

Bore-hole  records,  244,  250. 
holes,  242. 

Bottoms,  Slope,  413. 

Boxes  for  electric  fuses,  224. 

Box  regulator,  375,  377. 

Boyle’s  law,  195,  345. 

Brass,  Weight  of.  111,  112,  114,  115. 

Brattice,  Air,  394. 


Breast  boards,  270. 

wheels,  157. 

Bridges,  Air,  393. 

Briqueting,  448. 

British  imperial  measure  (liquid  and 
dry),  5. 

measures  of  area,  4. 
measures  of  length,  2. 
measures  of  volume,  5. 
thermal  unit,  168. 

Brown  coal,  170. 

Brown’s  method  of  mining  anthra- 
cite, 306. 

Brown  & Sharpe  gauge,  208. 

Buckets,  Conveying,  446. 

Buggy  breasts,  291. 

Buildings,  283. 

Bulling,  330. 

Buntons,  270. 

Burt’s  solar  attachment,  47. 

Butt  cleats,  284. 


Cables,  Electric,  209. 

Cableways  in  mining,  278. 

Calculation  of  areas,  77. 
of  mine  resistance,  366. 
of  wires  for  electric  transmission, 
210. 

California  method  of  mining,  300. 
stamps,  428. 

Calorie,  168. 

Calumet  classifier,  435. 

Cams  for  stamps,  429. 

Cannel  coal,  170. 

Capacity  of  boilers,  181. 
of  electric  cables,  209. 
of  mining  machines,  337. 
of  pumps,  161. 
of  shaking  screens,  432. 
of  standard  steel  buckets,  446. 

Capell  ventilator,  389. 

Carat,  12. 

Carbonic-acid  gas,  350. 
oxide  gas,  349. 

Castings,  Weight  of  iron,  copper,  lead, 
brass,  or  zinc.  111. 

Caving  a back  of  ore,  320. 
methods,  320. 
waste  only,  320. 

Cells,  Various  types  of,  231. 

Centers,  59. 

Centigrade  to  Fahrenheit,  366. 
to  Reaumur,  366. 

Centrifugal  fans,  386. 
pumps,  164. 
roller  mills,  426. 

Chain,  Surveyor’s,  42. 
cutter  machines,  337. 
pillars,  287. 

Chains,  Iron,  129. 

Chamber-and-pillar  method,  318. 

Chambering,  330. 

Channels,  Flow  in,  142. 

Character  of  fioor  and  roof  on  size  of 
pillars,  Infiuence  of,  280. 

Charging  a hole,  330. 

Charles’  law,  345. 


INDEX. 


625 


Chemical  compounds,  341. 
equations,  341. 
symbols,  341. 

Chemistry  of  gases,  341. 

Chimneys,  189. 

Chinese  measures  of  length,  4. 

Chock,  268. 

Choice  of  a boiler,  179, 180. 
Chokedamp,  350. 

Churn  drills,  242. 

Chute  breasts,  292. 

mining,  309. 

Circles  31 

areas  of,  1 to  1,000,  Table  of,  545. 
areas  of,  ^ to  100,  Table  of,  561. 
Circuit,  Electric,  205. 

Circular  mil,  207. 

Circulation  of  boilers,  181. 
Circumferences,  1 to  1,000,  Table  of, 
545. 

if  to  100,  Table  of,  561. 

Clanny  lamp,  356. 

Classifiers,  Hydraulic,  434. 

Classifying  apparatus,  431. 

Cleaning  safety  lamps,  358. 

Clearfield  method  of  mining,  295. 
Cleats,  284. 

Clinometer,  44. 

Closed  work,  279. 

Close  workings.  Shots  in,  861. 

Closing  surveys,  68. 

Coal,  169. 

Analyses,  168. 
analysis,  173. 

Anthracite,  169. 

Bituminous,  169. 

Blacksmith,  173. 

Brown,  170. 

Calorific  Power,  168. 

Cannel,  170. 

Coking,  170. 

Composition  of,  170. 
dealers’  computing  table,  452. 
Domestic,  173. 
dust.  Effect  of,  360. 

Free-burning,  170. 

Gas,  173. 

Hardness  of,  171. 

Iron-making,  172. 

Lignite,  170. 

Preparation  of,  418. 

Prices  of,  326,  327. 

Production  of  U.  S.,  326. 
Prospecting  for,  238. 

Running  of,  312. 

Semianthracite,  169. 
Semibituminous,  169. 

Sizes  of.  173,  434. 

Specific  gravity  of,  109, 171. 

Splint,  170. 

Steaming,  171. 

Storage  of,  291. 

Strength  of,  171. 
washers,  436. 

Weight  of,  170. 

Coals,  Cubic  feet  in  ton  of  various, 
109,  170. 

Cockermegs,  268. 


Coefficient  of  contraction  (water), 
135. 

of  discharge  (water),  135. 
of  discharge  with  weirs,  140. 
of  rolling  friction,  398. 
of  roughness  for  water  channels, 
144. 

of  velocity  (water),  135. 
Coefficients  of  friction  for  various 
materials,  95,  96. 
of  friction  of  air  in  mines,  367. 
Cog,  268. 

Coins,  10. 

Coke,  172. 

ovens.  Cost  of,  328. 

Coking  coals,  170. 

coal.  Cost  of,  328. 

Collar,  268. 

Collimation,  Line  of,  53. 

Colorado  method  of  mining,  302. 

Color  of  coal  ash,  171. 

Columns,  Safe  loads  for,  106. 
Combustibles,  166. 

Combustion,  Spontaneous,  291. 
Common  fractions,  15. 

Commutator,  216. 

Comparison  of  aluminum  and  copper 
for  electric  use,  209. 
of  hydraulic  formulas,  149. 
of  methods  of  shaft  sinking,  262. 
of  vacuum  and  plenum  systems  of 
ventilation,  386. 

Compass,  38. 

To  adjust,  38. 

To  use,  39. 
vernier,  39. 
field  notes,  44. 

Complement  of  angle,  34. 

Composition  of  atmosphere,  337. 
of  coals,  170. 
of  forces,  95. 
of  fuels,  169. 

Compound,  Chemical,  341. 
lever,  92. 

wound  dynamos,  219. 

Compressed  air,  194. 
haulage,  403. 
haulage  problems,  404. 
Compressibility  of  liquids,  133. 
Compressive  strength  of  anthracite, 
289. 

Condensers,  176. 

Conducting  power  of  various  sub- 
stances, 184. 

Conductors  (guides),  398. 

(electrical),  207. 
for  electric-haulage  plants,  214. 
Cone,  33. 

Conical  drums,  394. 

drum.  To  balance,  396. 

Connecting  outside  and  inside  sur- 
veys, 68. 

Connections  for  continuous-current 
motors,  223. 

Connellsville  method  of  mining,  293. 
Constant-current  circuit,  206. 
potential  circuits,  206. 
power,  372. 


626 


INDEX, 


Constant  pressure,  372. 
pressure  circuits,  206. 
quantity,  372. 
velocity,  372. 

Constants  for  mine  gases,  349. 

for  wooden  beams,  103. 
Construction  of  air  compressors,  194. 
of  dams,  133. 
of  a mine  furnace,  383. 

Contents  of  a coal  seam.  To  find,  52. 

- of  cylinders,  6. 

Continuous-current  motors.  Connec- 
tions for,  223. 
vernier,  45. 

Contraction, Coefficient  of  ( water)  ,135. 
Control  of  roof  pressure,  284. 
Conversion  factors  (hydraulic),  141. 
of  thermometer  readings,  366. 
tables,  7,  10. 

Conveyors,  Horsepower  of,  445. 
Coordinates,  51. 

Copper,  Electric  properties  of,  209. 
Weight  of.  111,  112,  114, 115. 

Wire,  208. 

Cornish  pumps,  158. 
rolls,  423. 

underhand  sloping,  316. 

Corps,  Mine,  66. 

Corresponding  mercury  and  air  col- 
umns, I'able  of,  347. 

Corrugated  rolls,  422. 

Cosecant,  35,  454. 

Cosine.  35,  453. 

Cost  of  briqueting,  449. 
of  coke  ovens,  328. 
of  coking  coal,  328. 
of  drilling,  244-247. 
of  haulage,  409. 
of  mining  anthracite,  322. 
of  sinking,  263. 
of  stamping,  430. 
of  unloading  coal,  447. 
of  well  drilling,  242. 

Cotangent,  35,  453. 

Cotangents,  Natural,  Table  of,  464. 
Coverings,  Boiler  and  pipe,  183. 
Coversed  sine,  35. 

Coyoting,  321. 

Cracking  rolls,  421. 

Crib,  268. 

Cribbing,  270. 

Cross-section  of  electric  wires,  207. 
Cross-sections,  Construction  of,  249. 
Crushing  load  of  wood,  105. 
machinery,  418,  431. 
mills,  426. 
rolls,  423. 

rolls.  Table  of,  425,  426. 

Cube,  33. 

root,  19,  545. 
roots.  Table  of,  545. 

Cubes,  Table  of,  545. 

Cubic  feet  occupied  by  ton  of  various 
coals,  449. 

Culm,  Flushing  of,  314. 

Current  estimates,  212. 

motors,  157. 

Curtains,  394. 


Curves  for  mine  roads,  411. 

Railroad,  78. 

on  slopes,  Vertical,  416. 

Cylinder,  33. 

Cylinders,  Contents  of,  6. 

in  a pump.  Ratio  of,  160. 

of  a hoisting  engine.  To  find  size 
of,  397. 

To  find  contents  of,  in  U.  S.  gal- 
lons or  bushels,  5. 

Cylindrical  boiler.  Maximum  work 
of,  178. 

boilers.  Economy  of,  188. 

drums,  394. 

drum.  To  find  period  of  winding, 
397. 

rings,  34. 


Dams,  154. 

Debris,  156. 

Earth,  156. 
in  mines,  133. 

Masonry,  156. 

Stone,  155. 

Wing,  156. 

Danish  measures  of  length,  3. 

Darcy’s  formulas  (hydraulic),  148. 
Davy  lamp,  356. 

Debris  dams,  156. 

Decimals,  16. 

Decimals  of  a foot  for  each  inch,  3. 
Declinatiom  Magnetic,  39. 

of  Polaris,  46. 

Deflected  angle,  45. 

Deflections  in  p o w e r - transmission 
ropes.  Table  of,  122. 

Density  of  a gas,  344. 

Departures,  537. 

Deposits  over  8 ft.  thick,  318. 

Depth  of  shafts.  Calculation  of,  340. 
of  suction,  162. 

Derangement  of  ventilating  current, 
359. 

Detaching  hooks,  398. 

Detection  of  small  percentages  of  gas, 
356. 

Detonation,  331. 

Diagram  for  reporting  on  mineral 
lands,  252. 

Diameter  of  holes  (blasting),  330. 
Diamond  drill,  243. 

weight,  12. 

Dies  for  stamps,  429. 

Differential  pulley,  94. 

Diffusion  of  gases,  346,  348. 

Dip  and  strike  from  bore-hole  records, 
250. 

workings.  Ventilation  of,  382. 
Direct-current  circuits,  210. 
dynamos,  215. 
motors,  220. 

Direction  of  face,  284. 

Directions  for  blasting  by  electricity, 
332. 

Discharge,  Coefficient  of  (water),  135. 
gates  (dams),  154. 
through  V notch,  138. 


INDEX. 


627 


Disintegrating  rolls,  423. 

Disk  fans,  385. 

Distance,  Errors  in,  77. 

from  center  to  center  of  breasts, 
Table,  287. 

Distribution  of  air  in  mine  ventila- 
tion, 373. 

Ditches,  142. 

Banks  of,  143. 

Capacity  of,  143. 

Grades  of,  143. 

Velocity  in,  142. 

Division  of  air-current.  Proportional, 
375. 

D.,  L.  & W.  telephone  system,  234. 
Dodge  crushers,  419. 

Domestic  coals,  173. 

Door  regulator,  375,  377. 

regulator,  Size  of  opening  for,  377. 
Doors,  393. 

Double-chute  battery,  309. 
cylindrical  drums,  394. 
entry,  284. 

Draft,  190. 

Drainage  in  shaft  sinking,  263. 
Drawbar  pull  of  electric  locomotives, 
407. 

Drawing  pillars,  289. 

Dredge  (centrifugal  pump),  164. 
Dredging,  279. 

Dressing  of  ores,  418. 

Drift  of  drill  holes,  243. 

Drill,  Diamond,  243. 
holes,  243. 

holes.  Arrangement  of,  335. 
records,  244,  250. 

Drilling,  242,  330. 

Driving  the  gangway,  264. 

Dron’s  formula  for  shaft  pillars,  285. 
Drop  for  stamps,  428. 

Drums,  Conical,  394. 

Double-cylindrical,  394. 
for  wire  rope,  123. 

Dry  measure  (IT.  S.),  5. 

Dunn’s  table  of  size  of  pillars,  286. 
Duplex  pumps,  158. 

Dust  briquets,  448. 

Effect  of,  360. 

Duty  of  anthracite  screens,  434. 
of  miners’  inch,  137. 
of  stamps,  430. 

Dynamite,  Thawing,  329. 

Dynamos,  215. 

Alternating-current,  224. 
Compound-wound,  219. 
Series-wound,  219. 

Shunt-wound,  219. 

Earth  Augers,  242. 

dams,  156. 

Economizers,  185. 

Effect  of  altitude  on  air  compression, 
195. 

Efficiency,  Manometrical,  390. 
Mechanical,  390. 
of  water-power,  156. 

Electrical  Expressions  and  Equiva- 
lents, 205. 

Electric  blasting,  332. 


Electric  circuit,  205. 
exploder,  332. 
haulage,  406. 

haulage  plants.  Conductors  for, 
214. 

haulage  problem,  407. 
locomotives.  Drawbar  pull  of,  407. 
locomotives.  Hauling  capacity  of, 
408. 

power,  204. 
pumps,  162. 

resistance,  Estimation  of,  209. 
signaling,  229-235. 
units,  203. 
wiring,  207. 

Electricity,  203. 

Electromotive  force,  203,  218. 
Elements,  341. 

in  ventilation,  363. 
of  mechanics,  91. 

Table  of,  342. 

Elevating  capacity  of  buckets,  446. 
Elevation  of  rails  for  mine  roads,  412. 
Elevations,  Barometric,  340. 

Elevators,  Water,  164. 

Ellipse,  3'2. 

End  cleats,  284. 
on,  285. 
plates,  270. 

Endless-rope  haulage,  401. 

Engine  drivers.  Rules  for,  191. 

planes,  399. 

Engines,  Sinking,  263. 

Steam,  190. 

Entries,  Number  of,  284. 

Equal  settling  factors.  Table  of,  439. 
settling  particles,  439. 
shadows,  47. 
splits  of  air,  374. 

Equations,  Chemical,  341. 
Equilibrium  of  liquids,  130. 
Equivalent  orifice,  367. 

Errors,  76. 
in  arc,  76. 
in  distance,  77. 
in  measurement,  77. 
in  surveying,  66,  76. 

Eschka’s  method  of  analysis  for  sul- 
phur, 174. 

Establishing  a meridian  wi^h  solar 
attachment,  47. 

Estimates  of  current,  212. 

Evolution,  19,  545. 

Excitation  of  dynamos,  218. 

Exhaust  fans,  386. 

Expansion  oi  gases,  344. 

Exploder,  Electric,  332. 

Exploring  workings,  361. 

Explosions,  Exploring  worki  ngs  after 
361. 

in  boilers,  179. 

Explosive  conditions  in  mines,  359. 
Explosives,  329. 

Pressures  developed  by,  334. 
Relative  strengths  of  various 
brands  of,  330. 

Values  of,  335. 

Eytelwein’s formulas  (hydraulic),  148 


628 


INDEX, 


Face  Cleats,  284. 

Direction  of,  284. 
on,  285. 

Factor  of  a mine,  Potential,  367. 
Factors,  Conversion  (hydraulic).  141. 
Fahrenheit  to  centigrade,  366. 

Fan  construction,  Principles  of,  391. 
tests,  392. 

ventilation,  373,  385. 

Fans,  Ventilating,  386. 

Fastenings  for  wire  rope,  126. 

Feeders  of  gas,  352. 

Feed-pumps,  161,  186. 

Feedwater  for  boilers,  186. 

Field  excitation  of  dynamos,  218. 
magnet,  216. 

notes  for  outside  compass  survey, 
44. 

Filling  methods,  319. 

Finger  bars,  432. 

Firedamp,  351. 

Fires,  Gob,  291. 

Firing  a boiler,  186. 
blasts,  331. 
by  detonation,  331. 

Fixed  carbon  in  coal,  171, 174, 

Flash  signals,  234. 

Flat  deposits,  318. 

Flat  ropes,  119,  394. 

Flights,  Capacity  of,  446. 

Flow  of  water  in  channels,  142, 144. 
in  rivers,  145. 
through  flumes,  146. 
through  orifices,  135. 
through  pipes,  147,  150. 
Flumes,  145,  443. 

Flow  of  water  through,  146. 

Grade  of,  145. 

Flushing  of  culm,  314. 

Foaming  (boilers),  186. 

Forced  draft,  190. 

Force  fans,  386. 

Forces,  Composition  of,  95. 

Foreign  coins.  Values  of,  11. 
Forepoling,  260,  270. 

Form  of  roll  teeth,  422. 

Forms  of  mine  timbering,  267. 
Formulas  for  air  splitting,  378. 
for  inclined  planes,  399. 
in  ventilation,  370. 

Foster’s  formula  for  shaft  pillars,  286. 
Foundations  (dams),  154. 

Fractions,  15. 

Common,  15. 

Decimal,  16. 

Table  of  equivalent  decimal,  16. 
Fragmental  deposits.  Mining  of,  278. 
Free-burning  coals,  170. 

gold  per  ton  of  ore.  Value  of,  241. 
Freezing  process,  260. 

Friction,  95. 

coefficients  for  air  in  mines,  367. 
coefficients  for  various  materials, 
95,  96. 

in  knees  and  bends,  153. 
of  air  in  pipes,  201. 
of  mine  cars,  96. 
of  water  in  pipes,  151. 


Friction  pull  on  endless  rope.  402. 
Frictional  resistance  of  shafting,  96. 
Frozen  ground.  Mining  of,  322. 
Frustums.  34. 

Fuel  dust  briquets,  448. 

Fuels,  166. 

Composition  of,  169. 

Furnace  stack,  385. 

Construction  of  ventilating,  383. 
ventilation,  373. 

ventilation.  Air  columns  in,  384. 
Fuse  boxes,  224. 

Fuses,  224. 

Fusible  plugs,  186. 


Galvanic  Action  Around  Boiiers,  187. 

Gangway  driving,  264. 

timbers,  268. 

Gas  coals,  173. 
feeders,  352. 

Testing  for,  354.  * 

Outbursts  of,  352,  360. 

Gases,  Chemistry  of,  341. 

Diffusion  of,  346.  348. 
enclosed  in  the  pores  of  coal,  353. 
found  in  mines,  348. 

Pressure  of,  345. 

Properties  of,  344. 

Transpiration  of,  346,  348. 

Gate  for  jig,  438. 

Gates  crusher,  Table  of,  422. 

Gauge  cocks,  186. 

of  mine  tracks,  411. 

Pressure,  185. 

Water,  365. 

Wire,  207,  208. 

Gauging  by  weirs,  138. 
water,  136. 

Gay-Lussac’s  law,  195,  345. 

Gears,  Train  of,  92. 

Gems  and  precious  stones.  Prospect- 
ing for,  241. 

General  mathematical  principles,  14. 

remarks  on  surveying,  49. 
Geological  maps.  Construction  of,  249, 
periods,  237. 

Geometrical  problems,  25. 

progression,  21. 

Geometry,  24. 

Geordy  lamp,  356. 

George’s  creek  method  of  mining,  297. 
Gilpin  county  stamps,  428. 

Glossary  of  mining  terms,  565. 

Gob  fires,  291. 

Gold  coins,  10. 

mine.  Opening  of,  258. 

Gonda  type  of  cell,  230. 

Gophering,  321. 

Gould’s  formulas  (hydraulic),  148. 
Grade  of  mine  road,  410. 

Gradient,  Hydraulic,  147. 

Graham’s  law,  346. 

Gravity  planes,  398. 

Specific,  107. 
specific.  Table  of,  108. 
stamps,  427. 

Gray  lamp,  358. 


INDEX. 


629 


Grizzlies,  431. 

Guibal  ventilator,  388. 
Guides,  398. 

Gyratory  crushers,  420. 


Half  on,  285. 

Hammer  crushers,  423. 

Handling  of  material,  443. 

Hard  coal,  169,  313. 

Hardness  of  coal,  171. 

Haulage,  398. 

by  compressed  air,  403. 

Cost  of,  409. 

Electric,  214,  406. 

Motor,  402. 
problems,  399,  407. 
road  signals,  235. 
rope,  122,  400. 

Speed  of,  408. 

Hauling  capacity  of  electric  locomo- 
tives, 408. 

Hawksley’s  formula  (hydraulic),  148. 

Head-bars,  431. 
block,  268. 
frames,  275,  397. 
frames.  Sinking,  262. 
gears,  275. 
sheaves,  397. 

Headboard,  268. 

Heating  surface  of  a boiler,  177. 
values  of  American  coals,  168. 

Heberle  gate,  438. 

High  explosives,  329. 

Hill,  E.,  198. 

Hints  for  mining  small  seams,  313. 
to  beginners  in  surveying,  80. 

Hoisting,  394. 

engine  cylinders,  397. 
engine.  To  find  size  of,  396. 
problems,  396. 

ropes.  Starting  strain  on,  126. 
ropes.  Stress  in,  123. 

Hooks,  Detaching,  398. 

Horizontal  distances,  50,  87,  537. 
distances,  Stadia  table  of,  87. 

Horsepower  for  box  regulators,  377. 
for  bucket  elevators,  445. 
for  door  regulators,  377. 
necessary  to  compress  air,  406. 
of  air-currents,  363. 
of  boilers,  177. 
of  coal  conveyor,  445. 
of  engine,  190. 
of  manila  ropes,  126. 
of  stamps,  430. 
of  a stream,  157. 
required  to  raise  water,  161. 

Hughes’s  formula  for  shaft  pillars, 
286. 

Hydraulic  classifiers,  434. 
gradient,  147. 
placer  mining,  278. 

Hydraulics,  135. 

Hydrocarbons,  349. 

Hydrogen  disulphide  350. 
Sulphuretted,  350. 

Hydrostatics,  130. 


I Beams,  Safe  Loads  for,  104. 
Illuminating  power  of  safety  lamps, 
359. 

Impulse  wheels,  158. 

Incandescent  lamps,  213. 

Inch,  Miners’,  136. 

Inclined  plane,  93. 

plane.  Stress  in  hoisting  ropes  on, 
123. 

roads.  Calculation  of  power  for, 
402. 

roads.  Haulage  on,  398. 
shafts,  Surveying,  73. 

Included  angle,  45. 

Incrustation  and  scale,  182. 

Indiana  method  of  mining,  298. 
Individual  angle,  45. 

Induction  motors,  227. 

Inertia,  Angle  of,  398. 

Influence  of  furnace  stack  on  venti- 
lation, 385. 

of  seasons  on  ventilation,  382. 
Injector,  186. 

Area  of  nozzle  of,  187. 

Delivery  in  gallons  per  hour  of, 
187. 

Inside  surveys,  56,  67. 

Inspection  of  boilers,  181. 

Insulated  wires,  212. 

Interstitial  currents,  439. 

factors,  440. 

Involution,  19,  545. 

Iowa  method  of  mining,  299. 

Iron  beams,  103. 
for  track,  117. 
pipe.  Weight  of,  113. 
supports,  272. 

Weight  of  flat,  115. 

Weight  of  wrought,  114, 

Irregular  mining  deposits,  321. 
Isogonic  chart,  40. 

Isothermal  compression,  195, 198. 


Jaw  Crushers,  419. 

Jeffrey-Robinson  coal  washer,  436. 
Jigs,  437. 

Joints  in  mine  timbering,  267. 


Kind'Chaudron  Method  of  Sinking,  262. 

Knees  in  pipes,  153. 

Koepe  system  of  hoisting,  395. 


Lamp  Tests  for  Gas,  354. 

Lamps,  Arc,  214. 

Incandescent,  213. 

Safety,  355. 

Testing,  355. 

Lancashire  boiler,  177. 

Landings,  Timbering  of,  272. 

Large  deposits  over  8 ft.  thick,  Min- 
ing,  318. 

Latches,  413. 

Latitude,  50,  537. 

with  Burt’s  solar,  48. 

Launders,  443. 


630 


INDEX. 


Law  of  settling  particles,  439. 

Laws  in  regard  to  air  splitting,  373. 
in  regard  to  quantity  of  air,  363. 
of  volume,  341. 

Leaching  methods  of  mining,  3^2. 
Lead,  Weight  of.  111,  113,  114,  115. 
Leclanche  cell,  229. 

Lehigh  region.  Costs  of  mining  in, 
323. 

Length,  Measures  of,  2. 

of  steep  pitch  on  inclined  plane, 
399. 

Leveling,  53. 

Trigonometric,  56. 

Level  notes,  55,  62. 

roads.  Haulage  on,  398. 
timbers,  268. 

Levels  (gangways),  316, 
in  metal  mines,  264. 

Levers,  91. 

Lid,  268. 

Life  of  shoes  and  dies,  429. 

of  wire  rope,  123. 

Lignite,  170. 

Line  shafting,  110. 

Liquid  measure  (U.  S.),  5. 

Liquids,  Compressibility  of,  133. 

Load  for  wire  rope,  125. 

that  a hoisting  engine  will  start, 
To  find,  396. 

Locating  errors,  76. 

special  work,  77. 

Locks  for  lamps,  358. 

Locomotive  haulage,  402. 

Logarithmic  functions.  Table  of,  492. 
Logarithms,  22,  473. 

of  numbers.  Table,  473. 
of  trigonometric  functions.  Table 
of,  492. 

Log  washer,  436. 

Long-hole  process  of  shaft  sinking, 
262. 

horn,  285. 
section,  64. 
splice,  128. 

Longitudinal  back  stoping  with  fill- 
ing, 319. 

Longwall  method,  281,  302. 
Modifications  of,  302. 

Timbering,  283. 

Loss  in  transmitting  air,  198. 
of  blood,  449. 

of  head  in  pipe  by  friction,  151. 
of  heat  from  steam  pipes,  184. 
of  pressure  of  air  in  pipes,  202. 
Low  explosives,  329. 

Lubricants  for  different  purposes,  102. 
Lubrication,  100. 


Machine  Mining,  336. 

Magnetic  prospecting,  248. 
variation,  39. 

Malleable-iron  buckets,  446. 

Manila  ropes.  Power  transmitted  by, 
126. 

Manometrical  efficiency,  390. 
Mapping,  74. 


Maps,  Geological,  249.  • 

Mariotte’s  law,  345. 

Marsaut  lamp,  358. 

Marsh  gas,  348. 

Masonry,  Bearing  value  of,  107. 
dams,  156. 
supports,  272. 

Material,  Handling  of,  443. 
Mathematical  signs,  14. 

Mathematics,  14. 

Measurement,  Error  in,  77. 
of  temperature,  366. 
of  ventilating  currents,  364. 
Measures  of  area,  4. 

American,  4. 

British,  4. 

Metric,  4. 

Measures  of  Length,  2. 

American,  2. 

Austrian,  3. 

British,  2.  ^ 

Chinese,  4. 

Danish,  3. 

Metric,  3. 

Norwegian,  3. 

Prussian,  3. 

Russian,  3. 

Swedish,  4’. 

Measures  of  volume  5. 

American,  5 
British,  5 
Metric,  5. 

Mechanical  efficiency,  390. 
mixture,  341. 
ventilators,  385. 

Mechanics,  91. 

Mensuration,  28. 
of  solids,  33. 
of  surfaces,  28. 

Mercurial  barometer,  339. 

Mercury  and  air  columns,  347. 

column  corresponding  to  water 
column,  340. 

Meridians,  46. 

Merivale’s  formula  for  shaft  pillars, 
285. 

Mesh  for  shaking  screens,  433. 

of  revolving  screens  for  anthra- 
cite, 434. 

Size  of,  433. 

Metal  linings  for  shafts,  260. 

Methods  and  appliances  in  mine  ven- 
tilation, 381. 

Methods  of  mining,  277. 

Alabama,  297. 
anthracite,  305. 

Blossburg,  298. 

Brown’s,  306. 

California,  300. 

Clearfield,  295. 

Colorado,  302. 

Connellsville,  293. 

George’s  creek,  297. 

Indiana,  298. 

Iowa,  299. 

mineral  deposits,  316. 
Newcastle,  Colo.,  302. 
Pittsburg,  295. 


INDEX. 


631 


Methods  of  Mining,  Reynoldsville, 
295 

Tesla,  Cal.,  300. 

West  Virginia,  296. 

Williams’,  312. 

Methods  of  surveying,  67. 

Metric  conversion  tables,  7-10. 
measures  of  area,  4. 
measures  of  length,  3. 
measures  of  volume,  5. 
system,  1,  2,  3,  9,  10. 
weight,  2. 

Mil,  207. 

Milling  system,  278. 

Mine-car  friction  tests,  98. 
cars.  Friction  of,  96. 
corps,  66. 
dams,  133. 
explosions,  361. 
gases,  348. 
gases.  Table  of,  349. 

Opening  a,  257. 
plan,  Arrangement  of,  381. 
resistances,  364,  366. 
roads,  410. 
sampling,  174. 
telephones,  233. 
timber  and  timbering,  265. 
tracks,  410. 

Mineral  available  in  a prospect,  251. 
deposits.  Methods  of  mining,  316. 
lands.  Report  on,  252. 

Miners’  inch,  136. 

Mining  terms.  Glossary  of,  565. 

Mixture,  Mechanical,  341. 

Moisture  in  coal,  171, 174. 

Molecule,  341. 

Money,  Tables  of,  10. 

Morris,  W.  H.,  127. 

Motor  haulage,  402. 

Motors,  214,  215. 

Current  (water),  157. 

Induction,  227. 

Regulation  of  speed  of,  222. 
Synchronous,  226. 

Movable  bars,  432. 
pulley,  94. 

Mueseler  lamp,  358. 

Multiphase  alternators,  225. 

Murphy  ventilator,  389. 


Nails,  Sizes,  Etc.  of,  114. 

Nasmyth  fan,  387. 

Natural  division  of  air-currents,  374. 
functions,  Tables  of,  453. 
gas.  Prospecting  for,  249. 
splitting.  Calculation  of,'  374. 
ventilation,  381. 

Needling,  268. 

Neville’s  formula  (hydraulic),  148. 
Newcastle,  Colorado,  method  of 
mining,  302. 

Nitrogen,  348. 

Non-conductors,  Relative  values  of, 
185. 

Norwegian  measures  of  length,  3. 
Notes  (survey),  60. 


Notes,  Compass  field,  44. 

for  outside  compass  survey,  44. 
Level,  55,  62. 
on  mapping,  74. 

Side,  60,  61. 

Stope-book,  62. 

Transit,  60. 

Nozzle,  Injector,  187. 

Number  of  cars  in  a trip  on  a self- 
acting incline,  399. 

Nuts,  Weight  of,  116. 


Occluded  Gases,  352. 

Occurrence  of  gases  in  mines,  351. 
Ohm’s  law,  204. 

Oils  for  safety  lamps,  356. 

Lubricating,  100, 102. 

Open  channels,  142. 
work,  277. 

Opening  a mine,  257. 

in  box  regulators,  376. 

Order  of  drop  of  stamps,  428. 

Ore  deposits,  238. 
dressing,  418. 

Handling  of,  443. 

Orifice,  Equivalent,  367. 
Oscillating  bars,  432. 

Outbursts  of  gas,  352,  360. 

Outside  surveys,  67. 

Overcasts.  393. 

Overhand  stoping,  304,  317. 
Overshot  wheels,  158. 

Oxygen,  348. 


Packing  for  Pumps,  159. 

Pack  walls,  283. 

Paint,  59. 

Pamely’s  formula  for  shaft  pillars,  286. 
Panel  system,  283. 

Parallel  circuits,  206. 

Parallelograms,  28. 

Parallelopiped,  33. 

Peele,  Robert,  194. 

Percentage,  20. 

Percussion  drills,  242. 

Period  of  winding  on  a cylindrical 
drum.  To  find,  397. 

Permitted  explosives,  329. 

Petroleum,  Fuel  value  of,  167. 

Prospecting  for,  249. 

Pick  machines,  336. 

Pillar  timber,  268. 
and  chamber,  280. 
and  stall,  281,  292. 
drawing,  289. 

Weight  on,  at  different  depths,  287. 
Wooden,  105. 

Pins,  43. 

Pipes,  Flow  through,  147, 150. 
Friction  in,  151. 

Pressure  of  water  in,  132. 
Thickness  of,  133. 
used  for  compressed-air  haulage, 
Table  of,  406. 

Piston  speed  of  pumps,  161. 


632 


INDEX, 


Pitch  at  which  anthracite  will  run, 
Table  of,  443. 
distance,  51. 

Pitching  work  surveys,  68. 

Pittsburg  method  of  mining,  295. 
i’lacer  deposits.  Prospecting  for,  240. 

mining,  278. 

Plane  trigonometry,  34. 

Planes,  Engine,  399. 

Gravity,  398. 

Plates,  metal,  Weight  of,  112. 

Platform  bars,  431. 

Plats,  Timbering  of,  272. 

Plenum  system  of  ventilation,  386. 
Plotting,  49. 

by  coordinates,  51. 

Plow-steel  rope,  120. 

Plugs,  186. 

Plumb-bob,  44. 

Plumbing  of  shafts,  69. 

Pneumatic  method  of  shaft  sinking 
260. 

stamps,  430. 

Pockets  of  gas,  352. 

Poetsch-Sooysmith  process  (freezing 
method),  260. 

Polaris  observation,  46. 

Polygons,  30. 

Post  and  breast  cap,  268. 

Potential  factor  of  a mine,  367. 

Pound  calorie,  168. 

Power,  Electrical,  204. 
for  hoisting,  395. 
in  mine  ventilation,  367. 
of  air-currents,  363. 
of  a hoisting  engine,  To  find,  396. 
of  an  explosive,  334. 
of  waterfall,  157. 
pumps,  162. 

required  for  inclined  roads,  402. 
stamps,  431. 

Water,  156. 

Practical  examples  in  the  solution  of 
triangles,  35. 

splitting  of  air-currents,  373. 
Precious  stones.  Prospecting  for,  241. 
Preliminary  work,  257. 

Preparation  of  anthracite.  Diagram 
of,  442. 

of  coal  and  ore,  418. 

Preservation  of  timber,  265. 

Pressure,  Absolute,  345. 

as  affecting  explosive  conditions, 
361. 

developed  by  explosives,  334. 
for  box  regulators,  376. 
gauge,  185. 

of  anthracite  coal  against  walls, 
445. 

of  bituminous  coal  against  walls, 
444. 

of  gases,  345. 

of  liquids  on  surfaces,  130. 
of  occluded  gases,  352. 
of  steam  at  different  tempera- 
tures, 188. 

of  water  in  pipes,  132. 
on  heading,  130. 


Pressure  of  water  on  plane  surface, 
132. 

Prices  per  ton  of  coal  at  mines, Table, 
327. 

Primary  splits,  374. 

Prism,  33. 

Prismoidal  formula,  34. 

Problem  in  compressed-air  haulage, 
404. 

Problems  in  geometrical  construc- 
tion, 25. 
in  haulage,  399. 
in  hoisting,  396. 

Progression,  Arithmetical,  20. 

Geometrical,  21. 

Properties  of  copper  wire,  208. 

of  materials,  107. 

Proportion,  or  Rule  of  Three,  18. 
Proportional  division  of  the  air-cur- 
rent, 375. 

Props,  Undersetting  of,  276,  277. 

Wooden,  105. 

Prospecting,  235. 
for  bitumen,  249. 
for  natural  gas,  249. 
for  petroleum,  249. 

Magnetic,  248. 

Prussian  measures  of  length,  3. 
Pulley,  94. 

Pulleys  and  belting,  193. 

Pulverizers,  423. 

Pump  machinery,  158. 
memoranda,  163. 
packing,  159. 
valves,  162. 

Pumps,  158. 

Air-lift,  164. 

Centrifugal,  164. 

Cornish,  158. 

Electrical,  162. 
for  acid  waters,  165. 

Power,  162. 

Simple  and  duplex,  158. 

Sinking,  165. 

Vacuum,  104. 

Push  button,  234. 

Pyramid,  33. 

Quadrant,  34. 

Quantity  of  air  required  by  State 
Laws,  363. 

for  dilution  of  mine  gases,  363. 
for  ventilation,  362. 
to  produce  necessary  velocity 
at  face,  363. 

Radial  Roller  Mills,  426. 

Radii  of  curves,  79. 

Rail  bending  for  mine  roads,  412. 

elevation  for  mine  roads,  412. 
Railroad  curves,  78. 

Rails  for  mine  roads,  411. 

per  mile  of  track,  117. 

Raises,  316. 

Rapid  firing  of  boilers,  187. 

method  of  splicing  a wire  rope, 
127. 

Rate  of  diffusion,  346. 


INDEX. 


633 


Rating  of  compressors,  195. 

Ratio  of  steam  and  water  cylinders  in 
pump,  160. 

Reaumur  to  Fahrenheit,  366. 
Reciprocals,  545. 

Recoil  of  an  explosion,  361. 
Reduction  of  inches  to  decimals  of  a 
foot,  2. 

Regular  polygon,  30. 

Regulation  of  motors  for  speed,  222. 
Regulators,  375. 

Relation  of  power,  pressure,  and  ve- 
locity, 364. 

Relative  volume  of  gases,  343. 
Relighting  stations,  359. 

RemcA^al  of  sulphur  from  coal,  441. 
Repair  of  boiler  coverings,  187. 
Repairs  to  boilers,  180. 

Reporting  on  mineral  lands,  252. 
Requirements  of  law  as  to  splitting, 
373. 

Reservoirs,  154. 

Resistance,  Electric,  203. 

Estimation  of  (electric),  209. 
in  electric  lines,  206. 
of  soils  to  erosion,  143. 

Mine,  364. 

Return-call  system,  232. 

Revolving  screen  mesh  for  anthracite, 
433,  434. 

Reynoldsville  method  of  mining,  295. 
Right-angled  V notch,  137. 

Rings,  34. 

Rise  workings.  Ventilation  of,  382. 
Rivers,  Flow  of  water  in,  145. 

Roads,  Haulage  on  inclined,  .398. 
Level,  398. 

Mine,  410. 

Rock-chute  mining,  310. 

V drills,  263. 

Handling  of,  443. 

Roller  mills,  426. 

Rollers,  412. 

Rolling  friction.  Coefficient  of,  398. 
Roll-jaw  crushers,  420. 

Rolls,  421. 

Amount  crushed  by,  424. 

Crushing,  423. 

Speeds  of,  424. 

Teeth  of,  422. 

Roof  pressure,  280. 

Control  of,  284. 

Room-and-pillar,  280. 
modifications  of,  291. 
openings,  281. 
pillars,  286. 

Rooming  with  filling,  319. 

Rope  haulage,  122,  400. 

Ropes,  118. 

fastenings,  126. 

Flat,  394. 

Manila,  126. 

Rotary  crushers,  420, 422. 

Roughness,  Coefficient  of,  144. 

Rule  of  Three,  18. 

Rules  for  engine  drivers,  191. 

Running  of  coal,  312. 

Russian  measures  of  length,  3. 


Safe  Loads  for  Cast'lron  Columns,  106. 

Safe  loads  for  I beams,  104. 

Safety  catches,  398. 
explosives,  329. 
lamp  oils,  356. 
lamps,  355,  356. 
lamps.  Locks  for,  358. 
lamps.  Illuminating  power  of,  359. 
valves,  185. 

Sampling  available  mineral,  251. 
of  coal,  173. 

Scaife  trough  washer,  437. 

Scale,  Removal  of,  from  boilers,  181. 
Scalp  wounds,  451. 

Schiele  ventilator,  388. 

Schmidt’s  law  of  faults,  239. 

Screens,  431,  432. 

Screw,  93. 

Diameter  and  number  of,  113. 
Seam  blasting,  331. 

Seasons,  Influence  of,  382. 

Secant,  35,  454. 

Secondary  splits,  374. 

Sederholm,  E.  T.,  125. 

Semianthracite  coal,  169. 
Semibituminous  coal,  169. 
Series-circuits,  205. 

parallel  method  of  regulation,  222. 
wound  dynamos,  219. 

Settling  boxes,  435. 

particles.  Law  of,  439. 

Shaft  bottoms.  Steel,  276. 
bottom  tracks,  416. 
pillars,  285. 
plumbing,  69. 
sinking.  Drainage  for,  263. 
sinking.  Ventilation,  263. 
timbering,  270. 

Shafting,  Frictional  resistance  of,  96. 

Strength  of,  110. 

Shafts,  259. 

Calculation  of  dejpth  of,  340. 

Form  of,  259. 

Methods  of  sinking,  259. 

Size  of,  259, 

Surface  tracks  at,  417. 

Table  of  depths  of,  etc.,  261. 
Shaking  screens,  432. 

Shanty,  268. 

Shearing  machines,  337. 

Sheaves  for  wire  rope,  123. 

Sheet-metal  gauges,  122d. 

Shoes  for  stamps,  429. 

Short  horn,  285. 

Shots  in  close  workings,  361. 

Shunt- wound  dynamos,  219. 

Side  notes,  60,  61. 

Signal  for  haulage  roads,  235. 
Signaling,  Electric,  229-235. 

Silver  coins,  10. 

Similar  airways,  372. 

Simple  bell  circuit,  230. 

Sine,  34,  453. 

Sines,  Natural,  Table  of,  453. 
Single-chute  battery,  309. 
entry,  284. 

phase  alternators,  225. 

wire  method  of  slope  surveying,74. 


634 


INDEX. 


' f, 

Sinking  a sha^ft,  5^59. 

Cost  of,  263. 
engines,  263. 
head-frames,  262. 
pumps,  165. 

Slope,  263. 

Speed  of,  263. 

Siphons,  149. 

Size  of  engine  for  engine-plane  haul- 
age, 399. 

of  hoisting  engine.  To  find,  396. 
of  mesh  for  screens,  433. 
of  opening  for  door  regulator,  377. 
of  opening  in  box  regulator,  376. 
of  pillars,  285. 
of  timber,  267. 

Sizes  of  anthracite,  percentages  of 
each,  323,  326. 
coal,  173,  434. 

Sizing  apparatus,  431. 

Slack,  167. 

Slicing  method,  319. 

Slightly  inclined  deposits,  318. 

Slope  bottoms,  413. 
level,  44. 
sinking,  263. 
surveying,  73. 
tracks,  413. 

Surface  tracks  at,  417. 

Small  percentages  of  gas,  356. 

seams,  mining  of,  313. 

Soft  coal,  169. 

Soils,  Resistance  of,  to  erosion,  143. 
Solar  attachment,  47. 

Sole,  268. 

Space  required  to  store  coins,  11. 
Special  forms  of  supports,  272. 
mining  methods,  322. 
work,  77. 

Specific  gravity,  107. 
of  coal,  171. 
of  gases,  344. 

of  various  substances.  Table 
of,  108,  109. 
volume,  341. 

Speed  of  crushing  rolls,  426. 
of  drilling,  244. 
of  haulage,  408. 
of  revolving  screens,  434. 
of  rolls,  423. 
of  sinking,  263. 
of  stamps,  429. 

of  water  through  pump  passages, 
160. 

regulation  of  motors,  222. 

Sphere,  33. 

Spikes,  Railroad,  117. 

Sizes,  etc.,  114. 

Spiling,  270. 

Spillways,  155. 

Spitzkasten,  435. 

Spitzlutten,  435. 

Splices  per  mile  of  track,  117. 

Splicing  a wire  rope,  127. 

Splint  coal,  170. 

Splitting  formulas,  378. 

of  air-currents,  373. 

Spontaneous  combustion,  291. 


' Sprags,  270. 

Square  feet  to  acres,  4. 
root,  19,  545. 
roots.  Table  of,  545. 
sets,  270.  . 
set  system,  321. 
work,  318. 

Squares,  Table  of,  545. 

Squibbing,  330. 

Stack,  Furnace,  385. 

Stadia  measurements,  81. 

table,  86. 

Stamps,  427. 
heads,  429. 

Pneumatic,  430. 

Power,  431.  • 

Speed  of,  429. 

Steam,  431. 

Standard  steel  buckets.  Weights  and 
capacities  of,  446. 

Starting  strain  on  hoisting  rope,  126. 
Stationary  screen  jigs,  437. 
screens,  431. 

Stations,  Distinguishing,  59. 
Establishment  of,  57. 

Kinds  of,  57. 

Marking,  58. 

Relighting,  359. 

Timbering  of,  272. 

Steam,  175. 
engine,  190. 
pipe  coverings,  183. 
pressure  at  different  tempera- 
tures, 188. 
shovel  mines,  278. 
stamps,  431. 

Steaming  coals,  171. 

Steel  beams,  103. 

shaft  bottoms,  276. 
supports,  272. 
tape,  43. 

Stems  for  stamps,  429. 

Stinkdamp,  350. 

Stone  dams,  155. 

Stope  books,  62. 

Sloping,  316. 

Overhand,  304. 
with  filling,  319. 

Stoppings,  393. 

Storage,  Coal,  291. 

Stowing,  283. 

Stream  horsepower,  157. 

Strength  of  anthracite,  289. 
of  electric  current,  203. 
of  materials,  102. 
of  metals,  115. 
of  roof,  280. 
of  shafting,  110. 
of  wire  ropes,  119. 

Stress  in  hoisting  ropes,  123. 

Strike  from  bore-hole  records,  250. 
Stulls,  268. 

Stuttles,  270. 

Suction,  162. 

in  jigging,  440. 

Sulphureted  hydrogen,  350. 

Sulphur  in  coal,  171,  174. 

Removal  of,  from  coal,  441. 


INDEX. 


635 


Sump,  264. 

Supplement  of  angle,  34. 

Surface  tracks  for  shafts  and  slopes, 
417. 

Surveying,  38. 
drill  holes,  243. 
methods,  67. 

Underground,  56,  67. 

Susquehanna  Coal  Co.  (friction  of 
mine  cars),  98. 

Swedish  measures  of  length,  4. 
Switches,  413. 

Symbols,  Chemical,  341. 

Synchronous  motors,  226. 

Systems  of  working  coal,  280. 

Table,  Coal  Dealers’  Computing,  452. 

Tables  of  Barrier  Pillars,  288. 
batteries,  231. 
circles,  545. 

circumferences  and  areas  of  cir- 
cles, ^ to  100,  561. 
combustibles,  166. 
elements,  342. 
hydraulic,  135-154. 
logarithms  of  numbers,  473. 
logarithms  of  trigonometric  func- 
tions, 492. 
mine  gases,  349. 
natural  sines  and  cosines,  453. 
natural  tangents  and  cotangents, 
464. 

rail  elevations,  412. 
reciprocals,  545. 

squares,  cubes,  square  roots,  cube 
roots,  circumferences  and  areas, 
545-560. 

Stadia,  88. 

strength  of  materials,  102-106. 
traverse  (latitudes  and  depar- 
tures), 537. 

well-known  shafts,  261. 

{For  tables  not  enumerated  above  see  the 
various  subjects.) 

Tail-rope  haulage,  400. 

Tamping,  331. 

Tangent,  35,  453. 

Tangents,  Natural,  Table  of,  464. 
Tappets  for  stamps,  429. 

Teeth  for  rolls,  422. 

Telephones  in  mines,  233. 

Telpherage,  278. 

Temperature,  Absolute,  344,  345. 

Measurement  of,  366. 

Tension  on  hauling  rope.  Calculation 
of,  401. 

Tertiary  splits,  374. 

Tesla,  Cal.,  method  of  mining,  300. 
Test  of  mine-car  frictions,  98. 

Testing  for  gas  by  lamp  flame,  354. 

lamps,  355. 

Tests,  Boiler,  188. 

Fan,  392. 

of  compressive  strength  of  an- 
thracite, 290. 

Thawing  dynamite,  329. 

Theory  of  air  compression,  194. 
jigging,  439. 


Theory  of  stadia  measurements,  81. 
Thermal  unit,  168- 

Thermometer  readings.  Conversion 
of,  366. 

Thermometers,  366. 

Thickness  of  boiler  iron,  187. 
pipe,  133. 

Thin  seams,  Mining,  313. 

Three-phase  alternators,  226. 
Thurston,  table  of  lubricants,  102. 

Ties  for  mine  roads,  410. 

Timber,  Crushing  load  of,  105. 
Gangway,  268. 
joints,  267. 

Level,  268. 
measure,  12. 

Placing  of,  266. 

Preservation  of,  265. 

Size  of,  267. 

Timbering,  265. 

Forms  of,  267. 
longwall  face,  284. 

Tools  for  sinking,  263. 

Torque,  220. 

Track  iron,  117. 

Tracks  for  shaft  bottoms,  416. 

Mine,  410. 

Tractive  efforts  of  compressed-air 
locomotives,  404. 

Train  of  gears,  92. 

Transformers.  228. 

Transit,  40. 

adjustment,  41. 
notes,  60. 
surveying,  45. 

Transmission  of  air  in  pipes,  196, 198. 
Electric,  210. 

pressure  through  water,  132. 

Rope,  122. 

Transpiration  of  gases,  346,  348. 
Transporting  a wounded  person, 
450. 

Transverse  rooming  with  filling, 
319. 

Trapeziums,  30. 

Trapezoids,  30. 

Traverse  tables,  537. 

Traversing  a survey,  51. 

Treatment  of  injured  persons,  449. 

persons  overcome  by  gas,  451. 
Tremain  stamp,  431. 

Trestles,  274. 

Triangles,  28,  35. 

Trigonometric  leveling,  56. 
Trigonometry,  34. 

Triple  entry,  284. 

Trommels,  433. 

Trough  washer,  437. 

Troy  weight,  1. 

True  north  from  Polaris,  46. 

with  the  Burt  solar,  48. 

T-square  method  of  plumbing  shafts, 
73. 

Tunnels,  265. 

Flow  of  water  through,  147. 
Turbines,  158. 

Turnouts,  413. 

Two-phase  alternators,  226. 


636 


INDEX. 


Undercasts,  393."  ll 
Undercutting,  283.  j 

Underground  prospecting,  \\ 

supports,  267. 
surveying,  56,  67. 

Underhand  stoping,  316. 

Undersetting  of  props,  267,  276,  277. 
Undershot  wheels,  157. 

Unequal  splits  of  air,  374. 

Units  of  electricity,  203. 

of  resistance.  Electric,  203. 
of  work,  Electric,  205. 

Unloading  coal.  Cost  of,  447. 

Useful  horsepower  during  winding. 
To  find,  397. 

Use  of  compass,  39. 

Vacuum  Pumps,  164. 

Vacuum  system  of  ventilation,  386. 
Value  of  a fuel,  166. 

Values  of  explosives,  335. 

Valves,  Pump,  162. 

Safety,  185. 

Variation,  Barometric,  339. 
of  ventilation  elements,  372. 

To  turn  off  the,  39. 

Velocity,  Coefficient  of  (water),  135. 
of  air-current,  364. 
of  a water  jet,  135. 
of  water  through  pump  passages, 
160. 

Ventilating  currents.  Measurements 
of,  364. 

Ventilation  elements,  363. 

elements,  Variation  of,  372. 
formulas,  370. 
in  shaft  sinking,  263. 
methods  and  appliances,  381. 
of  Mines,  337. 

of  rise  and  dip  workings,  382. 
Ventilators,  Mechanical,  385. 
Verniers,  Reading,  39. 

Versed  sine,  35. 

Vertical  angle,  51. 

curves  on  slopes,  416. 
distances,  50,  87,  537. 
distances,  stadia  table,  87. 

V Notch,  137; 

Volatile  combustible  matter  of  coal, 
171,  174. 

Volume  and  absolute  pressure,  345. 
and  absolute  temperature.  Rela- 
tion of,  345. 

Atomic,  341. 

Measures  of,  5. 

Specific,  341. 

Waddle  Ventilator,  387. 

Wall  plates,  270. 

Wardle’s  formula  for  shaft  pillars,  285. 
Washers,  Ore  and  coal,  436. 

Weight  of,  116. 

Waste  gates,  146. 
ways,  155. 

Water,  Battery,  430. 
buckets,  164. 

column  corresponding  to  any 
mercury  column,  340. 


Water  elevators,  164. 

fiow  through  orifices,  135. 
gauge,  186,  365. 

Gauging,  136. 
level,  186. 
memoranda,  163. 
power,  156. 

raised  by  single-acting  lift  pump, 
162. 

weight  of,  107, 130. 

Waterproof  push  button,  234. 
Waterwheels,  157. 

See  Wheels. 

Watt-hour,  205. 

Weather-proof  wire,  212. 

Wedge,  93. 

Weight,  Apothecaries’,  1. 

Atomic,  344. 

Avoirdupois,  2. 

Metric,  2. 

Troy,  1. 

Weight  of  atmosphere,  337. 

boltheads,  nuts,  and  washers,  116. 

bolts,  116. 

castings.  111. 

chains,  130. 

coal,  170. 

flat  wrought  iron,  115. 

^ases,  344. 
iron  pipe,  113. 
materials,  102. 

plates  of  steel,  wrought  iron,  etc., 
112. 

standard  steel  buckets,  446. 
water,  107,  130. 
wire  ropes,  119. 
wrought  iK)n,  114. 

Weight  on  pillars  at  different  depths. 
Table  of,  287. 

Weights  and  measures,  7. 

Weir  discharge,  140. 

Weirs,  138. 

Well  drilling.  Cost  of,  242. 

West  Virginia  method  of  mining, 
296. 

West  Vulcan  telephone  system,  234. 
Wheel  and  axle,  92. 

Wheels,  Water,  157. 

Breast,  157. 

Impulse,  158.  ^ 

Overshot,  158.  ( 

Turbines,  158.  y 

Undershot,  157. 

Whitedamp,  349. 

Whiting  system  of  hoisting,  395. 
Williams’  method  of  mining,  312. 
Wing  dams,  156. 

Winslow,  Arthur,  81. 

Winzes,  316. 

Wire  gauge  122d,  207. 

nails,  114. 

Wire  rope,  118. 

fastenings,  126. 

Life  of,  123. 

Size  of  drums  for,  123. 
splicing,  127. 

Weight  and  strength  of,  119. 
Wire,  Weather-proof,  212. 


INDEX. 


637 


Wiring,  Bell,  230. 

Electric,  207. 

Wolf  lamp,  358. 

Wood,  Crushing  load  of,  105. 
fuel,  Value  of,  166. 
screws,  113. 

Wooden  beams,  102. 

Constants  for,  103. 


Wooden  dams,  154. 

Working  load  for  wire  rope,  125. 

Methods  of,  277.  f 

Wrought  iron,  Flat,  115. 

Wyoming  region.  Costs  of  mining  in 
325. 

Zinc,  Weight  of,  111. 


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